catalogue of physics experiments

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Catalogueof Physics Experiments

Mechanics n

Heat n

Electricity n

Electronics n

Optics n

Atomic and nuclear physics n

Solid-state physics n

Register n

P1

Mechanics

P2

Heat

P3

Electricity

P4

Electronics

P5

Optics

P6Atomic

andnuclear physics

P7Solid-state

physics

P 1.1 Measuring methods

Measuring length, volumeand density, determiningthe gravitational constant

P 2.1 Thermalexpansion

Thermal expansion of solidbodies and liquids,anomaly of water

P 3.1 Electrostatics

Electrometer, Coulomb'slaw, lines of electric fluxand isoelectric lines, forceeffects, charge distribu-tions, capacitance, platecapacitor

P 4.1 Componentsand basic circuits

Current and voltagesources, special resistors,diodes, transistors, opto-electronics

P 5.1 Geometrical optics

Reflection, diffraction, lawsof imaging, image distor-tion, optical instruments

P 6.1 Introductory experiments

Oil-spot experiment, Milli-kan experiment, specificelectron charge, Planck'sconstant, dualism of waveand particle, Paul trap

P 7.1 Properties of crystals

Structure of crystals, x-raystructural analysis, elasticand plastic deformation

P 1.2 Forces

Force as vector, lever,block and tackle, inclinedplane, friction

P 2.2 Heat transfer

Thermal conduction, solarcollector

P 3.2 Principles of electricity

Charge transport, Ohm'slaw, Kirchhoff's laws,internal resistance ofmeasuring instruments,electrolysis, electro-chemistry

P 4.2 Operationalamplifier

Internal design of anoperational amplifier,operational amplifiercircuits

P 5.2 Dispersion and chromatics

Refractive index anddispersion, decompositionof white light, color mixing,absorption spectra

P 6.2 Atomic shell

Balmer series, line spectra,inelastic electron collisions,Franck-Hertz experiment,critical potential, ESR,Zeeman effect, opticalpumping

P 7.2 Conduction phenomena

Hall effect, electrical con-duction, photoconductivity,luminescence, thermoelec-tricity, superconductivity

P 1.3 Translationalmotionsof a mass point

Path, velocity, acceleration,Newton's laws, conservati-on of linear momentum,free fall, inclined projection,one-dimensional and two-dimensional motions

P 2.3 Heat as a formof energy

Mixing temperatures, heatcapacities, conversion ofmechanical and electricalenergy into heat energy

P 3.3 Magnetostatics

Permanent magnetism,electromagnetism, mag-netic dipole moment,effects of force, Biot-Savart's law

P 4.3 Open- andclosed-loop control

Open-loop control techno-logy, closed-loop controltechnology

P 5.3 Wave optics

Diffraction, two-beam inter-ference, Newton's rings,interferometer, holography

P 6.3 X-rays

Detection, attenuation, finestructure, Bragg reflection,Duane and Hunt's law,Moseley's law, Comptoneffect

P 7.3 Magnetism

Dia-, para- and ferro-magnetism, ferromagnetichysteresis

P 1.4 Rotationalmotionsof a rigid body

Angular velocity, angularacceleration, conservationof angular momentum,centrifugal force, motionsof a gyroscope, moment ofinertia

P 2.4 Phase transitions

Melting heat and evapora-tion heat, vapor pressure,critical temperature

P 3.4 Electromagnetic induction

Voltage impulse, induction,eddy currents, transformer,measuring the Earth'smagnetic field

P 4.4 Digital technology

Basic logical operations,switching networks andunits, arithmetic units,digital control systems,central processing unit,microprocessor

P 5.4 Polarization

Linear and circular pola-rization, birefringence,optical activity, Kerr effect,Pockels effect, Faradayeffect

P 6.4 Radioactivity

Detection, Poisson distribu-tion, radioactive decay andhalf-life, attenuation of R, T,H radiation

P 7.4 Scanning probemicroscopy

Scanning tunnelingmicroscope

P 5.5 Light intensity

Quantities and measuringmethods of lightingengineering, Stefan-Boltz-mann law, Kirchhoff’s lawsof radiation

P 6.5 Nuclear physics

Particle tracks, Rutherfordscattering, NMR, R spec-troscopy, H spectroscopy,Compton effect

P 5.6 Velocityof light

Measurement according toFoucault/Michelson,measuring with short lightpulses, measuring with anelectronically modulatedsignal

P 5.7 Spectrometer

Prism spectrometer, gratingspectrometer

P 1.5 Oscillations

Mathematical and physicalpendulum, harmonicoscillations, torsionaloscillations, coupling ofoscillations

P 2.5 Kinetic theory of gases

Brownian motion ofmolecules, laws of gases,specific heat of gases

P 3.5 Electricalmachines

Electric generators, electricmotors, three-phasemachines

P 1.6 Wave mechanics

Transversal and longitu-dinal waves, wave machi-ne, thread waves, waterwaves

P 2.6 Thermodynamic cycle

Hot-air engine, heat pump

P 3.6 DC and AC circuits

Capacitor and coil, impe-dances, measuring brid-ges, AC voltages and cur-rents, electrical work andpower, electromechanicaldevices

P 3.7 Electromagnetic oscillations and waves

Oscillator circuit, decimeterwaves, microwaves, dipoleradiation

P 3.8 Moving charge carriers in a vacuum

Tube diode, tube triode,Maltese-cross tube, Perrintube, Thomson tube

P 3.9 Electricalconduction in gases

Self-maintained and non-self-maintained discharge,gas discharge at reducedpressure, cathode andcanal rays

P 1.7 Acoustics

Oscillations of a string,wavelength and velocity ofsound, sound, ultrasound,doppler effect, Fourieranalysis

P 1.8 Aerodynamics andhydrodynamics

Barometry, hydrostaticpressure, buoyancy,viscosity, surface tension,aerodynamics, airresistance, wind tunnel

Light Intensity Optics

194

Determining the luminous intensity as a function of the distance from the light source – Recording and evaluating with CASSY (P 5.5.1.2)

Quantities and measuring methods of lightingengineeringP 5.5.1.1 Determining the radiant flux

density and the luminous intensity of a halogen lamp

P 5.5.1.2 Determining the luminousintensity as a function of thedistance from the light source –Recording and evaluating withCASSY

P 5.5.1.3 Verifying Lambert’s law ofradiation

There are two types of physical quantities used to characterizethe brightness of light sources: quantities which refer to the phys-ics of radiation, which describe the energy radiation in terms ofmeasurements, and quantities related to lighting engineering,which describe the subjectively perceived brightness under con-sideration of the spectral sensitivity of the human eye.

The first group includes the irradiance Ee, which is the radiatedpower per unit of area Fe. The corresponding unit of measure iswatts per square meter. The comparable quantity in lighting engi-neering is illuminance E, i. e. the emitted luminous flux per unit ofarea F, and it is measured in lumens per square meter, or lux forshort.

In the first experiment, the irradiance is measured using the Moll’sthermopile, and the luminous flux is measured using a luxmeter.The luxmeter is matched to the spectral sensitivity of the humaneye V (Ö) by means of a filter placed in front of the photoelement.A halogen lamp serves as the light source. From its spectrum,most of the visible light is screened out using a color filter; sub-sequently, a heat filter is used to absorb the infrared componentof the radiation.

The second experiment demonstrates that the luminous intensityis proportional to the square of the distance between a point-typelight source and the illuminated surface.

The aim of the third experiment is to investigate the angular distri-bution of the reflected radiation from a diffusely reflecting sur-face, e.g. matte white paper. To the observer, the surface appearsuniformly bright; however, the apparent surface area varies withthe cos of the viewing angle. The dependency of the luminousintensity is described by Lambert’s law of radiation:

Ee (F) = Ee (0) · cos F

P5.

5.1.

1

P5.

5.1.

3

P 5.5.1

P5.

5.1.

2(a

)

P5.

5.1.

2(b

)

Cat. No. Description

450 64 Halogen lamp housing 12 V, 50/100 W 1 1 1

450 63 Halogen lamp, 12 V/100 W 1 1

450 68 Halogen lamp, 12 V/50 W 1 1

52125 Transformer 2 ... 12 V 1 1 1

450 66 Picture slider for halogen lamp housing 1

450 60 Lamp housing 1

450 51 Lamp, 6 V/30 W 1

56273 Transformer, 6 V AC, 12 V AC/30 VA 1

468 03 Monochromatic light filter, red 1

460 26 Iris diaphragm 1

460 03 Lens f = + 100 mm 1 1

460 22 Holder with spring clips 1

55736 Moll’s thermopile 1 1

53213 Microvoltmeter 1 1

524 010 Sensor CASSY 1 1

666 243 Lux sensor 1 1 1

524 051 Lux box 1 1

524 200 CASSY Lab 1 1

666 230 Hand-held Lux-UV-IR-Meter 2 2 2

460 43 Small optical bench 1 1 1 2

460 40 Swivel joint with angle scale 1

59013 Insulated stand rod, 25 cm long 1 1 1

590 02 Small clip plug 1 1 1

30101 Leybold multiclamp 3 2 2 4

300 02 Stand base, V-shape, 20 cm 1 1 1

300 01 Stand base, V-shape, 28 cm 2

50146 Pair of cables, 100 cm, red and blue 1

50133 Connecting leads, dia. 2.5 mm2, 100 cm, black 2 2 2

additionally required: PC with Windows 95/NT or higher 1 1

How to use the catalogue

1) Branch

2) Subbranch

3) Topic Group

4) Experiment Topics(each experiment is identifiedby “P“ plus a 4-digit-number)

Short experimentdescriptions

Equipment Lists1st column P 5.5.1.1

2nd and 3rd column P 5.5.1.2(a)/ (b) same experimentwith a different setup

4th column P 5.5.1.3

6

We would appreciate to prepare and provide additional equipment lists on your request.

Mechanics

Table of contents Mechanics

8

P1 MechanicsP 1.1 Measuring methodsP 1.1.1 Measuring length 9

P 1.1.2 Measuring volume and density 10

P 1.1.3 Determining the gravitational constant 11–12

P 1.2 ForcesP 1.2.1 Static effects of forces 13

P 1.2.2 Force as vector 14

P 1.2.3 Lever 15

P 1.2.4 Block and tackle 16

P 1.2.5 Inclined plane 17

P 1.2.6 Friction 18

P 1.3 Translational motions of a mass point

P 1.3.1 One-dimensional motions on the track for students' experiments 19

P 1.3.2 One-dimensional motions on Fletcher's trolley 20–22

P 1.3.3 One-dimensional motionson the linear air track 23–25

P 1.3.4 Conservation of linear momentum 26–27

P 1.3.5 Free fall 28–29

P 1.3.6 Angled projection 30

P 1.3.7 Two-dimensional motions on the air table 31–32

P 1.4 Rotational motions of a rigid body

P 1.4.1 Rotational motions 33–34

P 1.4.2 Conservation of angular momentum 35

P 1.4.3 Centrifugal force 36–37

P 1.4.4 Motions of a gyroscope 38

P 1.4.5 Moment of inertia 39

P 1.5 OscillationsP 1.5.1 Mathematical

and physical pendulum 40

P 1.5.2 Harmonic oscillations 41

P 1.5.3 Torsion pendulum 42–43

P 1.5.4 Coupling of oscillations 44–45

P 1.6 Wave mechanicsP 1.6.1 Transversal and longitudinal waves 46

P 1.6.2 Wave machine 47

P 1.6.3 Circularly polarized waves 48

P 1.6.4 Propagation of water waves 49

P 1.6.5 Interference with water waves 50

P1.7 AcousticsP 1.7.1 Sound waves 51

P 1.7.2 Oscillations of a string 52

P 1.7.3 Wavelength and velocity of sound 53–55

P 1.7.4 Reflection of ultrasonic waves 56

P 1.7.5 Interference of ultrasonic waves 57

P 1.7.6 Acoustic Doppler effect 58

P 1.7.7 Fourier analysis 59

P 1.8 Aerodynamics and hydrodynamics

P 1.8.1 Barometry 60

P 1.8.2 Bouyancy 61

P 1.8.3 Viscosity 62

P 1.8.4 Surface tension 63

P 1.8.5 Introductory experiments in aerodynamics 64

P 1.8.6 Measuring air resistance 65

P 1.8.7 Measurements in a wind tunnel 66

Caliper gauge, micrometer screw, spherometer

P 1.1.1

P 1.1.1.1 Using a caliper gauge with vernier

P 1.1.1.2 Using a micrometer screw

P 1.1.1.3 Using a spherometer to deter-mine bending radii

Measuring length

The caliper gauge, micrometer screw and spherometer are pre-cision measuring instruments; their use is practiced in practicalmeasuring exercises.

In the first experiment, the caliper gauge is used to determine theouter and inner dimensions of a test body. The vernier scale ofthe caliper gauge increases the reading accuracy to 1/20 mm.

Different wire gauges are measured in the second experiment. Inthis exercise a fundamental difficulty of measuring becomesapparent, namely that the measuring process changes the meas-urement object. Particularly with soft wire, the measured resultsare too low because the wire is deformed by the measurement.

The third experiment determines the bending radii R of watch-glasses using a spherometer. These are derived on the basis ofthe convexity height h at a given distance r between the feet ofthe spherometer, using the formula

R = r2

+ h2h 2

P1.

1.1.

2

P1.

1.1.

3

Mechanics Measuring methods

9

P1.

1.1.

1


311 54 Precision vernier callipers 1

311 83 Precision micrometer 1

311 86 Spherometer 1

550 35 Copper wire, 100 m, 0.20 mm dia. 1

550 39 Brass wire, 50 m, 0.50 mm dia. 1

460 291 Glass mirror, 115 x 100 mm 1

662 092 Cover slips, 22 x 22 mm, set of 100 1

664154 Watch glass dish, 80 mm dia. 1

664157 Watch glass dish, 125 mm dia. 1

Vertical section through the measuring configuration with spherometerLeft: object with convex surface. Right: Object with concaves surface.

P 1.1.1.2

P 1.1.1.3

P 1.1.1.1

Measuring methods Mechanics

P 1.1.2Determining volume and density

P 1.1.2.1 Determining the volume anddensity of solids

P 1.1.2.2 Determining the density ofliquids using the Mohr densitybalance

P 1.1.2.3 Determining the density ofliquids using the pyknometerafter Gay-Lussac

P 1.1.2.4 Determining the density of air

Determining the density of air (P 1.1.2.4)

Depending on the respective aggregate state of a homogeneoussubstance, various methods are used to determine its density

r = mV

m: mass, V: volume

The mass and volume of the substance are usually measuredseparately.

To determine the density of solid bodies, a weighing is combinedwith a volume measurement. The volumes of the bodies aredetermined from the volumes of liquid which they displace froman overflow vessel. In the first experiment, this principle is testedusing regular bodies for which the volumes can be easily calcu-lated from their linear dimensions.

To determine the density of liquids, the Mohr density balance isused in the second experiment, and the pyknometer after Gay-Lussac is used in the third experiment. In both cases, the meas-uring task is to determine the densities of water-ethanol mixtures.The Mohr density balance determines the density from thebuoyancy of a body of known volume in the test liquid. Thepyknometer is a pear-shaped bottle in which the liquid to beinvestigated is filled for weighing. The volume capacity of thepyknometer is determined by weighing with a liquid of knowndensity (e.g. water).

In the final experiment, the density of air is determined using asphere of known volume with two stop-cocks. The weight of theenclosed air is determined by finding the difference between theoverall weight of the air-filled sphere and the empty weight of theevacuated sphere.

P1.

1.2.

3

P1.

1.2.

2

P1.

1.2.

1

P1.

1.2.

4

10


361 44 Glass cylinder with 3 tubes 1

665 754 Graduated cylinder, 100 ml : 1 2 2

665 755 Graduated cylinder, 250 ml : 2 1

590 06 Plastic beaker, 1000 ml 1

300 76 Laboratory stand II 1

311 54 Precision vernier callipers 1

315 05 School and laboratory balance 311, 311 g 1 1 1

316 07 Density balance (Mohr Westphal) 1

361 63 Set of 2 cubes and 1 ball 1

590 33 Set of 2 gauge blocks 1

666 145 Pycnometer, 50 ml 1

382 21 Stirring thermometer, -30 to +110 °C 1

379 07 Sphere with two cocks 1

667 072 Supporting ring for round-bottom flask, 250 ml 1

375 58 Hand vacuum and pressure pump 1

309 42 Colouring, red, water soluble 1

Ethanol, fully denaturated, 1 l 1 1

309 48 Cord, 10 m 1

Determining the density of

liquids using the Mohr

density balance (P 1.1.2.2)

671 9720

Determining the gravitational constant with the gravitation torsion balance after Cavendish –

measuring the excursion with a light pointer (P 1.1.3.1)

P 1.1.3

P 1.1.3.1 Determining the gravitationalconstant with the gravitationtorsion balance after Cavendish –measuring the excursion with a light pointer

Determining the gravitational constant

The heart of the gravitation torsion balance after Cavendish is alight-weight beam horizontally suspended from a thin torsionband and having a lead ball with the mass m2 = 15 g at each end.These balls are attracted by the two large lead spheres with themass m1 = 1.5 kg. Although the attractive force

F = G · m1 · m2

r2

r: distance between sphere midpoints

is less than 10-9 N, it can be detected using the extremely sensi-tive torsion balance. The motion of the small lead balls is ob-served and measured using a light pointer. Using the curve overtime of the motion, the mass m1 and the geometry of the arran-gement, it is possible to determine the gravitational constant Gusing either the end-deflection method or the accelerationmethod.

In the end-deflection method, a measurement error of less than5 % can be achieved through careful experimenting. The gravita-tional force is calculated from the resting position of the elasti-cally suspended small lead balls in the gravitational field of thelarge spheres and the righting moment of the torsion band. Therighting moment is determined dynamically using the oscillationperiod of the torsion pendulum.

The acceleration method requires only about 1 min. observationtime. The acceleration of the small balls by the gravitational forceof the large spheres is measured, and the position of the balls asa function of time is registered.

In this experiment, the light pointer is a laser beam which isreflected in the concave reflector of the torsion balance onto ascale. Its position on the scale is measured manually point bypoint as a function of time.

P1.

1.3.

1

Mechanics Measuring methods

11


332 101 Gravitation torsion balance 1

He-Ne laser 0.2/1 mW max., linearly polarized 1

313 05 Stopclock 1

311 77 Steel tape measure, 2m 1


301 03 Rotatable clamp 1

301 01 Leybold multiclamp 1

300 42 Stand rod, 47 cm 1

Diagram of light-pointer configuration

471 830

Measuring methods Mechanics

P 1.1.3Determining the gravitational constant

P 1.1.3.2 Determining the gravitationalconstant with the gravitationtorsion balance after Cavendish –recording the deflections andevaluating the measurementwith the IR position detectorand PC

P 1.1.3.3 Determining the gravitationalconstant with the gravitationtorsion balance after Cavendish –recording the deflections andevaluating the measurementwith the IR position detectorand recorder

Determining the gravitational constant with the gravitation torsion balance after Cavendish – recording the deflections and evaluating the measurement with the IR position detector and PC (P 1.1.3.2)

The IR position detector (IRPD) enables automatic measurementof the motion of the lead balls in the gravitation torsion balance.The four IR diodes of the IRPD emit an infrared beam; the con-cave mirror on the torsion pendulum of the balance reflects thisbeam onto a row of 32 adjacent phototransistors. A microcon-troller switches the four IR diodes on in sequence and thendetermines which phototransistor is illuminated each time. Theprimary S range of illumination is determined from the individualmeasurements. The IRPD is supplied complete with a disk con-taining Windows software for direct measurement and evaluation.

The data are registered via the serial interface RS 232 using acomputer, or alternatively with a Yt-recorder. The system offers achoice of either the end-deflection or the acceleration method formeasuring and evaluating.

P1.

1.3.

2

P1.

1.3.

3

12


332 101 Gravitation torsion balance 1 1

332 11 IR position detector 1 1

575 70 Yt-recorder, single channel 1

460 32 Precision optical bench, standardized cross section, 1 m 1 1

460 351 Optics rider, H = 60 mm/W = 50 mm 1 1


300 41 Stand rod, 25 cm 1 1

530 008 FUNCABLE 1

501 46 Pair of cables, 1 m, red and blue 1

additionally required:1 PC with Windows 95/NT or higher 1

Diagram of IR position detector

3

Confirming Hooke’s law using a helical spring (P 1.2.1.1) – Bending of a leaf spring (P 1.2.1.2)

P 1.2.1

P 1.2.1.1 Confirming Hooke’s law usingthe helical spring

P 1.2.1.2 Bending of a leaf spring

Static effects of forces

Forces can be recognized by their effects. Thus, static forces cane.g. deform a body. It becomes apparent that the deformation isproportional to the force acting on the body when this force is nottoo great.

The first experiment shows that the extension s of a helical springis directly proportional to the force Fs. Hooke’s law applies:

Fs = –D · s

D: spring constant

The second experiment examines the bending of a leaf springarrested at one end in response to a known force generated byhanging weights from the free end. Here too, the deflection isproportional to the force acting on the leaf spring.

P1.

2.1.

1

P1.

2.1.

2

Mechanics Statics

13

Schematic diagram of bending of a leaf spring


352 07 Helical spring, 5 N, 0.1 N/cm 1


352 051 Leaf spring I = 435 mm 1

340 85 Set of 6 weights, 50 g each 1 1

301 21 Stand base MF 2 2

301 27 Stand rod, 50 cm, 10 mm dia. 2 2


301 25 Clamping block MF 1

666 615 Universal bosshead, 28 mm dia., 50 mm 1

311 78 Tape measure, 1.5 m / 1 mm 1 1

301 29 Pair of pointers 1 1

Plug-in axle 1 1

20065559 Metal plate 1

309 48 Cord, 10 m 1

340 811

Statics Mechanics

P 1.2.2Force as a vector

P 1.2.2.1 Composition and resolution offorces

Composition and resolution of forces (P 1.2.2.1 a)

The nature of force as a vectorial quantity can be easily andclearly verified in experiments on the adhesive magnetic board.The point of application of all forces is positioned at the midpointof the angular scale on the adhesive magnetic board, and allindividual forces and the angles between them are measured.The underlying parallelogram of forces can be graphically dis-played on the adhesive magnetic board to facilitate understand-ing.

In this experiment, a force F is compensated by the spring forceof two dynamometers arranged at angles a1 and a2 with respectto F. The component forces F1 and F2 are determined as a func-tion of a1 and a2. This experiment verifies the relationships

F = F1 · cos a1 + F2 · cos a2

and

0 = F1 · sin a1 + F2 · sin a2.

P1.

2.2.

1(a

)

P1.

2.2.

1(b

)

14

Setup with demonstration-experiment frame (P 1.2.2.1 b)


301301 Adhesive magnetic board 1 1

301300 Demonstration-experiment frame 1

314215 Round dynamometer 5 N 2 2

301331 Magnetic base with hook 1 1

35208 Helical spring, 5 N, 0.25 N/cm 1 1

31177 Steel tape measure, 2 m 1 1

34261 Set of 12 weights, 50 g each 1 1

30101 Leybold multiclamp 4

30044 Stand rod, 100 cm 2

30107 Simple bench clamp 2


Parallelogram of forces

Two-sided lever (P 1.2.3.1)

P 1.2.3

P 1.2.3.1 One-sided and two-sided lever

P 1.2.3.2 Wheel and axle as a lever withunequal sides

Levers

In physics, the law of levers forms the basis for all forms ofmechanical transmission of force. This law can be explainedusing the higher-level concept of equilibrium of angular momen-tum.

The first experiment examines the law of levers:

F1 · x1 = F2 · x2

for one-sided and two-sided levers. The object is to determinethe force F1 which maintains a lever in equilibrium as a functionof the load F2, the load arm x2 and the power arm x1.

The second experiment explores the equilibrium of angularmomentum using a wheel and axle. This experiment broadensthe understanding of the concepts force, power arm and line ofaction, and explicitly proves that the absolute value of the angu-lar momentum depends only on the force and the distance be-tween the axis of rotation and the line of action.

P1.

2.3.

1

P1.

2.3.

2

Mechanics Statics

15

Equilibrium of angular momentum on a wheel and axle (P 1.2.3.2)


342 60 Lever on ball bearing, 1 m long 1

342 75 Metal wheel and axle 1


314 45 Spring balance, 2.0 N 1 1

314 46 Spring balance, 5.0 N 1 1

300 02 Stand base, V-shape, 20 cm 1 1

301 01 Leybold multiclamp 1 1

300 42 Stand rod, 47 cm 1 1

Statics Mechanics

P 1.2.4Block and tackle

P 1.2.4.1 Fixed pulley, loose pulley andblock and tackle as simplemachines

P 1.2.4.2 Fixed pulley, loose pulley andblock and tackle as simplemachines on the adhesivemagnetic board

Fixed pulley, loose pulley and block and tackle as simple machines on the adhesive magnetic board (P 1.2.4.2 b)

The fixed pulley, loose pulley and block and tackle are classicexamples of simple machines. Experiments with these machinesrepresent the most accessible introduction to the concept ofwork in mechanics. The experiments are offered in two equip-ment variations.

In the first variation, the block and tackle is set up on the labbench using a stand base. The block and tackle can be expand-ed to three pairs of pulleys and can support loads of up to 20 N.The pulleys are mounted virtually friction-free in ball bearings.

The setup on the adhesive magnetic board in the second varia-tion has the advantage that the amount and direction of the effec-tive forces can be represented graphically directly at the source.Also, this arrangement makes it easy to demonstrate the rela-tionship to other experiments on the statics of forces, providingthese can also be assembled on the adhesive magnetic board.

P1.

2.4.

2(a

)

P1.

2.4.

1

P1.

2.4.

2(b

)

16

Setup with block and tackle (P 1.2.4.1)


342 28 Pulley block, 20 N 1

301 301 Adhesive magnetic board 1 1

301 300 Demonstration-experiment-frame 1

341 65 Pulley with hook and rod 2*

340 911 Pulley, plug-in, 50 mm diameter 2 2

340 921 Pulley, plug-in, 100 mm diameter 2 2

340 930 Pulley bridge 2 2

340 87 Load hook 2 2

301330 Magnetic base with 4-mm socket 1 1

301331 Magnetic base with noon 1 1

301 332 Magnetic base with 4-mm axis 1 1

314 212 Round dynamometer 2 N 1 1

314 215 Round dynamometer 5 N 1 1

314181 Precision dynamometer, 20.0 N 1

315 36 Set 7 weights, 0.1 - 2 kg, with hook 1



300 44 Stand rod, 100 cm 1 2


301 07 Simple bench clamp 2

309 50 Demonstration cord, 20m (polyamide) 1 1


* additionally recommended

Inclined plane: force along the plane and force normal to the plane (P 1.2.5.1)

P 1.2.5

P 1.2.5.1 Inclined plane: force along the plane and forcenormal to the plane

P 1.2.5.2 Determining the coefficient ofstatic friction using the inclinedplane

Inclined plane

The motion of a body on an inclined plane can be describedmost easily when the force exerted by the weight G on the bodyis vectorially decomposed into a force F1 along the plane and aforce F2 normal to the plane. The force along the plane acts par-allel to a plane inclined at an angle a, and the force normal to theplane acts perpendicular to the plane. For the absolute values ofthe forces, we can say:

F1 = G · sin a and F2 = G · cos a

This decomposition is verified in the first experiment. Here, thetwo forces F1 and F2 are measured for various angles of inclina-tion a using precision dynamometers.

The second experiment uses the dependency of the force normalto the plane on the angle of inclination for quantitative determi-nation of the coefficient of static friction m of a body. The inclina-tion of a plane is increased until the body no longer adheres tothe surface and begins to slide. From the equilibrium of the forcealong the plane and the coefficient of static friction

F1 = m · F2

we can derive

m = tan a.

P1.

2.5.

1

P1.

2.5.

2

Mechanics Statics

17

Calculating the coefficient of static friction m (P 1.2.5.2)


341 21 Inclined plane with trolley and screw model 1 1


342 10 Pair of wooden blocks for friction experiments 1


Statics Mechanics

P 1.2.6Friction

P1.2.6.1 Static friction, sliding frictionand rolling friction

Static friction, sliding friction and rolling friction (P 1.2.6.1)

In discussing friction between solid bodies, we distinguish be-tween static friction, sliding friction and rolling friction. Static fric-tion force is the minimum force required to set a body at rest ona solid base in motion. Analogously, sliding friction force is theforce required to maintain a uniform motion of the body. Rollingfriction force is the force which maintains the uniform motion ofa body which rolls on another body.

To begin, this experiment verifies that the static friction force FHand the sliding friction force FG are independent of the size of thecontact surface and proportional to the resting force G on thebase surface of the friction block. Thus, the following applies:

FH = mH · G and FG = mG · G.

The coefficients mH and mG depend on the material of the frictionsurfaces. The following relationship always applies:

mH > mG.

To distinguish between sliding and rolling friction, the frictionblock is placed on top of multiple stand rods laid parallel to eachother. The rolling friction force FR is measured as the force whichmaintains the friction block in a uniform motion on the rollingrods. The sliding friction force FG is measured once more forcomparison, whereby this time the friction block is pulled overthe stand rods as a fixed base (direction of pull = direction of rodaxes). This experiment confirms the relationship:

FG > FR.

18

P1.

2.6.

1


315 36 Set 7 weights, 0.1 – 2 kg, with hook 1


314 47 Spring balance, 10.0 N 1

342 10 Pair of wooden blocks for friction experiments 1

Recording path-time diagrams of linear motions (P 1.3.1.1)

P 1.3.1

P1.3.1.1 Recording path-time diagramsof linear motions

One-dimensional motions on thetrack for students’ experiments

tape strips, or the instantaneous velocity, increase for equal timeintervals. The increase in length, and thus the instantaneousacceleration

ai = 1

(vi+1 – vi),Dt

is constant within the attainable measuring accuracy. From thevelocity-time diagram, we can recognize the linear function

v = a · ta: average acceleration

and from the path-time diagram the function

s = 1

a · t2.2

P1.

3.1.

1

Mechanics Translational motions of a mass point

19


STM equipment set Mechanics 3 (MEC 3) 1

Transformer, 6 V AC, 12 V AC/ 30 W 1

309 48 Cord, 10 m 1

Velocity-time diagram of a uniformly accelerated motion

The motion of Fletcher’s trolley on a track is recorded using astrip of paper which the trolley pulls through a recorder. The de-vice marks the respective position on the measurement tape atfixed intervals (e.g. Wt = 0.1 s).

The experiment first investigates uniform motions of the trolley.The marked positions on the register tape are measured andentered in a path-time diagram as value pairs (si, ti). From thediagram, it is possible to recognize the linear function

s = v · tv: average velocity

In the further evaluation, the paper register tape is cut at theposition marks and the sections are placed side by side in a row.Their lengths correspond to the instantaneous velocities

vi = 1

· (si+1 – si),Dt

which agree with the average velocity v within the context of themeasuring accuracy.

Uniformly accelerated motion of the trolley on the inclined trackis subsequently evaluated in the same way. Additionally, theinstantaneous velocities vi are plotted in a velocity-time diagramas value pairs (vi, ti). Unlike uniform motions, the lengths of the

521 210

588 813S

Translational motions of a mass point Mechanics

P 1.3.2One-dimensional motionswith Fletcher’s trolley

P 1.3.2.1 Recording the path-timediagrams of linear motions –measuring the time with theelectronic stopclock

Recording the path-time diagrams of linear motions – measuring the time with the electronic stopclock (P 1.3.2.1b)

Fletcher’s trolley is the classical experiment apparatus for inves-tigating linear translational motions. The trolley has a ball bear-ing, his axles are spring-mounted and completely immerged inorder to prevent being overloaded. The wheels are designed insuch a way that the trolley centers itself on the track and frictionat the wheel flanks is avoided.

Using extremely simple means, this experiment makes the defini-tion of the velocity v as the quotient of the path difference Ds andthe corresponding time difference Dt directly accessible to thestudents. The path difference Ds is read off directly from a scaleon the track. Depending on the chosen equipment configurationa or b, electronic measurement of the time difference is startedand stopped using either a key and a light barrier or two lightbarriers. To enable investigation of uniformly accelerated mo-tions, the trolley is connected to a thread which is laid over a pul-ley, allowing various weights to be suspended.

P1.

3.2.

1(a)

P1.

3.2.

1(b

)

20

Path-time diagram of a linear motion


337 130 Track, 1.5 m 1 1

337 110 Trolley 1 1

337 114 Additional weights 1* 1*

315 410 Slotted weight hanger, 10 g 1 1

315 418 Slotted weight, 10 g 4 4

337 462 Combination light barrier 2 1

337 463 Holder for combination spoked wheel 1 1

337 464 Combination spoked wheel 1 1

683 41 Holding magnet 1

313 033 Electronic stopclock P 1 1

501 16 Multicore cable, 6-pole, 1.5 m long 2 1

309 48 Cord, 10 m 1 1

501 46 Pair of cables, 1 m, red and blue


1

Recording the path-time diagrams of linear motions – recording and evaluating with CASSY (P 1.3.2.2)

P1.3.2

P 1.3.2.2 Recording the path-timediagrams of linear motions –recording and evaluating withCASSY

P 1.3.2.3 Definition of the Newton as aunit of force – recording andevaluating with CASSY

One-dimensional motionswith Fletcher’s trolley

The first experiment looks at motion events which can be trans-mitted to the combination spoked wheel by means of a thinthread on Fletcher’s trolley. The combination spoked wheel ser-ves as an easy-running deflection pulley, and at the same timeenables path measurement using the combination light barrier.The signals of the combination light barrier are recorded by thecomputer-assisted measuring system CASSY and converted to apath-time diagram. As this diagram is generated in real timewhile the experiment is running, the relationship between themotion and the diagram is extremely clear.

In the second experiment, a calibrated weight exercises an acce-lerating force of 1 N on a trolley with the mass 1 kg. As one mightexpect, CASSY shows the value

a = 1 m

s2

for the acceleration. At the same time, this experiment verifiesthat the trolley is accelerated to the velocity

v = 1 m

s

in the time 1 s.

P1.

3.2.

2

P1.

3.2.

3


21

337130 Track, 1.5 m 1 1

337 110 Trolley 1 1

315 410 Slotted weight hanger, 10 g 1

315 418 Slotted weight, 10 g 4

337 114 Additional weights 1*

337 115 Newton weights 1


337 464 Combination spoked wheel 1 1

683 41 Holding magnet 1 1

524 010 Sensor-CASSY 1 1

524 034 Timer box 1 1

524 200 CASSY Lab 1 1


309 48 Cord, 10 m 1 1

501 46 Pair of cables, 1 m, red and blue 1 1

additionally required:1 PC with windows 95/NT or higher 1 1


22


One-dimensional motions

P 1.3.2.4 Recording the path-time diagrams of linear motions –recording and evaluating withVideoCom

Recording the path-time diagrams of linear motions – recording and evaluating with VideoCom (P 1.3.2.4)

The single-line CCD video camera VideoCom represents a new,easy-to-use method for recording one-dimensional motions. Itilluminates one or more bodies in motion with LED flashes andimages them on the CCD line with 2048-pixel resolution via acamera lens (CCD: charge-coupled device). A piece of retrore-flecting foil is attached to each of the bodies to reflect the lightrays back to the lens. The current positions of the bodies aretransmitted to the computer up to 80 times per second via theserial interface. The automatically controlled flash operates atspeeds of up to 1/800 s, so that even a rapid motion on the line-ar air track or any other track can be sharply imaged. The soft-ware supplied with VideoCom represents the entire motion of thebodies in the form of a path-time diagram, and also enables fur-ther evaluation of the measurement data.

P1.

3.2.

4


337 130 Track, 1.5 m 1

337 110 Trolley 1

315 410 Slotted weight hanger, 10 g 1

315 418 Slotted weight, 10 g 4

337 114 Additional weights 1*

337 463 Holder for combination spoked wheel 1

337 464 Combination spoked wheel 1

683 41 Holding magnet 1

337 47 VideoCom 1

300 59 Camera tripod 1

309 48 Cord, 10 m 1

501 38 Connecting lead, Ø 2.5 mm2, 200 cm 4

additionally required: PC with Windows 95/NT or higher 1


P 1.3.2

with the Fletcher's trolley

Recording the path-time diagrams of linear motions – measuring the time with the Morse key and forked light barrier(P 1.3.3.1)

P 1.3.3

P 1.3.3.1 Recording the path-time diagrams of linear motions –measuring the time with theMorse key and forked lightbarrier

One-dimensional motionson the linear air track

The advantage of studying linear translational motions on thelinear air track is that interference factors such as frictionalforces and moments of inertia of wheels do not occur. The sliderson the linear air track are fitted with an interrupter flag whichobscures a light barrier. By adding additional weights, it is pos-sible to double and triple the masses of the sliders.

Using extremely simple means, this experiment makes the defini-tion of the velocity v as the quotient of the path difference Ds andthe corresponding time difference Dt directly accessible to thestudents. The path difference Ds is read off directly from a scaleon the track. Depending on the chosen equipment configuration,electronic measurement of the time difference is started byswitching off the holding magnet or using a light barrier. Theinstantaneous velocity of the slider can also be calculated fromthe obscuration time of a forked light barrier and the width of theinterrupter flag. To enable investigation of uniformly acceleratedmotions, the slider is connected to a thread which is laid over apulley, allowing weights to be suspended.


23

P5.

2.1.

1

P5.

2.1.

2P

1.3.

3.1

(d)

P1.

3.3.

1 (c

)

P1.

3.3.

1 (b

)

P1.

3.3.

1 (a

)


337 501 Linear air track, 1.5 m long, complete 1 1 1 1

337 53 Air supply for air track 1 1 1 1

667 823 Power controller 1 1 1 1

311 02 Metal scale, 1 m long 1 1 1 1

337 46 Forked light barrier, infra-red 1 2 1 2


524 034 Timer box 1 1

524 200 CASSY Lab 1 1

501 16 Multicore cable, 6-pole, 1.5 m long 1 2 1 2

575 48 Digital counter 1 1

300 40 Stand rod, 10 cm 1 1 1 1

501 46 Pair of cables, 1 m, red and blue 1 1 1 1


Path-time diagram for uniform motion


P 1.3.3One-dimensional motionson the linear air track

P 1.3.3.4 Recording the path-timediagrams of linear motions –measuring and evaluating withCASSY

P 1.3.3.5 Uniformly accelerated motionwith reversal of direction –measuring and evaluating withCASSY

P 1.3.3.6 Kinetic energy of a uniformlyaccelerated mass – recording and evaluating withCASSY

Recording the path-time diagrams of linear motions – measuring and evaluating with CASSY (P 1.3.3.4)

The computer-assisted measurement system CASSY is particu-larly suitable for simultaneously measuring transit time t, path s,velocity v and acceleration a of a slider on the linear air track.The linear motion of the slider is transmitted to the motion sens-ing element by means of a lightly tensioned thread; the signals ofthe motion sensing element are matched to the CASSY measur-ing inputs by the BMW box.

In terms of content, the first two experiments are comparable tothose conducted using the motion transducer and the Yt record-er. However, the PC greatly simplifies the evaluation of therecorded data. In addition, the data can be exported in the formof a table of discrete values to enable external evaluations.

The third experiment records the kinetic energy

E = m

· v2

2

of a uniformly accelerated slider of the mass m as a function ofthe time and compares it with the work

W = F · s

which the accelerating force F has performed. This verifies therelationship

E(t) = W(t).

24

P5.

2.1.

1

P5.

2.1.

2P

1.3.

3.4-

6


337 501 Linear air track, 1.5 m long, complete 1

337 53 Air supply for air track 1

667 823 Power controller 1

337 631 Motion transducer 1

501 16 Multicore cable, 6-pole, 1.5 m 1

524 032 BMW box 1

524 010 Sensor-CASSY 1

524 200 CASSY Lab 1

501 46 Pair of cables, 100 cm, red and blue 1

additionally required:PC with Windows 95/NT or higher 1

Path-time, velocity-time and acceleration-time diagram

Confirming Newton's first and second laws for linear motions – recording and evaluating with VideoCom (P 1.3.3.7)

P 1.3.3

P 1.3.3.7 Confirming Newton's first andsecond laws for linear motions –recording and evaluating withVideoCom

P 1.3.3.8 Uniformly accelerated motionwith reversal of direction –recording and evaluating withVideoCom

P 1.3.3.9 Kinetic energy of a uniformlyaccelerated mass – recording and evaluating withVideoCom

One-dimensional motionson the linear air track

The object of the first experiment is to study uniform and uni-formly accelerated motions of a slider on the linear air track andto represent these in a path-time diagram. The software also dis-plays the velocity v and the acceleration a of the body as a func-tion of the transit time t, and the further evaluation verifiesNewton's equation of motion

F = m · aF: accelerating force,m: mass of accelerated body

The other two experiments are identical in terms of content withexperiments P 1.3.3.5 and P 1.3.3.6.

P1.

3.3.

9

P1.

3.3.

8

P1.

3.3.

7


25


337 501 Linear air track, 1.5 m long, complete 1 1 1

300 40 Stand rod, 10 cm 1 1

311 02 Metal scale, 1 m long 1 1 1

337 53 Air supply for air track 1 1 1

667 823 Power controller 1 1 1

33747 VideoCom 1 1 1

300 59 Camera tripod 1 1 1

501 38 Connecting lead, Ø 2.5 mm2, 200 cm, black 4 4 4

additionally required: PC with Windows 95/NT or higher 1 1 1

Investigating uniformly accelerated motions with VideoCom


P 1.3.4Conservation of linearmomentum

P 1.3.4.1 Energy and linear momentumin elastic collision – measuring with two light bar-riers and CASSY

P 1.3.4.2 Energy and linear momentumin inelastic collision – measuring with two lightbarriers and CASSY

P 1.3.4.3 Rocket principle: conservation of linear momen-tum and repulsion

Elastic collision - measuring with two light barriers and CASSY (P 1.3.3.1/2b)

The use of a linear track makes possible superior quantitativeresults when verifying the conservation of linear momentum in anexperiment. Especially on the linear air track it is possible e.g. tominimize the energy “loss” for elastic collision.

In the first and second experiments, the obscuration times Dti oftwo light barriers are measured, e.g. for two bodies on a lineartrack before and after elastic and inelastic collision. These expe-riments investigate collisions between a moving body and a bodyat rest, as well as collisions between two bodies in motion. Theevaluation program calculates and, when selected, compares thevelocities

vi =d

,Dti

d: width of interrupter flags

the momentum values

pi = mi · vimi: masses of bodies

and the energies

Ei =1

· mi · vi2

2

of the bodies before and after collision.

In the final experiment, the recoil force on a jet slider is meas-ured for different nozzle cross-sections using a sensitive dyna-mometer in order to investigate the relationship between repulsi-on and conservation of linear momentum.

26

P5.

2.1.

1

P5.

2.1.

2

P1.

3.4.

2 (b

)

P1.

3.4.

2 (a

)

P1.

3.4.

1 (b

)

P1.

3.4.

1 (a

)

P1.

3.4.

3


337 501 Linear air track, 1.5 m long, complete 1 1 1

337 53 Air supply for air track 1 1 1

667 823 Power controller 1 1 1

337 46 Forked light barrier, infra-red 2 2

337 56 Jet slider with 3 jets 1

337 59 Dynamometric device 1

314 081 Precision dynamometer, 0.01 N 1

337 130 Track, 1.5 m 1 1

337 110 Trolley 2 2

337 114 Additional weights 1 1

337 112 Impact spring for trolley 1


524 010 Sensor-CASSY 1 1 1 1

524 200 CASSY Lab 1 1 1 1

524 034 Timer box 1 1 1 1


additionally required: PC with Windows 95/NT or higher 1 1 1 1

Newton's third law and laws of collision – recording and evaluating with VideoCom (P 1.3.4.4b)

P 1.3.4

P 1.3.4.4 Newton's third law and laws of collision – recording and evaluating withVideoCom

Conservation of linearmomentum

The single-line CCD video camera is capable of recording pic-tures at a rate of up to 80 pictures per second. This time resolu-tion is high enough to reveal the actual process of a collision(compression and extension of springs) between two sliders onthe linear air track. In other words, VideoCom registers the posi-tions s1(t) and s2(t) of the two sliders, their velocities v1(t) andv2(t) as well as their accelerations a1(t) and a2(t) even during theactual collision. The energy and momentum balance can be veri-fied not only before and after the collision, but also during thecollision itself.

This experiment records the elastic collision of two bodies withthe masses m1 and m2. The evaluation shows that the linearmomentum

p(t) = m1 · v1(t) + m2 · v2(t)

remains constant during the entire process, including the actualcollision. On the other hand, the kinetic energy

E(t) =m1 · v1

2(t) + m2 · v2

2(t)2 2

reaches a minimum during the collision, which can be explainedby the elastic strain energy stored in the springs. This experimentalso verifies Newton's third law in the form

m1 · a1(t) = – m1 · a2(t)

From the path-time diagram, it is possible to recognize the timet0 at which the two bodies have the same velocity

v1(t0) = v2(t0)

and the distance s2 – s1 between the bodies is at its lowest. Attime t0, the acceleration values (in terms of their absolute values)are greatest, as the springs have reached their maximum tension.

P1.

3.4.

4 (b

)

P1.

3.4.

4 (a

)


27


337 130 Track, 1.5 m 1

337 110 Trolley 2

337 114 Additional weights 1

337 112 Impact spring for trolley 2

337 501 Linear air track, 1.5 m long, complete 1

337 53 Air supply for air track 1

667 823 Power controller 1

311 02 Metal scale, 1 m long 1

337 47 VideoCom 1 1

300 59 Camera tripod 1 1


Confirmation of Newton’s third law


P 1.3.5Free fall

P 1.3.5.1 Free fall: time measurement with thecontact plate and the counter P

P 1.3.5.2 Free fall: time measurement with the forked light barrier and digitalcounter

Free fall: time measurement with the contact plate and the counter P (P 1.3.5.1)

To investigate free fall, a steel ball is suspended from an electro-magnet. It falls downward with a uniform acceleration due to theforce of gravity

F = m · g

m: mass of ball, g: gravitational acceleration

as soon as the electromagnet is switched off. The friction of aircan be regarded as negligible as long as the falling distance, andthus the terminal velocity, are not too great; in other words, theball falls freely.

In the first experiment, electronic time measurement is started assoon as the ball is released through interruption of the magnetcurrent. After traveling a falling distance h, the ball falls on acontact plate, stopping the measurement of time t. The measure-ments for various falling heights are plotted as value pairs in apath-time diagram. As the ball is at rest at the beginning oftiming, g can be determined using the relationship

h = 1

g · t 2.2

In the second experiment, the ball passes one, or optionally twolight barriers on its way down; their distance from the holdingmagnet h is varied. In addition to the falling time t, the obscura-tion time Dt is measured and, for a given ball diameter d, theinstantaneous velocity

vm =d

Dt

of the ball is determined. A velocity-time diagram vm(t) is pre-pared in addition to the path-time diagram h(t). Thus, the relation-ship

vm = g · t

can be used to determine g.

P1.

3.5.

2 (a

)

P1.

3.5.

1

P1.

3.5.

2 (b

)

28


336 23 Large contact plate 1

336 21 Holding magnet with clamp 1 1 1

200 67288 Steel ball, 16 mm dia. 1 1

Low-voltage power supply, 3,6,9,12 V AC/DC,3 A 1

Counter P 1

504 52 Morse key 1


578 51 STE Si diode 1 N 4007 1 1

33746 Forked light barrier, infra-red 1 2


311 22 Vertical scale, 1 m long 1 1 1


30011 Saddle base 1 1 1

300 41 Stand rod, 25 cm 1 1 1

300 44 Stand rod, 100 cm 1

300 46 Stand rod, 150 cm 1 1

301 01 Leybold multiclamp 2 1 1

309 48 Cord, 10 m 1 1


501 35 Connecting lead, 200 cm, red, Ø 2.5 mm2 1 1 1

501 25 Connecting lead, 50 cm, red, Ø 2.5 mm2 1

501 26 Connecting lead, 50 cm, blue, Ø 2.5 mm2 2 1 1

501 30 Connecting lead, 100 cm, red, Ø 2.5 mm2 1

501 31 Connecting lead, 100 cm, blue, Ø 2.5 mm2 1

501 36 Connecting lead, 200 cm, blue, Ø 2.5 mm2 1 1 1

521 230

575 451

Free fall: recording and evaluating with VideoCom (P 1.3.5.4)

P 1.3.5

P 1.3.5.3 Free fall: multiple time measurementswith the g-ladder

P 1.3.5.4 Free fall: recording and evaluating withVideoCom

Free fall

The disadvantage of preparing a path-time diagram by recordingthe measured values point by point is that it takes a long timebefore the dependency of the result on experiment parameterssuch as the initial velocity or the falling height becomes apparent.Such investigations become much simpler when the entire mea-surement series of a path-time diagram is recorded in one mea-suring run using the computer.

In the first experiment, a ladder with several rungs falls through aforked light barrier, which is connected to the CASSY computerinterface device to measure the obscuration times. This meas-urement is equivalent to a measurement in which a body fallsthrough multiple equidistant light barriers. The height of the fall-ing body corresponds to the rung width. The measurement dataare recorded and evaluated using CASSY LAB. The instan-taneous velocities are calculated from the obscuration times andthe rung width and displayed in a velocity-time diagram v(t). Themeasurement points can be described by a straight line

v(t) = v0 + g · tg: gravitational acceleration

whereby v0 is the initial velocity of the ladder when the first rungpasses the light barrier.

In the second experiment, the motion of a falling body is trackedas a function of time using the single-line CCD camera VideoComand evaluated using the corresponding software. The measure-ment series is displayed directly as the path-time diagram h(t).This curve can be described by the general relationship

s = v0 · t + 1

g · t22


29

P1.

3.5.

3

P1.

3.5.

4


33746 Forked light barrier, infra-red 1

501 16 Multicore cable, 6-pole, 1.5 m long 1

524 034 Timer Box 1

529 034 g-ladder 1

524 010 Sensor CASSY 1

524 200 CASSY Lab 1

33747 VideoCom 1

300 59 Camera tripod 1

337472 Falling body for VideoCom 1

33621 Holding magnet with clamp 1

30001 Stand base, V-shape, 28 cm 1

30002 Stand base, V-shape, 20 cm 1





50138 Connecting lead, Ø 2.5 mm2, 200 cm, black 4

additionally recommended: 1 PC with Windows 95/NT or higher 1 1

Free fall:

multiple time measurements

with the g-ladder (P1.3.5.3)


P 1.3.6Angled projection

P 1.3.6.1 Point-by-point recording of theprojection parabola as a func-tion of the velocity and angle ofprojection

P 1.3.6.2 Principle of superposing: comparing angled projectionand free fall

Point-by-point recording of the projection parabola as a function of the velocity and angle of projection (P 1.3.6.1)

The trajectory of a ball launched at a projection angle a with aprojection velocity v0 can be reconstructed on the basis of theprinciple of superposing. The overall motion is composed of amotion with constant velocity in the direction of projection and avertical falling motion. The superposition of these motions resultsin a parabola, whose height and width depend on the angle andvelocity of projection.

The first experiment measures the trajectory of the steel ballpoint by point using a vertical scale. Starting from the point ofprojection, the vertical scale is moved at predefined intervals; thetwo pointers of the scale are set so that the projected steel ballpasses between them. The trajectory is a close approximation ofa parabola. The observed deviations from the parabolic form maybe explained through friction with the air.

In the second experiment, a second ball is suspended from aholding magnet in such a way that the first ball would strike it ifpropelled in the direction of projection with a constant velocity.Then, the second ball is released at the same time as the first ballis projected. We can observe that, regardless of the launchvelocity v0 of the first ball, the two balls collide; this providesexperimental confirmation of the principle of superposing.

P1.

3.6.

1

P1.

3.6.

2

30


336 56 Large projection apparatus 1 1

336 21 Holding magnet with clamp 1

DC voltage source, approx. U = 10 V, e.g.Low-voltage power supply, 3,6,9,12 V AC/DC, 3 A 1

311 03 Wooden ruler, 1 m long 1

311 22 Vertical scale, 1 m long 1

311 77 Steel tape measure, 2 m 1

30011 Saddle base 1

300 44 Stand rod, 100 cm 1


301 06 Bench clamp 2 2


501 26 Connecting lead, Ø 2.5 mm2, 50 cm, blue 1

501 35 Connecting lead, Ø 2.5 mm2, 200 cm, red 1


Schematic diagram comparing angled projection and free fall (P 1.3.6.2)

521 230

Uniform linear motion and uniform circular motion (P 1.3.7.1)

P 1.3.7

P 1.3.7.1 Uniform linear motion and uniform circular motion

P 1.3.7.2 Uniformly accelerated motion

P 1.3.7.3 Two-dimensional motion on aninclined plane

P 1.3.7.4 Two-dimensional motion inresponse to a central force

P 1.3.7.5 Superimposing translationaland rotational motions on arigid body

Two-dimensional motionson the air table

The air table makes possible recording of any two-dimensionalmotions of a slider for evaluation following the experiment. Toachieve this, the slider is equipped with a recording device whichregisters the position of the slider on metallized recording paperevery 20 ms.

The aim of the first experiment is to examine the instantaneousvelocity of straight and circular motions. In both cases, theirabsolute values can be expressed as

v =Ds

,Dt

where Ds is the straight path traveled during time Dt for linearmotions and the equivalent arc for circular motions.

In the second experiment, the slider without an initial velocitymoves on the air table inclined by the angle a. Its motion can bedescribed as a one-dimensional, uniformly accelerated motion.The marked positions permit plotting of a path-time diagram fromwhich we can derive the relationship

s =s

· a · t2 where a = g · sin a2


31

P5.

2.1.

1

P5.

2.1.

2

P1.

3.7.

1-3

P1.

3.7.

5

P1.

3.7.

4


337 801 Large air table 1 1 1

352 10 Helical spring, 2 N; 0.03 N/cm 1

In the third experiment, a motion “diagonally upward” is impartedon the slider on the inclined air table, so that the slider describesa parabola. Its motion is uniformly accelerated in the direction ofinclination and virtually uniform perpendicular to this direction.

The aim of the fourth experiment is to verify Kepler’s law of areas.Here, the slider moves under the influence of a central forceexerted by a centrally mounted helical screw. In the evaluation,the area

DA = Ir x DsI

“swept” due to the motion of the slider in the time Dt is deter-mined from the radius vector r and the path section Ds as well asfrom the angle between the two vectors.

The final experiment investigates simultaneous rotational andtranslational motions of one slider and of two sliders joinedtogether in a fixed manner. One recorder is placed at the centerof gravity, while a second is at the perimeter of the “rigid body”under investigation. The motion is described as the motion of thecenter of gravity plus rotation around that center of gravity.


P 1.3.7Two-dimensional motionson the air table

P 1.3.7.6 Two-dimensional motion of twoelastically coupled bodies

P 1.3.7.7 Experimentally verifying theequality of a force and itsopposing force

P 1.3.7.8 Elastic collision in two dimen-sions

P 1.3.7.9. Inelastic collision in two dimen-sions

Elastic collision in two dimensions (P 1.3.7.8)

The air table is supplied complete with two sliders. This meansthat this apparatus can also be used to investigate e.g. two-dimensional collisions.

In the first experiment, the motions of two sliders which are elas-tically coupled by a rubber band are recorded. The evaluationshows that the common center of gravity moves in a straight lineand a uniform manner, while the relative motions of the two sli-ders show a harmonic oscillation.

In the second experiment, elastically deformable metal rings areattached to the edges of the sliders before the start of the ex-periment. When the two rebound, the same force acts on eachslider, but in the opposite direction. Therefore, regardless of themasses m1 and m2 of the two sliders, the following relationshipapplies for the total two-dimensional momentum.

m1 · v1 + m2 · v2 = 0

32

P5.

2.1.

1

P5.

2.1.

2P

1.3.

7.6-

9


337 801 Large air table 1

The last two experiments investigate elastic and inelastic colli-sions between two sliders. The evaluation consists of calculatingthe total two-dimensional momentum

p = m1 · v1 + m2 · v2

and the total energy

E =m1 · v2

1 +m2 · v2

22 2

both before and after collision.

Path-time diagrams of rotational motions - time measurements with the counter P (P 1.4.1.1 a)

P 1.4.1

P 1.4.1.1 Path-time diagrams of rotation-al motions - time measure-ments with the counter P

Rotational motions

The low-friction Plexiglas disk of the rotation model is set inuniform or uniformly accelerated motion for quantitative investi-gations of rotational motions. Forked light barriers are used todetermine the angular velocity; their light beams are interruptedby a 10° flag mounted on the rotating disk. When two forked lightbarriers are used, measurement of time t can be started andstopped for any angle f. This experiment determines the meanvelocity

v = f .t

If only one forked light barrier is available, the obscuration timeDt is measured, which enables calculation of the instantaneousangular velocity

v = 10h.Dt

In this experiment, the angular velocity v and the angular accel-eration a are recorded analogously to acceleration in translation-al motions. Both uniform and uniformly accelerated rotationalmotions are investigated. The results are graphed in a velocity-time diagram v(t). In the case of a uniformly accelerated motionof a rotating disk initially at rest, the angular acceleration can bedetermined from the linear function

v = a · t.

P1.

4.1.

1 (a

)

P1.

4.1.

1 (b

)

Mechanics Rotational motions of a rigid body

33


347 23 Rotation model 1 1

33746 Forked light barrier, infra-red 1 2

Counter P 1 1

1 2

300 76 Laboratory stand II 1 1

301 07 Simple bench clamp 1 1

500 411 Connecting lead, red, 25 cm 1 1

575 451

501 16 Multicore cable, 6-pole, 1.5 m

Rotational motions of a rigid body Mechanics

P 1.4.1Rotational motions

P 1.4.1.2 Path-time diagrams of rotationalmotions – measuring and eval-uating with CASSY

Path-time diagrams of rotational motions – measuring and evaluating with CASSY (P 1.4.1.2)

The use of the computer-assisted measured-value recordingsystem CASSY facilitates the study of uniform and uniformlyaccellerated rotational motions. A thread stretched over the sur-face of the rotation model transmits the rotational motion to themotion sensing element whose signals are adapted to themeasuring inputs of CASSY by the motion transducer box.

The topic of this experiment are homogeneous and constantlyaccellerated rotational motions, which are studied on the analo-gy of homogeneous and constantly accellerated translationalmotions.

34

P1.

4.1.

2


347 23 Rotation model 1

337 631 Motion sensing element 1


524 200 CASSY Lab 1

524 032 Motion transducer box 1




300 11 Saddle base 1





Conservation of angular momentum for elastic torsion impact (P 1.4.2.1)

P 1.4.2

P 1.4.2.1 Conservation of angularmomentum for elastic torsionimpact

P 1.4.2.2 Conservation of angularmomentum for inelastic torsionimpact

Conservation of angular momentum

Torsion impacts between rotating bodies can be described anal-ogously to one-dimensional translational collisions when theaxes of rotation of the bodies are parallel to each other andremain unchanged during the collision. This condition is reliablymet when carrying out measurements using the rotation model.The angular momentum is specified in the form

L = l · v

I: moment of inertia, v: angular velocity.

The principle of conservation of angular momentum states thatfor any torsion impact of two rotating bodies, the quantity

L = l1 v1 + l2 · v2

before and after impact remains the same.

The two experiments investigate the nature of elastic and in-elastic torsion impact. Using two forked light barriers and thecomputer-assisted measuring system CASSY, the obscurationtimes of two interrupter flags are registered as a measure of theangular velocities before and after torsion impact. The CASSYLab uses the obscuration times Dt and the angular field Df = 10°of the interrupter flags to calculate the angular velocities

v = 10°

Dt

as well as the angular momentums and energies before and afterimpact.

P1.

4.2.

1-2


35


347 23 Rotation model 1



524 034 Timer box 1



524 200 CASSY Lab 1

additionally required: 1 PC with Windows 95/NT or higher 1


P 1.4.3Centrifugal force

P 1.4.3.1 Centrifugal force on a revolvingbody - measuring with the cen-trifugal force apparatus

Centrifugal force on a revolving body - measuring with the centrifugal force apparatus (P 1.4.3.1)

To measure the centrifugal force

F = m · v2 · r

a body with the mass m is caused to move in the centrifugal forceapparatus with the angular velocity v along an arc with the radi-us r. The body is attached to a mirror elastically mounted abovethe axis of rotation via a wire. The centrifugal force tilts the mir-ror, whereby the change in the arc radius caused by this tilt isnegligible. The tilt is proportional to the centrifugal force and canbe detected using a light pointer. The arrangement is calibratedusing a precision dynamometer while the centrifugal force appa-ratus is idle.

In this experiment the centrifugal force F is determined as a func-tion of the angular velocity v for two different radii r and two dif-ferent masses m. The angular velocity is determined from theorbit period T of the light pointer, which is measured manuallyusing a stopclock. This experiment verifies the relationship

F “ v2, F “ m and F “ r.

P1.

4.3.

1

36


347 22 Centrifugal force apparatus 1

347 35 Experiment motor 1

347 36 Control unit for experiment motor 1

450 51 Lamp, 6 V/30 W 1


460 20 Aspherical condenser 1

Transformer, 6 V AC,12 V AC/30 VA 1



313 07 Stopclock I, 30 s / 15 min 1


30011 Saddle base 1

Light pointer deflection s as a function of the square of the angular velocity v

521 210

300 41 I Stand rod, 25 cm I 1301 01 I Leybold multiclamp I 1

Centrifugal force on a revolving body – measuring with the central force apparatus (P 1.4.3.2)

P 1.4.3.

P 1.4.3.2 Centrifugal force on a revolvingbody – measuring with thecentral force apparatus

Centrifugal force

In the central force apparatus, the centrifugal force

F = m · C2 · rr: radius of orbit, C: angular velocity

is transmitted to a revolving body of the mass m by means of asystem of angled levers and a needle bearing on a leaf springwith strain gauge. The transmission ratio of the lever system isselected so that the change in the orbit radius r for the revolvingbody is negligible. The force exerted on the strain gauge ismeasured using a newton meter; its analog output signal is ledout to the Y-input of an XY recorder. A tachometer connected tothe central force apparatus measures the angular velocity andgenerates an analog signal which is fed into the X-input of therecorder.

In this experiment, the relationship

F “ C2

is derived directly from the parabolic shape of the recordercurve. To verify the proportionalities

F “ r and F “ m

the curves are recorded for different orbit radii r and variousmasses m.


37

P1.

4.3.

2


347 21 Central force apparatus 1

314 251 Newton meter 1


521 35 Variable extra low voltage transformer S 1

33741 Tachymeter 1

XY-Yt recorder 1

301 06 Bench clamp 1


Centrifugal force F as a function of the angular velocity C

575 664


P 1.4.4Motions of a gyroscope

P 1.4.4.1 Precession of a gyroscope

P 1.4.4.2 Nutation of a gyroscope

Precession of a gyroscope (P 1.4.4.1)

Gyroscopes generally execute extremely complex motions, asthe axis of rotation is supported at only one point and changesdirections constantly. We distinguish between the precessionand the nutation of a gyroscope.

The aim of the first experiment is to investigate the precession ofa symmetrical gyroscope which is not supported at its center ofgravity. A forked light barrier and a digital counter are used tomeasure the precession frequency fp of the axis of symmetryaround the fixed vertical axis for different distances d betweenthe resting point and the center of gravity as a function of the fre-quency f with which the gyroscope rotates on its axis of symme-try. This experiment quantatively verifies the relationship

CP = d · G

I · Cwhich applies for the corresponding angular frequencies CP andC and for a known weight G and known moment of inertia I of thegyroscope around its axis of symmetry.

The second experiment takes a quantitative look at the nutationof a force-free gyroscope supported at its center of gravity. Here,the aim is to measure the nutation frequency fN of the axis ofsymmetry around the axis of angular momentum, which is fixedin space, as a function of the frequency f with which the gyro-scope turns on its axis of symmetry. The aim of the evaluation isto verify the relationship which applies for small angles betweenthe axis of angular momentum and the axis of symmetry:

CN = I · CID

To achieve this, an additional measurement is carried out torecord not only the principle moment of inertia I around the axisof symmetry, but also the principle moment of inertia ID aroundthe axis perpendicular to it.

38

P1.

4.4.

1-2


348 18 Large gyroscope 1

575 48 Digital counter 1


50116 Multicore cable, 6-pole, 1.5 m 2






590 24 Set of 10 load pieces, 100 g each 1

311 52 Vernier calipers, plastic 1

314 201 Precision dynamometer 100.0 N 1

Precession (left) and nutation (right) of a gyroscope. (d: axis of figure, L: axis of angular momentum, C: instantaneous axis of rotation)

P 1.4.4.1 P 1.4.4.2

Definition of moment of inertia (P 1.4.5.1)

P 1.4.5

P 1.4.5.1 Definition of moment of inertia

P 1.4.5.2 Moment of inertia and bodyshape

P 1.4.5.3 Steiner’s law

Moment of inertia

For any rigid body whose mass elements mi are at a distance ofri from the axis of rotation, the moment of inertia is

l = S mi · ri2

i

For a particle of mass m in an orbit with the radius r, we can say

l = m · r 2.

The moment of inertia is determined from the oscillation period ofthe torsion axle on which the test body is mounted and which iselastically joined to the stand via a helical spring. The system isexcited to harmonic oscillations. For a known directed angularquantity D, the oscillation period T can be used to calculate themoment of inertia of the test body using the equation

l = D · ( T )2.

2ö

In the first experiment, the moment of inertia of a ”mass point” isdetermined as a function of the distance r from the axis of rota-tion. In this experiment, a rod with two weights of equal mass ismounted transversely on the torsion axle. The centers of gravityof the two weights have the same distance r from the axis of rota-tion, so that the system oscillates with no unbalanced weight.

The second experiment compares the moments of inertia of ahollow cylinder, a solid cylinder and a solid sphere. Thismeasurement uses two solid cylinders with equal mass butdifferent radii. Additionally, this experiment examines a hollowcylinder which is equal to one of the solid cylinders in mass andradius, as well as a solid sphere with the same moment of iner-tia as one of the solid cylinders.

The third experiment verifies Steiner’s law using a flat circulardisk. Here, the moments of inertia IA of the circular disk aremeasured for various distances a from the axis of rotation, andcompared with the moment of inertia Is around the axis of thecenter of gravity. This experiment confirms the relationship

IA – IS = M · a2

P1.

4.5.

2

P1.

4.5.

1

P1.

4.5.

3


39


347 80 Torsion axle 1 1 1

347 81 Set of cyliders for torsion axle 1

347 82 Ball for torsion axle 1

347 83 Circular disc for torsion axle 1

313 07 Stopclock I 30 s/15 min 1 1 1

314141 Precision dynamometer, 1.0 N 1 1 1


Steiner's law (P 1.4.5.3)

Oscillations Mechanics

P 1.5.1Mathematic and physical pendulum

P 1.5.1.1 Determining the gravitationalacceleration with a mathematicpendulum

P 1.5.1.2 Determining the gravitationalacceleration with a reversiblependulum

Determining the gravitational acceleration with Determining the gravitational acceleration with a mathematic pendulum (P 1.5.1.1) a reversible pendulum (P 1.5.1.2)

A simple, or “mathematic” pendulum is understood to be a point-shaped mass m suspended on a massless thread with the lengths. For small deflections, it oscillates under the influence of grav-ity with the period

T = 2ö · ö sg

Thus, a mathematic pendulum could theoretically be used todetermine the gravitational acceleration g precisely throughmeasurement of the oscillation period and the pendulum length.

In the first experiment, the ball with pendulum suspension is usedto determine the gravitational acceleration. As the mass of theball is much greater than that of the steel wire on which it is sus-pended, this pendulum can be considered to be a close approx-imation of a mathematic pendulum. Multiple oscillations arerecorded to improve measuring accuracy. For gravitationalacceleration, the error then depends essentially on the accuracywith which the length of the pendulum is determined.

The reversible pendulum used in the second experiment has twoedges for suspending the pendulum and two sliding weights for“tuning” the oscillation period. When the pendulum is properlyadjusted, it oscillates on both edges with the same period

T0 = 2ö · ösred

g

and the reduced pendulum length sred corresponds to the veryprecisely known distance d between the two edges. For gravita-tional acceleration, the error then depends essentially on theaccuracy with which the oscillation period T0 is determined.

P1.

5.1.

1

P1.

5.1.

2

40


346 39 Ball with pendulum suspension 1

346 111 Reversible pendulum 1

311 77 Steel tape measure, 2 m 1 1

313 07 Stopclock I 30 s /15 min 1 1

Measurement diagram for reversible pendulum (P 1.5.1.2)

Oscillation of a spring pendulum – recording path, velocity and acceleration with CASSY (P 1.5.2.1)

P 1.5.2

P 1.5.2.1 Oscillation of a spring pendu-lum – recording path, velocity andacceleration with CASSY

P 1.5.2.2 Dependency of the oscillationperiod of a spring pendulum onthe oscillating mass

Harmonic oscillations

When a system is deflected from a stable equilibrium position,oscillations can occur. An oscillation is considered harmonicwhen the restoring force F is proportional to the deflection x fromthe equilibrium position.

F = D · xD: directional constant

The oscillations of a spring pendulum are often used as a clas-sic example of this.

In the first experiment, the harmonic oscillations of a spring pen-dulum are recorded as a function of time using the motion trans-ducer and the computer-assisted measured value recordingsystem CASSY. In the evaluation, the oscillation quantities path x,velocity v and acceleration a are compared on the screen. Thesecan be displayed either as functions of the time t or as a phasediagram.

The second experiment records and evaluates the oscillations ofa spring pendulum for various suspended masses m. The rela-tionship

T = 2ö · ö Dm

for the oscillation period is verified.

P1.

5.2.

1-2

Mechanics Oscillations

41



342 61 Set of 12 weights, 50 g each 1


337 631 Motion sensing element 1

524 032 Motion transducer box 1



524 200 CASSY Lab 1



300 46 Stand rod, 150 cm 1


301 08 Clamp with hook 1

309 48 Cord, 10 m 1


additionally required: 1 PC with Windows 95/NT or higher 1


P 1.5.3Torsion pendulum

P 1.5.3.1 Free rotational oscillations –measuring with a hand-heldstopclock

P 1.5.3.2 Forced rotational oscillations –measuring with a hand-heldstopclock

Forced rotational oscillations – measuring with a hand-held stopclock (P 1.5.3.2)

The torsion pendulum after Pohl can be used to investigate freeor forced harmonic rotational oscillations. An electromagneticeddy current brake damps these oscillations to a greater or less-er extent, depending on the set current. The torsion pendulum isexcited to forced oscillations by means of a motor-driven eccen-tric rod.

The aim of the first experiment is to investigate free harmonicrotational oscillations of the type

f(t) = f0 · cosvt · e–d · t where v = öv20 –d2

v0: characteristic frequency of torsion pendulum

To distinguish between oscillation and creepage, the dampingconstant F is varied to find the current I0 which corresponds tothe aperiodic limiting case. In the oscillation case, the angularfrequency v is determined for various damping levels from theoscillation period T and the damping constant d by means of theratio

fn +1 = e– d · T

fn2

of two sequential oscillation amplitudes. Using the relationship

v2 = v20 – d2

we can determine the characteristic frequency v0.

In the second experiment, the torsion pendulum is excited tooscillations with the frequency v by means of a harmonicallyvariable angular momentum. To illustrate the resonance behavior,the oscillation amplitudes determined for various damping levelsare plotted as a function of v2 and compared with the theoreticalcurve

f0 = M0 ·

1

I ö(v2 – v20)2 + d2 · v2

I: moment of inertia of torsion pendulum

(cf. diagram).

P1.

5.3.

1

P1.

5.3.

2

42


346 00 Torsion pendulum 1 1

346 012 Torsion pendulum power supply 1 1

531 100 Amperemeter, DC, I ≤ 2 A, e.g.Multimeter METRAmax 2 1 1

531 100 Voltmeter, DC, U ≤ 24 V, e. g.Multimeter METRAmax 2 1

313 07 Stopclock I 30 s/15 min 1 1

500 442 Connection lead, 100 cm, blue 1 1


Resonance curves for two different damping constants

Chaotic rotational oscillations – recording with CASSY (P 1.5.3.4)

P 1.5.3

P 1.5.3.3 Free rotational oscillations –recording with CASSY

P 1.5.3.4 Forced harmonic and chaoticrotational oscillations – recording with CASSY

Torsion pendulum

The computer-assisted CASSY measured-value recordingsystem is ideal for recording and evaluating the oscillations ofthe torsion pendulum. The numerous evaluation options enable acomprehensive comparison between theory and experiment.Thus, for example, the recorded data can be displayed as path-time, velocity-time and acceleration-time diagrams or as a phasediagram (path-velocity diagram).

The aim of the first experiment is to investigate free harmonicrotational oscillations of the general type

f(t) = (f(0) · cosvt + G.

(0) · sinvt) · e-ut

where v = ßv20 – u2

v0 : characteristic frequency of torsion pendulum

This experiment investigates the relationship between the initialdeflection f(0) and the initial velocity v(0). In addition, the damp-ing constant u is varied in order to find the current l0 which cor-responds to the aperiodic limiting case.

To investigate the transition between forced harmonic and cha-otic oscillations, the linear restoring moment acting on the torsionpendulum is deliberately altered in the second experiment byattaching an additional weight to the pendulum. The restoringmoment now corresponds to a potential with two minima, i.e. twoequilibrium positions. When the pendulum is excited at a con-stant frequency, it can oscillate around the left minimum, the rightminimum or back and forth between the two minima. At certainfrequencies, it is not possible to predict when the pendulum willchange from one minimum to another. The torsion pendulum isthen oscillating in a chaotic manner.


43

P5.

2.1.

1

P5.

2.1.

2P

1.5.

3.4

P1.

5.3.

3


346 00 Torsion pendulum 1 1

346 012 Torsion pendulum power supply 1 1

337 631 Motion transducer 1 1

524 032 BMW box 1 1

501 16 Multicore cable, 6-pole, 1.5 m 1 1


524 200 CASSY Lab 1 1

Ammeter, DC, I ≤ 2 A, e.g.531 100 Multimeter METRAmax 2 1 1

Voltmeter, DC, U ≤ 24 V, e.g. 531 100 Multimeter METRAmax 2 1


500 442 Connecting lead, blue, 100 cm 1 1

501 46 Pair of cables, 100 cm, red and blue 1 3


Potential energy of double pendulums with and without additional mass


P 1.5.4Coupling of oscillations

P 1.5.4.1 Coupled pendulums – measuring with a hand-heldstopclock

P1.5.4.2 Coupled pendulums –measuring and evaluating withVideoCom

Coupled pendulums – measuring with a hand-held stopclock (P 1.5.4.1)

Two coupled pendulums oscillate in phase with the angular fre-quency v+ when they are deflected from the equilibrium positionby the same amount. When the second pendulum is deflected inthe opposite direction, the two pendulums oscillate in phaseopposition with the angular frequency v–.

Deflecting only one pendulum generates a coupled oscillationwith the angular frequency

v = v+ + v–

2

in which the oscillation energy is transferred back and forth be-tween the two pendulums. The first pendulum comes to rest aftera certain time, while the second pendulum simultaneouslyreaches its greatest amplitude. Then the same process runs inreverse. The time from one pendulum stand still to the next iscalled the beat period Ts. For the corresponding beat frequency,we can say

vs = v+ – v–

The aim of the first experiment is to observe in-phase, phase-opposed and coupled oscillations. The angular frequencies v+,v–, vs and v are calculated from the oscillation periods T+, T-, TSand T measured using a stopclock and compared with eachother.

In the second experiment, the coupled motion of the two pendu-lums is investigated using the single-line CCD camera VideoCom.The results include the path-time diagrams s1(t) and s2(t) of pen-dulums 1 and 2, from which the path-time diagrams s+(t) = s1(t)+ s2(t) of the purely in-phase motion and und s-(t) = s1(t) – s2(t)of the purely opposed-phase motion are calculated. The cor-responding characteristic frequencies are determined using -Fourier transforms. Comparison identifies the two characteristicfrequencies of the coupled oscillations s1(t) and s2(t) as thecharacteristic frequencies v+ of the function s+(t) and v+ of thefunction s-(t).

P1.

5.4.

1

P1.

5.4.

2

44


346 45 Double pendulum 1 1

33747 VideoCom 1

300 59 Tripod 1

460 97 Scaled metal rail, 0.5 m 1 1

313 07 Stopclock I, 30 s /15 min 1


300 42 Stand rod, 47 cm 1 1

300 44 Stand rod, 100 cm 2 2


309 48 Cord, 10 m 1 1

additionally required:1 PC with Windows 95 or Windows NT 1

Phase shift of the coupled oscillation – recorded with VideoCom (P 1.5.4.2)

Coupling of longitudinal and rotational oscillations with Wilberforce’s pendulum (P 1.5.4.3)

P 1.5.4

P 1.5.4.3 Coupling of longitudinal androtational oscillations with Wilberforce’s pendulum

Coupling of oscillations

Wilberforce’s pendulum is an arrangement for demonstratingcoupled longitudinal and rotational oscillations. When a helicalspring is elongated, it is always twisted somewhat as well.Therefore, longitudinal oscillations of the helical screw alwaysexcite rotational oscillations also. By the same token, the rota-tional oscillations generate longitudinal oscillations, as torsionalways alters the spring length somewhat.

The characteristic frequency fr of the longitudinal oscillation isdetermined by the mass m of the suspended metal cylinder,while the characteristic frequency fR of the rotational oscillationis established by the moment of inertia I of the metal cylinder. Bymounting screwable metal disks on radially arranged threadedpins, it becomes possible to change the moment of inertia I with-out altering the mass m.

The first step in this experiment is to match the two frequenciesfT und fR by varying the moment of inertia I. To test this condition,the metal cylinder is turned one full turn around its own axis andraised 10 cm at the same time. When the frequencies have beenproperly matched, this body executes both longitudinal and rota-tional oscillations which do not affect each other. Once this hasbeen done, it is possible to observe for any deflection how thelongitudinal and rotational oscillations alternately come to astandstill. In other words, the system behaves like two classicalcoupled pendulums.

P1.

5.4.

3


45


346 51 Wilberforce's pendulum 1


30011 Saddle base 1

313 17 Stopclock II 60 s/30 min 1

Wave mechanics Mechanics

P 1.6.1Transversal and longitudinal waves

P 1.6.1.1 Standing transversal waves ona string

P 1.6.1.2 Standing longitudinal waves ona helical spring

Standing transversal waves on a string (P 1.6.1.1) Standing longitudinal waves on a helical spring (P 1.6.1.2)

A wave is formed when two coupled, oscillating systems sequen-tially execute oscillations of the same type. The wave can beexcited e.g. as a transversal wave on an elastic string or as a lon-gitudinal wave along a helical spring. The propagation velocity ofan oscillation state — the phase velocity v — is related to theoscillation frequency f and the wavelength l through the formula

v = l · f

When the string or the helical spring is fixed at both ends, reflec-tions occur at the ends. This causes superposing of the “out-going” and reflected waves. Depending on the string length s,there are certain frequencies at which this superposing of thewaves forms stationary oscillation patterns – standing waves.The distance between two oscillation nodes or two antinodes ofa standing wave corresponds to one half the wavelength. Thefixed ends correspond to oscillation nodes. For a standing wavewith n oscillation antinodes, we can say

s = n · ln .2

This standing wave is excited with the frequency

fn = n ·v .2s

The first experiment examines standing string waves, while thesecond experiment looks at standing waves on a helical spring.In both cases, the relationship

fn “ n

is verified. Two helical springs with different phase velocities vare provided for use.

P1.

6.1.

1

P1.

6.1.

2

46


20066 629 Rubber band 1 1



579 42 STE motor with rocker 1 1

Function generator S 12, 0.1 Hz to 20 kHz 1 1

311 78 Tape measure, 1.5m / 1 mm 1 1




301 25 Clamping block MF 1 1

666 615 Universal bosshead, 28 mm dia., 50 mm 1

301 29 Pair of pointers 1 1

314 04 Support clip, for plugging in 1 1


522 621

Wavelength, frequency and phase velocity for travelling waves (P 1.6.2.1)

P 1.6.2

P 1.6.2.1 Wavelength, frequency andphase velocity for travellingwaves

Wave machine

The “modular wave machine” equipment set enables us to set upa horizontal torsion wave machine, while allowing the size andcomplexity of the setup within the system to be configured asdesired. The module consists of 21 pendulum bodies mountedon edge bearings in a rotating manner around a common axis.They are elastically coupled on both sides of the axis of rotation,so that the deflection of one pendulum propagates through theentire system in the form of a wave.

The aim of this experiment is to explicitly confirm the relationship

v = l · f

between the wavelength l, the frequency f and the phase velocityv. A stopclock is used to measure the time t required for any wavephase to travel a given distance s for different wavelengths; thesevalues are then used to calculate the phase velocity

v =st

The wavelength is then “frozen” using the built-in brake, to per-mit measurement of the wavelength l. The frequency is deter-mined from the oscillation period measured using the stopclock.

When the recommended experiment configuration is used, it ispossible to demonstrate all significant phenomena pertaining tothe propagation of linear transversal waves. In particular, theseinclude the excitation of standing waves by means of reflectionat a fixed or loose end.

P1.

6.2.

1

Mechanics Wave mechanics

47


401 20 Modular wave machine, basic module 1 2

401 22 Drive module for modular wave machine 1

40123 Damping module for modular wave machine 1

401 24 Brake unit for modular wave machine 2

DC voltage source, U = 0 – 12 V, e. g.521 35 Variable extra low voltage transformer S 1

521 25 Transformer 2 . . . . 12 V 1

313 07 Stopclock I 30 s /15 min 1



Relationship between the frequency and the wavelength of a propagating wave


P 1.6.3Circularly polarized waves

P 1.6.3.1 Investigating circularly polarizedstring waves in the experimentsetup after Melde

P 1.6.3.2 Determining the phase velocityof circularly polarized stringwaves in the experiment setupafter Melde

Investigating circularly polarized string waves in the experiment setup after Melde (P 1.6.3.1)

The experiment setup after Melde generates circularly polarizedstring waves on a string with a known length s using a motor-driven eccentric. The tensioning force F of the string is varieduntil standing waves with the wavelength

ln = 2sn

n: number of oscillation nodes

appear.

In the first experiment, the wavelengths ln of the standing stringwaves are determined for different string lengths s and stringmasses m at a fixed excitation frequency and plotted as a func-tion of the respective tensioning force Fm. The evaluation con-firms the relationship

l “ ö Fm*

with the mass assignment

m* = ms

m: string mass, s: string length

In the second experiment, the same measuring procedure is car-ried out, but with the addition of a stroboscope. This is used todetermine the excitation frequency f of the motor. It also makesthe circular polarization of the waves visible in an impressivemanner when the standing string wave is illuminated with lightflashes which have a frequency approximating that of the stan-dard wave. The additional determination of the frequency f en-ables calculation of the phase velocity c of the string waves usingthe formula

c = l · f

as well as quantitative verification of the relationship

c = ö F .m*

P1.

6.3.

1

P1.

6.3.

2

48


401 03 Vibrating thread apparatus 1 1


451 281 Stroboscope, 1. . .330 Hz 1

315 05 School and laboratory balance 311, 311 g 1

Generating circular water waves (P 1.6.4.1)

P 1.6.4

P 1.6.4.1 Generating circular and straightwater waves

P 1.6.4.2 Applying Huygens’ principle towater waves

P 1.6.4.3 Propagation of water waves intwo different depths

P 1.6.4.4 Refraction of water waves

P 1.6.4.5 Doppler effect in water waves

P 1.6.4.6 Reflection of water waves at astraight obstacle

P 1.6.4.7 Reflection of water waves atcurved obstacles

Propagation of water waves

A prism, a biconvex lens and a biconcave lens are investigatedas practical applications for water waves.

The fifth experiment observes the Doppler effect in circular waterwaves for various speeds u of the wave exciter.

The last two experiments examine the reflection of water waves.When straight and circular waves are reflected at a straight wall,the “wave beams” obey the law of reflection. When straight wavesare reflected by curved obstacles, the originally parallel waverays travel in either convergent or divergent directions, depend-ing on the curvature of the obstacle. We can observe a focusingto a focal point, respectively a divergence from an apparent focalpoint, just as in optics.

Mechanics Wave mechanics

49

Fundamental concepts of wave propagation can be explainedparticularly clearly using water waves, as their propagation canbe observed with the naked eye.

The first experiment investigates the properties of circular andstraight waves. The wavelength Ö is measured as a function ofeach excitation frequency f and these two values are used to cal-culate the wave velocity

v = f · ÖThe aim of the second experiment is to verify Huygens’ principle.In this experiment, straight waves strike an edge, a narrow slitand a grating. We can observe a change in the direction of pro-pagation, the creation of circular waves and the superposing ofcircular waves to form one straight wave.

The third and fourth experiments aim to study the propagation ofwater waves in different water depths. A greater water depth cor-responds to a medium with a lower refractive index n. At the tran-sition from one “medium” to another, the law of refraction applies:

sina1 =Ö1

sina2 Ö2

a1, a2: angles with respect to axis of incidence in zones 1and 2

Ö1, Ö2: wavelength in zones 1 and 2

P1.

6.4.

3

P1.

6.4.

2

P1.

6.4.

1

P1.

6.4.

4-7


401 501 Wave trough with stroboscope 1 1 1 1

313 033 Electronic stopclock P 1


Convergent beam path behind a biconvex lens (P 1.6.4.4)


P 1.6.5Interference with water waves

P 1.6.5.1 Two-beam interference of waterwaves

P 1.6.5.2 Lloyd’s experiment using waterwaves

P 1.6.5.3 Diffraction of water waves at aslit and an obstacle

P 1.6.5.4 Diffraction of water waves at amultiple slit

P 1.6.5.5 Generating standing waves infront of a reflecting barrier

Two-beam interference of water waves (P 1.6.5.1)

Experiments on the interference of waves can be carried out inan easily understandable manner, as the diffraction objects canbe seen and the propagation of the diffracted waves observedwith the naked eye.

In the first experiment, the interference of two coherent circularwaves is compared with the diffraction of straight waves at adouble slit. The two arrangements generate identical interferencepatterns.

The second experiment reproduces Lloyd’s experiment on gen-erating two-beam interference. A second wave coherent to thefirst is generated by reflection at a straight obstacle. The result isan interference pattern which is equivalent to that obtained fortwo-beam interference with two discrete coherent exciters.

In the third experiment, a straight wave front strikes slits andobstacles of various widths. A slit which has a width of less thanthe wavelength acts like a point-shaped exciter for circularwaves. If the slit width is significantly greater than the wavelength,the straight waves pass the slit essentially unaltered. Weaker, cir-cular waves only propagate in the shadow zones behind theedges. When the slit widths are close to the wavelength, a cleardiffraction pattern is formed with a broad main maximum flankedby lateral secondary maxima. When the waves strike an obstacle,the two edges of the obstacle act like excitation centers for cir-cular waves. The resulting diffraction pattern depends greatly onthe width of the obstacle.

The object of the fourth experiment is to investigate the diffrac-tion of straight water waves at double, triple and multiple slitswhich have a fixed slit spacing d. This experiment shows that thediffraction maxima become more clearly defined for an increas-ing number n of slits. The angles at which the diffraction maximaare located remain the same.

50

The last experiment demonstrates the generation of standingwaves by means of reflection of water waves at a wall arrangedparallel to the wave exciter. The standing wave demonstratespoints at regular intervals at which the crests and troughs of theindividual traveling and reflected waves cancel each other out.The oscillation is always greatest at the midpoint between twosuch nodes.

P1.

6.5.

1-4

P1.

6.5.

5


401 501 Wave trough with stroboscope 1 1


Diffraction of water waves at a narrow obstacle (P 1.6.5.3)

Acoustic beats – recording with CASSY (P 1.7.1.3)

P 1.7.1

P 1.7.1.1 Mechanical oscillations andsound waves using the record-ing tuning fork

P 1.7.1.2 Acoustic beats – display on the oscilloscope

P 1.7.1.3 Acoustic beats – recording with CASSY

Sound waves

Acoustics is the study of sound and all its phenomena. This dis-cipline deals with both the generation and the propagation ofsound waves.

The object of the first experiment is the generation of soundwaves by means of mechanical oscillations. The mechanicaloscillations of a tuning fork are recorded on a glass plate coatedwith carbon black. At the same time the sound waves are regis-tered using a microphone and displayed on an oscilloscope. Therecorded signals are the same shape; fundamental oscillationsand harmonics are visible in both cases.

The second experiment demonstrates the wave nature of sound.Here, acoustic beats are investigated as the superposing of twosound waves generated using tuning forks with slightly differentfrequencies f1 and f2. The beat signal is received via a micro-phone and displayed on the oscilloscope. By means of further(mis-) tuning of one tuning fork by moving a clamping screw, thebeat frequency

fS = f2 – f1is increased, and the beat period (i. e. the interval between twonodes of the beat signal)

TS = 1

fS

is reduced.

In the third experiment, the acoustic beats are recorded andevaluated via the CASSY computer interface device. The indi-vidual frequencies f1 and f2, the oscillation frequency f and thebeat frequency fS are determined automatically and comparedwith the calculated values

f =f1 + f2

2

fS = f2 – f1.

Mechanics Acoustics

51

P1.

7.1.

2

P1.

7.1.

1

P1.

7.1.

3


414 76 Recording tuning fork, 128 Hz 1

459 32 Set of 20 candles 1

414 72 Pair of resonance tuning forks, 440 Hz 1 1

586 26 Multi-purpose microphone 1 1 1

575 211 Two-channel oscilloscope 303 1 1

575 35 BNC/4 mm adapter, 2-pole


524 200 CASSY Lab 1


additionally recommended:1 PC with Windows 95/ NT or higher 1

Mechanical oscillations and sound waves using the recording tuning fork (P 1.7.1.1)

1 1

Acoustics Mechanics

P 1.7.2Oscillations of a string

P 1.7.2.1 Determining the oscillation frequency of a string as a function of the string lengthand tensile force

Determining the oscillation frequency of a string as a function of the string length and tensile force (P 1.7.2.1)

In the fundamental oscillation, the string length s of an oscillatingstring corresponds to half the wavelength. Therefore, the follow-ing applies for the frequency of the fundamental oscillation:

f = c

,2s

where the phase velocity c of the string is given by

c = ö F

A · r

F: tensioning force, A: area of cross-section, r: density

In this experiment, the oscillation frequency of a string is deter-mined as a function of the string length and tensioning force. Themeasurement is carried out using a forked light barrier and thecomputer-assisted measuring system CASSY, which is used hereas a high-resolution stop-clock. The aim of the evaluation is toverify the relationships

f “ öF and f “ 1 .

s

P1.

7.2.

1

52


414 01 Monochord 1

314 201 Precision dynamometer 100.0 N 1


524 034 Timer box 1



524 200 CASSY Lab 1






Frequency f as a function of the string length s

Kundt’s tube: determining the wavelength using the cork-powder method (P 1.7.3.1)

P 1.7.3

P 1.7.3.1 Kundt’s tube: determining the wavelengthusing the cork-powder method

P 1.7.3.2 Determining the wavelength ofstanding sound waves

Wavelength and velocity of sound

Just like other waves, reflection of sound waves can producestanding waves in which the oscillation nodes are spaced at

d =l

2

Thus, the wavelength l of sound waves can be easily measuredat standing waves.

The first experiment investigates standing waves in Kundt’s tube.These standing waves are revealed in the tube using cork pow-der which is stirred up in the oscillation nodes. The distancebetween the oscillation nodes is used to determine the wave-length l.

In the second experiment, standing sound waves are generatedby reflection at a barrier. This setup uses a function generatorand a loudspeaker to generate sound waves in the entire audiblerange. A microphone is used to detect the intensity minima, andthe wavelength b is determined from their spacings.

P1.

7.3.

1

P1.

7.3.

2

Mechanics Acoustics

53


413 01 Kundt's tube 1

586 26 Multi-purpose microphone 1

587 08 Broad-band speaker 1

587 66 Reflection plate 1

Function generator S 12, 0.1 Hz to 20 kHz, supply: 12 V DC 1

Voltmeter, DC, U ≤ 3 V, e. g.531 100 Multimeter METRAmax 2 1


460 97 Scaled metal rail, 0.5 m 1

30011


Determining the wavelength of standing sound waves (P 1.7.3.2)

522 621

Saddle base 3

Acoustics Mechanics

P 1.7.3Wavelength and velocity of sound

P 1.7.3.3 Determining the velocity ofsound in the air as a functionof the temperature

P 1.7.3.4 Determining the velocity ofsound in gases

Determining the velocity of sound in the air as a function of the temperature (P 1.7.3.3)

Sound waves demonstrate only slight dispersion, i.e. group andphase velocities demonstrate close agreement for propagation ingases. Therefore, we can determine the velocity of sound c assimply the propagation speed of a sonic pulse. In ideal gases, wecan say

c = p · k

where k = Cpö r CV

p: pressure, r: density, k: adiabatic coefficientCp, CV: specific heat capacities

The first experiment measures the velocity of sound in the air asa function of the temperature P and compares it with the linearfunction resulting from the temperature-dependency of pressureand density

c(P) = c(0) · (1 + a · P) where a = 1

2 273 K

The value c(0) determined using a best-fit straight line and theliterature values p(0) and r(0) are used to determine the adia-batic coefficient k of air according to the formula

k = c(0)2 · r(0)

p(0)

The second experiment determines the velocity of sound c incarbon dioxide and in the inert gases helium and neon. The eval-uation demonstrates that the great differences in the velocities ofsound of gases are essentially due to the different densities ofthe gases. The differences in the adiabatic coefficients of thegases are comparatively small.

P1.

7.3.

3

P1.

7.3.

4

54


413 60 Apparatus for sound and velocity 1 1

516 249 Stand for coils and tubes 1 1

587 08 Broad-band speaker 1 1

586 26 Multi-purpose microphone 1 1

521 25 Transformer 2....12 V 1

576 89 Battery case 2 x 4.5 volts 1 1

503 11 Set of 20 batteries 1.5 V (type MONO) 1 1


524 200 CASSY Lab 1 1

524 045 Temperature box 1

524 034 Timer box 1

666 193 Temperature sensor, NiCr-Ni 1

460 97 Scaled metal rail, 0.5 m 1 1

30011 Saddle base 2 2

660 999 Minican gas can, carbon dioxide 1

660 984 Minican gas can, helium 1

660 985 Minican gas can, neon 1

660 980 Fine regulating valve for Minican gas cans 1

667194 Silicone tubing, i.d. 7 x 1.5 mm, 1 m 1

500 422 Connection lead, blue, 50 cm 1 1



additionally required:1 PC with Windows 95/NT or higher 1 1

1

Determining the velocity of sound in solid bodies (P 1.7.3.5)

P 1.7.3

P 1.7.3.5 Determining the velocity ofsound in solid bodies

Wavelength and velocity of sound

In solid bodies, the velocity of sound is determined by the modu-lus of elasticity E and the density r. For the velocity of sound ina long rod, we can say

c = öEr

In the case of solids, measurement of the velocity of sound thusyields a simple method for determining the modulus of elasticity.

The object of this experiment is to determine the velocity ofsound in aluminum, copper, brass and steel rods. This measure-ment exploits the multiple reflections of a brief sound pulse at therod ends. The pulse is generated by striking the top end of therod with a hammer, and initially travels to the bottom. The pulseis reflected several times in succession at the two ends of therod, whereby the pulses arriving at one end are delayed with re-spect to each other by the time Dt required to travel out and back.The velocity of sound is thus

c = 2s

Dts: length of rod

To record the pulses, the bottom end of the rod rests on a piezo-electric element which converts the compressive oscillations ofthe sound pulse into electrical oscillations. These values arerecorded using the CASSY system for computer-assistedmeasured-value recording. CASSY can be used here either as astorage oscilloscope or as a high-resolution stopclock which isstarted and stopped by the edges of the voltage pulses.

Mechanics Acoustics

55

P1.

7.3.

5


413 65 Set of 3 metal rods, 1.5 cm 1

300 46 Stand rod, 150 cm 1

587 25 Rochelle salt crystal 1


524 200 CASSY Lab 1


501 38 Connecting lead 200 cm, black, Ø 2.5 mm2 2


Acoustics Mechanics

P 1.7.4Reflection of ultrasonic waves

P 1.7.4.1 Reflection of flat ultrasonicwaves at a plane surface

P 1.7.4.2 Principle of an echo sounder

Reflection of flat ultrasonic waves at a plane surface (P 1.7.4.1)

When investigating ultrasonic waves, identical, and thus inter-changeable transducers are used as transmitters and receivers.The ultrasonic waves are generated by the mechanical oscilla-tions of a piezoelectric body in the transducer. By the sametoken, ultrasonic waves excite mechanical oscillations in thepiezoelectric body.

The aim of the first experiment is to confirm the law of reflection“angle of incidence = angle of reflection” for ultrasonic waves. Inthis setup, an ultrasonic transducer as a point-type source is setup in the focal point of a concave reflector, so that flat ultrasonicwaves are generated. The flat wave strikes a plane surface at anangle of incidence a and is reflected there. The reflected inten-sity is measured at different angles using a second transducer.The direction of the maximum reflected intensity is defined as theangle of reflection b.

The second experiment utilizes the principle of an echo sounderto determine the velocity of sound in the air, as well as to deter-mine distances. An echo sounder emits pulsed ultrasonic signalsand measures the time at which the signal reflected at the

56

boundary surface is received. For the sake of simplicity, thetransmitter and receiver are set up as nearly as possible in thesame place. When the velocity of sound c is known, the time dif-ference t between transmission and reception can be used in therelationship

c = 2s

t

to determine the distance s to the reflector or, when the distanceis known, the velocity of sound.Principle of an echo sounder (P 1.7.4.2)

P1.

7.4.

1

P1.

7.4.

2


416 000 Ultrasonic transducer 40 kHz 2 2

416 014 Generator 40 kHz 1 1

416 013 AC amplifier 1 1

389 241 Concave mirror, dia. 39 cm 1

416 020 Sensor holder for concave mirror 1

587 66 Reflection plate 50 x 50 cm 1 1


575 24 Screened cable BNC/4 mm 1 2

460 43 Small optical bench 2




30011 Saddle base 3




301 27 Stand rod, 50 cm, 10 mm dia. 1

311 02 Metal scale, 1 m long 1


361 03 Spirit level 1

Diffraction of ultrasonic waves at a double slit, multiple slit and grating (P 1.7.5.4)

P 1.7.5

P 1.7.5.1 Beating of ultrasonic waves

P 1.7.5.2 Interference of two ultrasonicbeams

P 1.7.5.3 Diffraction of ultrasonic wavesat a single slit

P 1.7.5.4 Diffraction of ultrasonic wavesat a double slit, multiple slitand grating

Interference of ultrasonic waves

Experiments on the interference of waves can be carried out in acomprehensible manner using ultrasonic waves, as the diffrac-tion objects are visible with the naked eye. In addition, it is notdifficult to generate coherent sound beams.

In the first experiment, beating of ultrasonic waves is investigatedusing two transducers which are operated using slightly differentfrequencies f1 and f2. The signal resulting from the superposingof the two individual signals is interpreted as an oscillation withthe periodically varying amplitude

A(t) “ cos(ö · (f2 – f1) · t).

The beat frequency fS determined from the period TS betweentwo beat nodes and compared with the difference f2 – f1.

In the second experiment, two identical ultrasonic transducersare operated by a single generator. These transducers generatetwo coherent ultrasonic beams which interfere with each other.The interference pattern corresponds to the diffraction of flatwaves at a double slit when the two transducers are operated inphase. The measured intensity is thus greatest at the diffractionangles a where

sin a = n · l

where n = 0, ±1, ±2, ...d

l: wavelength, d: spacing of ultrasonic transducers

The last two experiments use an ultrasonic transducer as apoint-shaped source in the focal point of a concave reflector. Theflat ultrasonic waves generated in this manner are diffracted at asingle slit, a double slit and a multiple slit. An ultrasonic trans-ducer and the slit are mounted together on the turntable for com-puter-assisted recording of the diffraction figures. This configu-ration measures the diffraction at a single slit for various slitwidths b and the diffraction at multiple slits and gratings fordifferent numbers of slits N.

Mechanics Acoustics

57

P1.

7.5.

3

P1.

7.5.

2

P1.

7.5.

1

P1.

7.5.

4


416 000 Ultrasonic transducer 40 kHz 3 3 2 2

416 013 AC amplifier 1 1 1 1

416 014 Generator 40 kHz 2 1 1 1

416 020 Sensor holder for concave mirror 1 1

416 021 Rack for diffraction objects 1 1

416 030 Slit and grating for ultrasonic experiments 1 1

311 902 Rotating platform with motor drive 1 1 1

389 241 Concave mirror, dia. 39 cm 1 1

575 211 Two-channel oscilloscope 303 1

575 24 Screened cable BNC/4 mm 1

524 010 Sensor CASSY 1 1 1

524 031 Current supply box 1 1 1

524 200 CASSY Lab 1 1 1

DC power supply, 0 ... 16 V/5 A 1 1 1

501 031 Connecting lead, 8 m, screened 1 1 1





300 41 Stand rod, 25 cm 1 1 1

300 42 Stand rod, 47 cm 1 1 1


500 424 Connection lead, 50 cm, blue 1 1 1

501 46 Pair of cables, 100 cm, red and blue 2 2 2

additionally required: 1 PC with Windows 95/98/NT 1 1 1

521 545

Acoustics Mechanics

P 1.7.6Acoustic Doppler effect

P 1.7.6.1 Investigating the Doppler effectwith ultrasonic waves

Investigating the Doppler effect with ultrasonic waves (P 1.7.6.1)

The change in the observed frequency for a relative motion of thetransmitter and receiver with respect to the propagation mediumis called the acoustic Doppler effect. If the transmitter with thefrequency f0 moves at a velocity v relative to a receiver at rest, thereceiver measures the frequency

f =f0 where c: velocity of sound

1 – vc

If, on the other hand, the receiver moves at a velocity v relative toa transmitter at rest, we can say

f = f0 · (1 + v )c

The change in the frequeny f – f0 is proportional to the frequen-cy f0. Investigation of the acoustic Doppler effect on ultrasonicwaves thus suggests itself.

In this experiment, two identical ultrasonic transducers are usedas the transmitter and the receiver, and differ only in theirconnection. One transducer is mounted on a measuring trolleywith electric drive, while the other transducer is at rest on the labbench. The frequency of the received signal is measured using ahigh-resolution digital counter. To determine the speed of thetransducer in motion, the time Wt which the measuring trolleyrequires to traverse the measuring distance is measured using astopclock.

58

P1.

7.6.

1


416 000 Ultrasonic transducer 40 kHz 2

416 013 AC amplifier 1

416 014 Generator 40 kHz 1

501 031 Connecting lead, 8 m, screened 1




313 07 Stopclock I, 30s/15min 1

337 07 Trolley with electric drive 1

Battery 1.5 V (type mignon cell) 2

460 81 Precision metal rail, 1 m 2

460 85 Rail connector 1

460 88 Pair of feet 1

30011 Saddle base 2




301 10 Clamp with ring 1

501 644 Set of 6 two-way adapters, black 1


The propagation of sound with the sound source and the observer at rest (left), with the sound source moving (middle), and with the observer moving (right)

20066264

Fourier analysis of sounds (P 1.7.7.4)

P 1.7.7

P 1.7.7.1 Investigation of fast Fouriertransforms: simulation of Fourier analysisand synthesis

P 1.7.7.2 Fourier analysis of the periodicsignals of a function generator

P 1.7.7.3 Fourier analysis of an electricaloscillator circuit

P 1.7.7.4 Fourier analysis of sounds

Fourier analysis

Fourier analysis and synthesis of sound waves are importanttools in acoustics. Thus, for example, knowing the harmonics ofa sound is important for artificial generation of sounds or speech.

The first two experiments investigate Fourier transforms of peri-odic signals which are either numerically simulated or generatedusing a function generator.

In the third experiment, the frequency spectrum of coupled elec-tric oscillator circuits is compared with the spectrum of anuncoupled oscillator circuit. The Fourier transform of the uncou-pled, damped oscillation is a Lorentz curve

L(f) = L0 · H2

,

(f – f0)2 + H2

in which the width increases with the ohmic resistance of theoscillator circuit. The Fourier-transformed signal of the coupledoscillator circuits shows the split into two distributions lying sym-metrically around the uncoupled signal, with their spacingdepending on the coupling of the oscillator circuits.

The aim of the final experiment is to conduct Fourier analysis ofsounds having different tone colors and pitches. As examples,the vowels of the human voice and the sounds of musical instru-ments are analyzed. The various vowels of a language differmainly in the amplitudes of the harmonics. The fundamentalfrequency f0 depends on the pitch of the voice. This is approx.200 Hz for high-pitched voices and approx. 80 Hz for low-pitchedvoices. The vocal tone color is determined by variations in theexcitation of the harmonics. The audible tones of musical instru-ments are also determined by the excitation of harmonics.

Mechanics Acoustics

59

P1.

7.7.

3

P1.

7.7.

2

P1.

7.7.

1

P1.

7.7.

4


576 74 Plug-in board A4 1

57719 STE resistor 1 V, 2 W 1

577 20 STE resistor 10 V, 2 W 1

577 21 STE resistor 5.1 V, 2 W 1



578 15 STE capacitor 1 µF, 100 V 2

579 10 STE key switch n.o., single pole 1

562 14 Coil with 500 turns 2

586 26 Multi-purpose microphone 1

522 56 Function generator P, 100 mHz to 100 kHz 1


524 200 CASSY Lab 1 1 1 1

30011 Saddle base 1


additionally recommended: 1 PC with Windows 95/NT or higher 1 1 1 1

Fourier analysis of an electrical oscillator

circuit (P 1.7.7.3)

Aerodynamics and hydrodynamics Mechanics

P 1.8.1Barometry

P 1.8.1.1 Definition of pressure

P 1.8.1.2 Hydrostatic pressure as a non-directional quantity

Definition of pressure (P 1.8.1.1)

In a gas or liquid at rest, the same pressure applies at all points:

p = F .A

It is measurable as the distributed force F acting perpendicular-ly on an area A.

The first experiment aims to illustrate the definition of pressure asthe ratio of force and area by experimental means using two gassyringes of different diameters which are connected via a T-sec-tion and a hand pump. The pressure generated by the handpump is the same in both gas syringes. Thus, we can say for theforces F1 and F2 acting on the gas syringes

F1=

A1

F2 A2

A1, A2: cross-section areas

The second experiment explores the hydrostatic pressure

p = U · g · hU: density, g: gravitational acceleration

in a water column subject to gravity. The pressure is measuredas a function of the immersion depth h using a liquid pressuregauge. The displayed pressure remains constant when the gaugeis turned in all directions at a constant depth. The pressure isthus a non-directional quantity.

60

P1.

8.1.

1

P1.

8.1.

2


361 30 Set of 2 gas syringes with holder 1


590 24 Set of 10 load pieces, 100 g each 1



1


Pressure-gauge reading as a

function of the immersion depth

(experiment P 1.8.1.2)Hydrostatic pressure as a non-directional quantity (P 1.8.1.2)

361 57 Liquid pressure gauge with U-tube manometer

361 575 I Glass vessel for liquid pressure gauge I I 1

Confirming Archimedes’ principle (P 1.8.2.1)

P 1.8.2

P 1.8.2.1 Confirming Archimedes’ principle

P 1.8.2.2 Measuring the buoyancy as afunction of the immersiondepth

Buoyancy

Archimedes’ principle states that the buoyancy force F acting onany immersed body corresponds to the weight G of the dis-placed liquid.

The first experiment verifies Archimedes’ principle. In this exper-iment, a hollow cylinder and a solid cylinder which fits snuglyinside it are suspended one beneath the other on the beam of abalance. The deflection of the balance is compensated to zero.When the solid cylinder is immersed in a liquid, the balanceshows the reduction in weight due to the buoyancy of the bodyin the liquid. When the same liquid is filled in the hollow cylinderthe deflection of the balance is once again compensated to zero,as the weight of the filled liquid compensates the buoyancy.

In the second experiment, the solid cylinder is immersed invarious liquids to the depth h and the weight

G = r · g · A · hr: density, g: gravitational acceleration, A: cross-section

of the displaced liquid is measured as the buoyancy F using aprecision dynamometer. The experiment confirms the relation-ship

F “ r

As long as the immersion depth is less than the height of thecylinder, we can say:

F “ h

At greater immersion depths the buoyancy remains constant.

Mechanics Aerodynamics and hydrodynamics

61

P1.

8.2.

1

P1.

8.2.

2


Archimedes cylinder 1 1

315 01 Hydrostatic precision balance, 200 g 1

315 31 Set of weights, 10 mg – 200 g 1



664111 Beaker, 100 ml, ts, hard glass 1

664113 Beaker, 250 ml, ts, hard glass 1 1

Glycerine, 99 %, 250 ml 1 1

Ethanol, completely denaturated, 1 l 1 1

362 02

672 1210671 9720


P 1.8.3Viscosity

P 1.8.3.1 Assembling a falling-ballviscosimeter to determine theviscosity of viscous fluids

P 1.8.3.2 Falling-ball viscosimeter: measuring the viscosity ofsugar solutions as a function ofthe concentration

P 1.8.3.3 Falling-ball viscosimeter: measuring the viscosity ofNewtonian fluids as a functionof the temperature

Falling-ball viscosimeter after Höppner (P 1.8.3.2)

The falling-ball viscometer is used to determine the viscosity ofliquids by measuring the falling time of a ball. The substanceunder investigation is filled in the vertical tube of the viscosi-meter, in which a ball falls through a calibrated distance of 100mm. The resulting falling time t is a measure of the dynamic vis-cosity h of the liquid according to the equation

J = K · (U1 – U2) · t

U2: density of the liquid under study,

whereby the constant K and the ball density U1 may be read fromthe test certificate of the viscosimeter.

The object of the first experiment is to set up a falling-ball visco-simeter and to study this measuring method, using the viscosityof glycerine as an example.

The second experiment investigates the relationship betweenviscosity and concentration using concentrated sugar solutionsat room temperature. In the third experiment, the temperature-regulation chamber of the viscosimeter is connected to a circu-lation thermostat to measure the dependency of the viscosity ofa Newtonian fluid (e. g. olive oil) on the temperature.

62

P1.

8.3.

2

P1.

8.3.

1

P1.

8.3.

3


379 001 Guinea-and-feather apparatus 1


200 67288 Steel ball, 16 mm dia., for 371 05 1

504 52 Morse key 1

Low-voltage power supply 1

Counter P 1

510 48 Pair of magnets, cylindrical 1


300 44 Stand rod, 100 cm 1



301 11 Clamp with jaw clamp 1

Glycerine, 99 %, 250 ml 6


500 422 Connection lead, 50 cm, blue 4

590 08 Measuring cylinder, 100 ml, plastic 1*

311 54 Precision vernier callipers 1*

667 793 Precision electronic balance LS 200, 200 g : 0.1 g 1*

665 906 Falling-ball viscosimeter C 1 1

313 07 Stopclock I, 30s/15min 1 1

666 768 Controlled-temperature recirculation unit, 30 ... 100°C 1

667194 Silicone tubing, int. dia. 7 x 1.5 mm, 1 m 2


521 230

575 451

311 77 I Steel tape measure, 2 m I 1 I Ii I I I

672 1210

Measuring the surface tension using the tear-away method (P 1.8.4.1)

P 1.8.4

P 1.8.4.1 Measuring the surface tensionusing the tear-away method

Surface tension

To determine the surface tension D of a liquid, a metal ring is sus-pended horizontally from a precision dynamometer. The metalring is completely immersed in the liquid, so that the entire sur-face is wetted. The ring is then slowly pulled out of the liquid,drawing a thin sheet of liquid behind it. The liquid sheet tearswhen the tensile force exceeds a limit value

F = s · 4S · RR: edge radius

This experiment determines the surface tension of water andethanol. It is shown that water has a particularly high surface ten-sion in comparison to other liquids (literature value for water:0.073 Nm-1, for ethanol: 0.022 Nm-1).


63

P1.

8.4.

1


36746 Apparatus for measuring surface tension 1

664175 Crystallization dish, 95 mm dia., height = 55 mm 1


311 52 Vernier callipers, plastic 1



1

301 08 Clamp with hook 1

300 43 Stand rod, 75 cm

671 9740 I Ethanol, fully denaturated, 250 ml I 1675 3400 I Water, pure, 1 l I 1


P 1.8.5Introductory experiments inaerodynamics

P 1.8.5.1 Static pressure in a reducedcross-section – measuring the pressure withthe precision manometer

P 1.8.5.2 Determining the volume flowwith a Venturi tube – measuring the pressure withthe precision manometer

P 1.8.5.3 Determining the wind speedwith a pressure head sensor –measuring the pressure withthe precision manometer

P 1.8.5.4 Static pressure in a reducedcross-section – measuring the pressure with apressure sensor and CASSY

P 1.8.5.5 Determining the volume flowwith a Venturi tube – measuring the pressure with apressure sensor and CASSY

P 1.8.5.6 Determining the wind speedwith a pressure head sensor –measuring the pressure with apressure sensor and CASSY

Determining the volume flow with a Venturi tube – measuring the pressure with the precision manometer (P 1.8.5.2)

The study of aerodynamics relies on describing the flow of airthrough a tube using the continuity equation and the Bernoulliequation. These state that regardless of the cross-section A ofthe tube, the volume flow

V.

= v · Av: flow speed

and the total pressure

p0 = p + pS where pS = r

· v 2

2

p: static pressure, pS: dynamic pressure, r: density of air

remain constant as long as the flow speed remains below thespeed of sound.

In order to verify these two equations, the static pressure in aVenturi tube is measured for different cross-sections in the firstexperiment. The static pressure decreases in the reduced cross-section, as the flow speed increases here.

The second experiment uses the Venturi tube to measure thevolume flow. Using the pressure difference Dp = p2 - p1 betweentwo points with known cross-sections A1 and A2, we obtain

2 · Dp · A22v1 · A1 = ßr · (A2

2 – A21)

The third experiment aims to determine flow speeds. Here, dy-namic pressure (also called the “pressure head”) is measuredusing the pressure head sensor after Prandtl as the differencebetween the total pressure and the static pressure, and this valueis used to calculate the speed at a known density U.

64

P1.

8.5.

4–

5

P1.

8.5.

3

P1.

8.5.

1–2

P1.

8.5.

6


373 04 Suction and pressure fan 1 1 1 1

373 09 Venturi tube with 7 gauge points 1 1

373 10 Precision manometer 1 1

373 13 Pressure head 1 1


1 1

524 200 CASSY Lab 1 1



300 41 Stand rod, 25 cm 1 1

300 42 Stand rod, 47 cm 1 1


additionally recommended: 1 PC with Windows 95/NT or higher 1 1

Note: In the first three experiments, the precision manometer isused to measure pressures. In addition to a pressure scale, it isprovided with a further scale which indicates the flow speeddirectly when measuring with the pressure head sensor. In thelast three experiments the pressure is measured with a pressuresensor and recorded and evaluated using the computer-assistedmeasuring system CASSY.

524 066 Pressure sensor S, ± 70 hPa

Drag coefficient cW: relationship between air resistance and body shape - measuring the pressure with the precision manometer (P 1.8.6.2)

P 1.8.6

P 1.8.6.1 Air resistance as a function ofwind speed – measuring pressure with theprecision manometer

P 1.8.6.2 Drag coefficient cW: relationship between air resis-tance and body shape – measuring the pressure withthe precision manometer

P 1.8.6.3 Pressure curve on an airfoil profile – measuring the pressure with theprecision manometer

P 1.8.6.4 Air resistance as a function ofwind speed – measuring the pressure withthe pressure sensor and CASSY

P 1.8.6.5 Drag coefficient cW: relationship between air resistance and body shape – measuring the pressure withthe pressure sensor and CASSY

P 1.8.6.6 Pressure curve on an airfoil profile – measuring the pressure withthe pressure sensor andCASSY

Measuring air resistance

A flow of air exercises a force FW on a body in the flow which isparallel to the direction of the flow; this force is called the airresistance. This force depends on the flow speed v, the cross-section A of the body perpendicular to the flow direction and theshape of the body. The influence of the body shape is describedusing the so-called drag coefficient cw, whereby the air resis-tance is determined as:

Fw = cw · U

· v2 · A2

The first experiment examines the relationship between the airresistance and the flow speed using a circular disk, while thesecond experiment determines the drag coefficient cw for variousflow bodies with equal cross-sections. In both cases, the flowspeed is measured using a pressure head sensor and the airresistance with a dynamometer.

The aim of the third experiment is to measure the static pressurep at various points on the underside of an airfoil profile. Themeasured curve not only illustrates the air resistance, but alsoexplains the lift acting on the airfoil.

Note: In the first three experiments, the precision manometer isused to measure pressures. In addition to a pressure scale, it isprovided with a further scale which indicates the flow speeddirectly when measuring with the pressure head sensor. In thelast three experiments the pressure is measured with a pressuresensor and recorded and evaluated using the computer-assistedmeasuring system CASSY.


65

P1.

8.6.

4–

5

P1.

8.6.

3

P1.

8.6.

1–2

P1.

8.6.

6


373 04 Suction and pressure fan 1 1 1 1

373 06 Open aerodynamics working section 1 1 1 1

373 071 Aerodynamics accessories 1 1 1

373 075 Measurement trolley for wind tunnel 1 1

373 14 Sector dynamometer 1 1

373 13 Pressure head 1 1 1

373 10 Precision manometer 1 1

373 70 Air foil model 1 1


1 1

524 200 CASSY Lab 1 1

300 02 Stand base, V-shape, 20 cm 1 2 1 1


300 42 Stand rod, 47 cm 1 1 1


additionally recommended:1 PC with Windows 95/NT or higher 1 1



P 1.8.7Measurements in a wind tunnel

P 1.8.7.1 Recording the airfoil profilepolars in a wind tunnel

P 1.8.7.2 Measuring students’ own air-foils and panels in the windtunnel

P 1.8.7.3 Verifying the Bernoulli equation –measuring with the precisionmanometer

P 1.8.7.4 Verifying the Bernoulli equation –measuring with the pressuresensor and CASSY

Recording the airfoil profile polars in a wind tunnel (P 1.8.7.1)

The wind tunnel provides a measuring configuration for quantita-tive experiments on aerodynamics that ensures an airflow whichhas a constant speed distribution with respect to both time andspace. Among other applications, it is ideal for measurements onthe physics of flight.

In the first experiment, the air resistance fW and the lift FA of anairfoil are measured as a function of the angle of attack a of theairfoil against the direction of flow. In a polar diagram, FW isgraphed as a function of FA with the angle of attack a as theparameter. From this polar diagram, we can read e. g. the opti-mum angle of attack.

In the second experiment, the students perform comparablemeasurements on airfoils of their own design. The aim is to deter-mine what form an airfoil must have to obtain the smallest possi-ble quotient FW/FA at a given angle of attack a.

The last two experiments verify the Bernoulli equation. The differ-ence between the total pressure and the static pressure is meas-ured as a function of the cross-section, whereby the cross-sec-tion of the wind tunnel is gradually reduced by means of a built-in ramp. If we assume that the continuity equation applies, thecross-section A provides a measure of the flow speed v due to

v = v0 · A0

A

v0: flow speed at cross-section A0

The experiment verifies the following relationship, which followsfrom the Bernoulli equation:

Dp “ 1

A2

66

P1.

8.7.

3

P1.

8.7.

1-2

P1.

8.7.

4


373 12 Wind tunnel 1 1 1

373 04 Suction and pressure fan 1 1 1

373 075 Measurement trolley for wind tunnel 1 1 1

373 08 Aerodynamics accessories 2 1

373 14 Sector dynamometer 1

373 13 Pressure head 1 1

373 10 Precision manometer 1


1

524 200 CASSY Lab 1


30011 Saddle base 1



Table of contents Heat

68

P2 HeatP 2.1 Thermal expansionP 2.1.1 Thermal expansion of solid bodies 69

P 2.1.2 Thermal expansion of liquids 70

P 2.1.3 Thermal anomaly of water 71

P 2.2 Heat transferP 2.2.1 Thermal conduction 72

P 2.2.2 Solar collector 73

P 2.3 Heat as a form of energyP 2.3.1 Mixing temperatures 74

P 2.3.2 Heat capacities 75

P 2.3.3 Conversion of mechanical energy into heat energy 76

P 2.3.4 Conversion of electrical energy into heat energy 77

P 2.4 Phase transitionsP 2.4.1 Melting heat and evaporation heat 78

P 2.4.2 Measuring vapor pressure 79

P 2.4.3 Critical temperature 80

P 2.5 Kinetic theory of gasesP 2.5.1 Brownian motion of molecules 81

P 2.5.2 Laws of gases 82

P 2.5.3 Specific heat of gases 83

P 2.6 Thermodynamic cycleP 2.6.1 Hot-air motor:

qualitative experiments 84–85

P 2.6.2 Hot-air motor: quantitative experiments 86–87

P 2.6.3 Heat pump 88

P 2.1.1

P 2.1.1.1 Thermal expansion of solid bodies – measuring using STM equipment

P 2.1.1.2 Thermal expansion of solid bodies – measuring using the expansionapparatus

P 2.1.1.3 Measuring the longitudinalexpansion of solid bodies as afunction of temperature

Thermal expansion of solid bodies

Heat Thermal expansion

69

Measuring the longitudinal expansion of solid bodies as a function of temperature (P 2.1.1.3)

The relationship between the length s and the temperature P of aliquid is approximately linear:

s = s0 · (1 + a · P)s0: length at 0°C, P: temperature in °C

The linear expansion coefficient a is determined by the materialof the solid body. We can conduct measurements on this topicusing e.g. thin tubes through which hot water or steam flows.

In the first experiment, steam is channeled through different tubesamples. The thermal expansion is measured in a simple ar-rangement, and the dependency on the material is demonstrated.

The second experiment measures the increase in length ofvarious tube samples between room temperature and steam tem-perature using the expansion apparatus. The effective length s0of each tube can be defined as 200, 400 or 600 mm.

In the final experiment, a circulation thermostat is used to heatthe water, which flows through various tube samples. The expan-sion apparatus measures the change in the lengths of the tubesas a function of the temperature P (cf. diagram).

P2.

1.1.

3

P2.

1.1.

2

P2.

1.1.

1


381 331 Pointer for linear expansion 1

381 332 Al-tube, l = 22 cm, d = 8 mm 1

381 333 Fe-tube, l = 44 cm, d = 8 mm 1

340 82 Dual scale 1

314 04 Support clip, for plugging in 2

301 21 Stand base MF 2




301 09 Bosshead S 2

666 555 Universal Bunsen clamp S 1

664 248 Erlenmeyer flask, 50 ml 1

200 69304 Rubber stopper with hole 1

665 226 Connector, straight, 6 .... 8 mm dia. 1

667194 Tubing, silicone, int. dia. 7 mm/1.5 mm, 1 m 1 1 2

664183 Petri dish, 100 x 20 mm 1

311 78 Tape measure, 1.5 m/1 mm 1

303 22 Alcohol burner, metal 1

381 341 Expansion apparatus 1 1

361 15 Dial gauge 1 1

381 36 Holder for dial gauge 1 1

382 34 Thermometer, -10 to +110 °C 1 1

303 28 Steam generator, 550 W/230 V 1

664185 Petri dish, 150 x 25 mm 1

666 768 Circulation thermostat 30 ... 100 °C 1

Thermal expansion of solid bodies – measuring using the expansion apparatus(P 2.1.1.2)

Thermal expansion Heat

P 2.1.2Thermal expansionof liquids

P 2.1.2.1 Determining the volumetricexpansion coefficient of liquids

Determining the volumetric expansion coefficient of liquids (P 2.1.2.1 b)

In general, liquids expands more than solids when heated. Therelationship between the Volume V and the temperature P of aliquid is approximately linear here:

V = V0 · (1 + g · P)

V0: volume at 0°C, P: temperature in °C

When determining the volumetric expansion coefficient g, it mustbe remembered that the vessel in which the liquid is heated alsoexpands.

In this experiment, the volumetric expansion coefficients of waterand methanol are determined using a volume dilatometer madeof glass. An attached riser tube with a known cross-section isused to measure the change in volume. i. e. the change in volumeis determined from the rise height of the liquid.

P2.

1.2.

1 (a

)

P2.

1.2.

1 (b

)

70


382 15 Dilatometer, 50 ml 1 1

382 34 Thermometer, -10° to + 110 °C 1

666 193 Temperature sensor NiCr-Ni 1

666 190 Digital thermometer with 1 input 1

315 05 School and laboratory balance 311, 311 g 1 1

666 767 Hot plate, 150 mm dia., 1500 W 1 1

664104 Beaker, 400 ml, ss., hard glass 1 1


300 42 Stand rod, 47 cm 1 1


666 555 Universal clamp, 0...80 mm dia. 2 2

Ethanol, fully denaturated, 1 l 1 1671 9720

Investigating the density maximum of water (P 2.1.3.1 b)

P 2.1.3

P 2.1.3.1 Investigating the density maxi-mum of water

Thermal anomaly of water

When heated from a starting temperature of 0 °C, water demon-strates a critical anomaly: it has a negative volumetric expansioncoefficient up to 4 °C, i.e. it contracts when heated. After reachingzero at 4 °C, the volumetric expansion coefficient takes on apositive value. As the density corresponds to the reciprocal ofthe volume of a quantity of matter, water has a density maximumat 4 °C.

This experiment verifies the density maximum of water by meas-uring the expansion in a vessel with riser tube. Starting at roomtemperature, the complete setup is cooled in a constantly stirredwater bath to about 1 °C, or alternatively allowed to graduallyreach the ambient temperature after cooling in an ice chest orrefrigerator. The rise height h is measured as a function of thetemperature P. As the change in volume is very slight in relationto the total volume V0, we obtain the density

r(P) = r(0 °C) · (1 – A

· h(P) )V0

A: cross-section of riser tube

P2.

1.3.

1 (b

)

P2.

1.3.

1 (a

)

Heat Thermal expansion

71


667 505 Device for demonstrating the anomaly of water 1 1

382 36 Thermometer, -10° to + 40 °C 1



666 845 Magnetic stirrer, 0...2000 rpm 1 1

664195 Glass tank, 300 x 200 x 150 mm 1 1

665 008 Funnel, 50 mm dia., plastic 1 1

307 66 Rubber tubing, i. d. 8 mm 1 1


300 42 Stand rod, 47 cm 1 1


301 10 Clamp with ring 1 1

666 555 Universal Bunsen clamp S 1 1

Heat transfer Heat

P 2.2.1Thermal conduction

P 2.2.1.1 Determining the heat conduc-tivity of building materials usingthe single-plate method

P 2.2.1.2 Determining the heat conduc-tivity of building materials withthe aid of a reference materialof known thermal conductivity

P 2.2.1.3 Damping of temperature varia-tions using multi-layer walls

Determining the heat conductivity of building materials with the aid of a reference material of known thermal conductivity (P 2.2.1.2)

In the equilibrium state, the heat flow through a plate with thecross-section area A and the thickness d depends on the tem-perature difference P2 – P1 between the front and rear sides andon the thermal conductivity l of the plate material:

DQ= l · A ·

P2 – P1

Dt d

The object of the first two experiments is to determine the ther-mal conductivity of building materials. In these experiments,sheets of building materials are placed in the heating chamberand their front surfaces are heated. The temperatures P1 and P2are measured using measuring sensors. The heat flow is deter-mined either from the electrical power of the hot plate or bymeasuring the temperature using a reference material withknown thermal conductivity l0 which is pressed against the sheetof the respective building material from behind.

P2.

2.1.

2

P2.

2.1.

1

P2.

2.1.

3

72


389 29 Calorimetric chamber 1 1 1

389 30 Set of building materials for calorimetric chamber 1 1 1

521 25 Transformer 2....12 V 1 1 1

666 198 Digital temperature controller and indicator 1

666 190 Digital thermometer with 1 input 1*

666 209 Digital thermometer with 4 inputs 1 1

666 193 Temperature sensor NiCr-Ni 2 3 3

Ammeter, AC, I < 2 A, e.g.531 100 Multimeter METRAmax 2 1

Voltmeter, AC, U < 12 V, e.g.531 100 Multimeter METRAmax 2 1

313 17 Stopclock II, 60 s/30 min 1 1

450 64 Halogen lamp housing, 12 V, 50/100 W 1

450 63 Halogen lamp, 12 V/100 W 1

30011 Saddle base 1

501 33 Connecting lead, 100 cm, black, Ø 2,5 mm2 3 2 2


* alternatively: digital thermometer with 4 inputs (666 20

Temperature variations in multi-layer walls (P 2.2.1.3)

The final experiment demonstrates the damping of temperaturevariations by means of two-layer walls. The temperature changesbetween day and night are simulated by repeatedly switching alamp directed at the outside surface of the wall on and off. Thisproduces a temperature “wave” which penetrates the wall; thewall in turn damps the amplitude of this wave. This experimentmeasures the temperatures PA on the outer surface, PZ betweenthe two layers and PI on the inside as a function of time.

9)

Determining the efficiency of a solar collector as a function of the throughput volume of water (P 2.2.2.1)

P 2.2.2

P 2.2.2.1 Determining the efficiency of asolar collector as a function ofthe throughput volume of water

P 2.2.2.2 Determining the efficiency of asolar collector as a function ofthe thermal insulation

Solar collector

A solar collector absorbs radiant energy to heat the water flowingthrough it. When the collector is warmer than its surroundings, itloses heat to its surroundings through radiation, convection andheat conductivity. These losses reduce the efficiency

J =DQ

DE

i. e. the ratio of the emitted heat quantity DQ to the absorbed radi-ant energy DE.

In both experiments, the heat quantity DQ emitted per unit of timeis determined from the increase in the temperature of the waterflowing through the apparatus, and the radiant energy absorbedper unit of time is estimated on the basis of the power of the lampand its distance from the absorber. The throughput volume of thewater and the heat insulation of the solar collector are varied inthe course of the experiment.

P2.

2.2.

1-2

Heat Heat transfer

73


389 50 Solar collector 1

579 22 STE miniature pump 1

450 70 Flood light lamp, 1000 W 1

521 35 Variable extra-low voltage transformer S 1

666 209 Digital thermometer with 4 inputs 1



313 17 Stopclock II, 60 s/30 min 1






666 555 Universal clamp, 0...80 mm dia. 1


307 70 Plastic tubing, PVC, i. d. 8 mm 1


Heat quantity Heat

P 2.3.1Mixing temperatures

P 2.3.1.1 Measuring the temperature of amixture of hot and cold water

Measuring the temperature of a mixture of hot and cold water (P 2.3.1.1 a)

When cold water with the temperature P1 is mixed with warm orhot water having the temperature P2, an exchange of heat takesplace until all the water reaches the same temperature. If no heatis lost to the surroundings, we can formulate the following for themixing temperature:

Pm = m1 P1 +

m2 P2m1 + m2 m1 + m2

m1, m2: mass of cold and warm water respectively

Thus the mixing temperature Pm is equivalent to a weighted meanvalue of the two temperatures P1 and P2.

The use of the Dewar flask in this experiment essentially preventsthe loss of heat to the surroundings. This vessel has a doublewall; the intermediate space is evacuated and the interior surfaceis mirrored. The water is stirred thoroughly to ensure a completeexchange of heat. This experiment measures the mixing tem-perature Pm for different values for P1, P2, m1, and m2.

P2.

3.1.

1 (a

)

P2.

3.1.

1 (b

)

74


386 48 Dewar vessel 1 1

384161 Lid for Dewar vessel 1 1

382 34 Thermometer, -10° to + 110 °C 1



315 23 School and laboratory balance 610 tare, 610 g 1 1

313 07 Stopclock I, 30 s/15 min 1 1

666 767 Hot plate, 150 mm dia., 1500 W 1 1

664104 Beaker, 400 ml, ss, hard glass 2 2

Determining the specific heat capacity of solids (P 2.3.2.1 a)

P 2.3.2

P 2.3.2.1 Determining the specific heatcapacity of solids

Heat capacities

When a body is heated or cooled, the absorbed heat capacity DQis proportional to the change in temperature DP and to the massm of the body:

DQ = c · m · DPThe proportionality factor c, the specific heat capacity of thebody, is a quantity which depends on the respective material.

To determine the specific heat capacity, various materials in par-ticle form are weighed, heated in steam to the temperature P1 andpoured into a weighed-out quantity of water with the temperatureP2. After careful stirring, heat exchange ensures that the particlesand the water have the same temperature Pm. The heat quantityreleased by the particles:

DQ1 = c1 · m1 · (P1 · Pm)m1: mass of particlesc1: specific heat capacity of particles

is equal to the heat quantity absorbed by the water

DQ2 = c2 · m2 · (Pm · P2)m2: mass of water

The specific heat capacity of water c2 is assumed as a given. Thetemperature P1 corresponds to the temperature of the steam.Therefore, the specific heat quantity c1 can be calculated fromthe measurement quantities P2, Pm, m1 and m2 .

Heat Heat quantity

75

P2.

3.2.

1 (a

)

P2.

3.2.

1 (b

)


386 48 Dewar vessel 1 1

384161 Lid for Dewar vessel 1 1

384 34 Heating apparatus 1 1

384 35 Copper shot, 200 g 1 1

384 36 Glass shot, 100 g 1 1

315 76 Lead shot, 200 g 1 1

303 28 Steam generator, 550 W/230 V 1 1

382 34 Thermometer, -10° to + 110 °C 1



315 23 School and laboratory balance 610 tare, 610 g 1 1


300 42 Stand rod, 47 cm 1 1



667 614 Heat-protective gloves, pair; length: 290 mm 1 1


667194 Silicone tubing, i. d. 7 x 1.5 mm, 1 m 1 1

Heat quantity Heat

P 2.3.3Conversion ofmechanical energy

P 2.3.3.1 Converting mechanical energyinto heat energy –recording and evaluatingmeasured values manually

P 2.3.3.2 Converting mechanical energyinto heat energy –recording and evaluatingmeasured values with CASSY

Converting mechanical energy into heat energy – recording and evaluating measured values manually (P 2.3.3.1)

Energy is a fundamental quantity of physics. This is because thevarious forms of energy can be converted from one to anotherand are thus equivalent to each other, and because the totalenergy is conserved in the case of conversion in a closedsystem.

These two experiments show the equivalence of mechanical andheat energy. A hand crank is used to turn various calorimetervessels on their own axes, and friction on a nylon belt causesthem to become warmer. The friction force is equivalent to theweight G of a suspended weight. For n turns of the calorimeter,the mechanical work is thus

Wn = G · n · S · dd: diameter of calorimeter

This results in an increase in the temperature of the calorimeterwhich corresponds to the specific heat capacity

Qn = m · c · (Pn – P0),c: specific heat capacity, m: weight, Pn: temperature after n turns

To confirm the relationship

Qn = Wn

the two quantities are plotted together in a diagram. In the firstexperiment, the measurement is conducted and evaluatedmanually point by point. The second experiment takes advantageof the computer-assisted measuring system CASSY.

76

P2.

3.3.

1 (b

)

P2.

3.3.

1 (a

)

P2.

3.3.

2


388 00 Equivalent of heat, basic apparatus 1 1 1

388 01 Water calorimeter 1 1 1

388 02 Copper-block calorimeter with heating coil 1 1 1

388 03 Aluminum-block calorimeter with heating 1 1 1

388 04 Large aluminum-block calorimeter with heating coil 1 1 1

388 05 Thermometer for calorimeters 1

388 24 Weight with hook, 5 kg 1 1 1


666 193 Temperature sensor NiCr-Ni 1 1



524 045 Temperature box (NiCrNi/NTC) 1

524 034 Timer box 1


524 200 CASSY Lab 1



300 41 Stand rod, 25 cm 1 1


301 11 Clamp with jaw clamp 1 1


Converting electrical into heat energy - measuring with the joule and wattmeter (P 2.3.4.2)

P 2.3.4

P 2.3.4.1 Converting electrical into heat energy – measuring with the voltmeterand ammeter

P 2.3.4.2 Converting electrical into heat energy – measuring with the joule andwattmeter

Conversion of electricalenergy

Just like mechanical energy, electrical energy can also be con-verted into heat. We can use e.g. a calorimeter vessel with a wirewinding to which a voltage is connected to demonstrate this fact.When a current flows through the wire, Joule heat is generatedand heats the calorimeter.

The supplied electrical energy

W(t) = U · l · t

is determined in the first experiment by measuring the voltage U,the current I and the time t, and in the second experiment meas-ured directly using the joule and wattmeter. This results in achange in the temperature of the calorimeter which correspondsto the specific heat capacity

Q(t) = m · c · (P(t) – P(0)),c: specific heat capacity, m: mass, P(t): temperature at time t

To confirm the equivalence

Q(t) = W(t)

the two quantities are plotted together in a diagram.

P2.

3.4.

2 (a

)

P2.

3.4.

1 (b

)

P2.

3.4.

1 (a

)

P2.

3.4.

2 (b

)

Heat Heat quantity

77


384 20 Electric calorimeter attachment 1 1

386 48 Dewar vessel calorimeter with base 1 1

388 02 Copper-block calorimeter with heating coil 1 1

388 03 Aluminum-block calorimeter with heating 1 1

388 04 Large aluminum-block calorimeter with heating coil 1 1

388 06 Pair of connecting cables 1 1

Voltage source, 0 … 12 V, e. g.521 35 Variable extra-low voltage transformer S 1 1 1 1

382 34 Thermometer, -10° to + 110 °C 1

388 05 Thermometer for calorimeters 1

666 190 Digital thermometer with 1 input 1 1


Voltmeter, AC, U < 12 V, e.g.531 100 Multimeter METRAmax 2 1 1

Ammeter, I < 6 A, e.g.531 712 Multimeter METRAmax 3 1 1

313 07 Stopclock I, 30s/15min 1 1


665 755 Graduated cylinder, 250 ml: 2 1 1

501 28 Connecting lead, Ø 2.5 mm2, 50 cm, black 3 3

501 45 Pair of cables, 50 cm, red and blue 1 1 1 1

531 83 Joule and wattmeter 1 1

Phase transitions Heat

P 2.4.1Melting heat and evaporation heat

P 2.4.1.1 Determining the specificevaporation heat of water

P 2.4.1.2 Determining the specificmelting heat of ice

Determining the specific evaporation heat of water (P 2.4.1.1)

When a substance is heated at a constant pressure, its tempera-ture generally increases. When that substance undergoes aphase transition, however, the temperature does not increaseeven when more heat is added, as the heat is required for thephase transition. As soon as the phase transition is complete, thetemperature once more increases with the additional heat sup-plied. Thus, for example, the specific evaporation heat QV per unitof mass is required for evaporating water, and the specific melt-ing heat QS per unit of mass is required for melting ice.

To determine the specific evaporation heat Qv of water, puresteam is fed into the calorimeter in the first experiment, in whichcold water is heated to the mixing temperature Pm. The steamcondenses to water and gives off heat in the process; the con-densed water is cooled to the mixing temperature. The experi-ment measures the starting temperature P2 and the mass m2 ofthe cold water, the mixing temperature Pm and the total mass

m = m1 + m2

By comparing the amount of heat given off and absorbed, we canderive the equation

QV =m1 · c · (Pm – P1) + m2 · c · (Pm – P2)

.m1

P1 ≈ 100 hC, c: specific heat capacity of water

In the second experiment, pure ice is filled in a calorimeter,where it cools water to the mixing temperature Pm, in order todetermine the specific melting heat. The ice absorbs the meltingheat and melts into water, which warms to the mixing tempera-ture. Analogously to the first experiment, we can say for thespecific melting heat:

QS =m1 · c · (Pm – P1) + m2 · c · (Pm – P2)

.m1

P1 = 0 hC

P2.

4.1.

2 (a

)

P2.

4.1.

1 (b

)

P2.

4.1.

1 (a

)

P2.

4.1.

2 (b

)

78


386 48 Dewar vessel 1 1 1 1

38417 Water separator 1 1

303 28 Steam generator, 550 W/230 V 1 1

303 25 Immersion heater 1 1

382 34 Thermometer, -10° to + 110 °C 1 1

666 190 Digital thermometer with 1 input 1 1


315 23 School and laboratory balance 610 Tara, 610 g 1 1 1 1


300 42 Stand rod, 47 cm 1 1



664104 Beaker, 400 ml, ss, hard glass 1 1 1 1

667194 Silicone tubing, int. dia. 7 x 1.5 mm, 1 m 1 1

590 06 Plastic beaker, 1000 ml 1 1

Recording the vapor pressure curve of water up to 50 bar (P 2.4.2.2)

P 2.4.2

P 2.4.2.1 Recording the vapor pressurecurve of water up to 1 bar

P 2.4.2.2 Recording the vapor pressurecurve of water up to 50 bar

Measuring vapor pressure

The vapor pressure p of a liquid-vapor mixture in a closedsystem depends on the temperature T. Above the critical tem-perature, the vapor pressure is undefined. The substance isgaseous and cannot be liquefied no matter how high the pres-sure. The increase in the vapor-pressure curve p(T) is deter-mined by several factors, including the molar evaporation heat qvof the substance:

T · dp

= qv (Clausius-Clapeyron)

dT v1 – v2

T: absolute temperaturev1: molar volume of vaporv2: molar volume of liquid

As we can generally ignore v2 and qv hardly varies with T, we canderive a good approximation from the law of ideal gases:

ln p = ln p0 – qv

R · T

In the first experiment, the vapor pressure curve of water belowthe normal boiling point is recorded with the computer-assistedmeasuring system CASSY. The water is placed in a glass vessel,which was sealed beforehand while the water was boiling atstandard pressure. The vapor pressure p is measured as a func-tion of the temperature T when cooling and subsequently heatingthe system, respectively.

The high-pressure steam apparatus is used in the second exper-iment for measuring pressures of up to 50 bar. The vapor pres-sure can be read directly from the manometer of this device. Athermometer supplies the corresponding temperature. The meas-ured values are recorded and evaluated manually point by point.

P2.

4.2.

1

P2.

4.2.

2

Heat Phase transitions

79


664 315 Double-necked round-bottom flask, 250 ml, ST 19/26, GL 18 1

665 305 Core/threads ST 19/26, with GL 18 1

667186 Vacuum rubber tubing, int. dia. 8 x 5 mm, 1 m 1

665 255 Stopcock, 3-way valve, with ST stopcock, 8 mm dia., T-shape 1

378 031 Small flange DN 16 KF with hose nozzle 1

378 045 Centering ring DN 16 KF 1

378 050 Clamping ring DN 10/16 KF 1

378 701 High-vacuum grease 1


524 200 CASSY Lab 1

1

1

524 045 Temperature-box (NiCrNi/NTC) 1

1

666 216 NiCr-Ni-temperature sensor 1



666 555 Universal clamp, 0 ... 80 mm dia.


302 68 Ring with stem 1 1

666 685 Wire gauze, 160 x 160 mm 1 1

666 711 Butane gas burner, gas and air regulation 1 1

666 712 Butane cartridges 200g, set of 3 1 1

667 614 Heat protective gloves, pair 1 1

38516 High-pressure steam boiler 1

Beaker, 25 ml, ss, hard glass 1



667 613 Safety goggles for wearing over glasses 1

additionally recommended:PC with Windows 95/NT or higher 1

309 00 335 Rod 10 x 225 mm with thread M6

501 11 Extension cable, 15-pole

524 065 Absolute pressure sensor S, 0...1500 hPa

1

664 109

Phase transitions Heat

P 2.4.3Critical temperature

P 2.4.3.1 Investigating a liquid-vapormixture at the critical point

Investigating a liquid-vapor mixture at the critical point (P 2.4.3.1 b)

The critical point of a real gas is defined by the critical pressurepc, the critical density Uc and the critical temperature Tc. Belowthe critical temperature, the substance is gaseous for a suffi-ciently great molar volume – it is termed a vapor – and is liquidat a sufficiently small molar volume. Between these extremes, aliquid-vapor mix exists, in which the vapor component increaseswith the molar volume. As liquid and vapor have different densi-ties, they are separated in a gravitational field. As the tempera-ture rises, the density of the liquid decreases and that of thevapor increases, until finally at the critical temperature both den-sities have the value of the critical density. Liquid and vapor mixcompletely, and the phase boundary disappears. Above the cri-tical temperature, the substance is gaseous, regardless of themolar volume.

This experiment investigates the behavior of sulfur hexafluoride(SF6) close to the critical temperature. The critical temperatureof this substance is Tc = 318.7 K and the critical pressure ispc = 37.6 bar. The substance is enclosed in a pressure chamberdesigned so that hot water or steam can flow through the man-tle. The dissolution of the phase boundary between liquid andgas while heating the substance, and its restoration during cool-ing, are observed in projection on the wall. As the systemapproaches the critical point, the substance scatters short-wavelight particularly intensively; the entire contents of the pressurechamber appears red-brown. This critical opalescence is due tothe variations in density, which increase significantly as thesystem approaches the critical point.

Note: The dissolution of the phase boundary during heating canbe observed best when the pressure chamber is heated asslowly as possible using a circulation thermostat.

P2.

4.3.

1(a)

P2.

4.3.

1(b

)

80


371 401 Pressure chamber for demonstrating the critical temperature 1 1

450 60 Lamp housing 1 1

450 51 Lamp, 6 V/30 W 1 1

460 20 Aspherical condensor 1 1

460 03 Lens, f = + 100 mm 1 1

461 11 Right angled prism 1 1

Transformer, 6 V AC, 12 V AC/ 30 W 1 1

382 33 Thermometer, -10 to +150 °C 1

666 193 Temperatur sensor, NiCr.Ni 1

666 190 Digital thermometer with one input 1

303 28 Steam generator, 550 W/230 V 1

667194 Silicone tubing. int. dia. 7 x 1.5 mm, 1 m 2 2

664104 Beaker, 400 ml, ss, hard glass 1

666 768 Circulation thermostat, + 30 - 100 °C 1

460 43 Small optical bench 1 1



521 210

Brownian motion of smoke particles (P 2.5.1.1)

P 2.5.1

P 2.5.1.1 Brownian motion of smoke particles

Brownian motion of molecules

A particle which is suspended in a gas constantly executes amotion which changes in its speed and in all directions. J. Perrinfirst explained this molecular motion, discovered by R. Brown,which is caused by bombardment of the particles with the gasmolecules. The smaller the particle is, the more noticeably itmoves. The motion consists of a translational component and arotation, which also constantly changes.

In this experiment, the motion of smoke particles in the air isobserved using a microscope.

P2.

5.1.

1

Heat Kinetic theory of gases

81


662 078 Microscope MIC 805 1

372 51 Smoke chamber 1


450 51 Lamp, 6 V/30 W 1

460 20 Aspherical condensor 1

Transformer, 6 V AC, 12 V AC/ 30 W 1


Schematic diagram of Brownian motion of molecules

521 210

Kinetic theory of gases Heat

P 2.5.2Laws of gases

P 2.5.2.1 Pressure-dependency of thevolume of a gas at a constanttemperature (Boyle-Mariotte’slaw)

P 2.5.2.2 Temperature-dependency of thevolume of a gas at a constantpressure (Gay-Lussac’s law)

P 2.5.2.3 Temperature-dependency of thepressure of a gas at a constantvolume (Amontons’ law)

Pressure-dependency of the volume of a gas at a constant temperature (Boyle-Mariotte’s law) (P 2.5.2.1)

The gas thermometer consists of a glass tube closed at the bot-tom end, in which a mercury stopper seals the captured air at thetop. The volume of the air column is determined from its heightand the cross-section of the glass tube. When the pressure at theopen end is altered using a hand pump, this changes the pres-sure on the sealed side correspondingly. The temperature of theentire gas thermometer can be varied using a water bath.

In the first experiment, the air column is maintained at a constantroom temperature T. At an external pressure p0, it has a volumeof V0 bounded by the mercury stopper. The pressure p in the aircolumn is reduced by evacuating air at the open end, and theincreased volume V of the air column is determined for differentpressure values p. The evaluation confirms the relationship

p · V = p0 · V0 for T = const. (Boyle-Mariotte’s law)

In the second experiment, the gas thermometer is placed in awater bath of a specific temperature which is allowed to grad-ually cool. The open end is subject to the ambient air pressure,so that the pressure in the air column is constant. This experi-ment measures the volume V of the air column as a function ofthe temperature T of the water bath. The evaluation confirms therelationship

V “ T for p = const. (Gay-Lussac’s law)

In the final experiment, the pressure p in the air column is con-stantly reduced by evacuating the air at the open end so that thevolume V of the air column also remains constant as the tempe-rature drops. This experiment measures the pressure p of the aircolumn as a function of the temperature T of the water bath. Theevaluation confirms the relationship

p “ T for V = const. (Amontons’ law)

P2.

5.2.

2

P2.

5.2.

1

P2.

5.2.

3

82


382 00 Gas thermometer 1 1 1

666 190 Digital thermometer with one input 1 1

666 193 Temperatur sensor, NiCr.Ni 1 1


300 42 Stand rod, 47 cm 1 1 1

301 11 Clamp with jaw clamp 2 2 2

375 58 Hand vacuum and pressure pump 1 1

666 767 Hot plate, 150 mm dia., 1500 W 1 1


Pressure-dependency of the volume at a constant temperature (P 2.5.2.1)

Determining the adiabatic exponent Cp/CV of air after Determining the adiabatic exponent Cp/CV of various Rüchard (P 2.5.3.1) gases using the gas elastic resonance apparatus (P 2.5.3.2)

P 2.5.3

P 2.5.3.1 Determining the adiabaticexponent Cp/CV of air afterRüchard

P 2.5.3.2 Determining the adiabaticexponent Cp/CV of variousgases using the gas elasticresonance apparatus

Spezific heat of gases

In the case of adiabatic changes in state, the pressure p and thevolume V of a gas demonstrate the relationship

p · V K = const.

whereby the adiabatic exponent is defined as

k = Cp

CV

i.e. the ratio of the specific heat capacities Cp and CV of the re-spective gas.

The first experiment determines the adiabatic exponent of airfrom the oscillation period of a ball which caps and seals a gasvolume in a glass tube, whereby the oscillation of the ball aroundthe equilibrium position causes adiabatic changes in the state ofthe gas. In the equilibrium position, the force of gravity and theopposing force resulting from the pressure of the enclosed gasare equal. A deflection from the equilibrium position by Wxcauses the pressure to change by

Dp = – k · p ·A · Dx

,V

A: cross-section of riser tube

which returns the ball to the equilibrium position. The ball thusoscillates with the frequency

f0 = 1

· ök · p · A2 ,

2S m · V

around its equilibrium position.

In the second experiment, the adiabatic exponent is determinedusing the gas elastic resonance apparatus. Here, the air columnis sealed by a magnetic piston which is excited to forced oscilla-tions by means of an alternating electromagnetic field. The aim ofthe experiment is to find the characteristic frequency f0 of thesystem, i.e. the frequency at which the piston oscillates withmaximum amplitude. Other gases, such as carbon dioxide andnitrogen, can alternatively be used in this experiment.

P2.

5.3.

1

P2.

5.3.

2

Heat Kinetic theory of gases

83


371 04 Marriot’s flask, 10 l 1

371 05 Oscillation tube, apparatus for determination of cp/cV 1

313 07 Stopclock I, 30s/15min 1

31719 Aneroid barometer, 980 – 1045 mbar 1


Vaseline, 50 g 1

371 07 Gas elastic resonance apparatus 1

665 914 Gas syringe with 3-way stopcock, 100 ml:1 1

665 918 Holder for gas syringe, 100 ml, plastic 1

Function generator S 12, 0.1 Hz to 20 kHz 1

Counter P 1

Ammeter, AC, I = 1 A, e.g.531 100 Multimeter METRAmax 2 1


660 980 Fine regulating valve for Minican gas cans 1

660 985 Minican gas can, neon 1

660 999 Minican gas can, carbon dioxide 1

665 255 Three-way valve with ST-stopcock, 8 mm dia., T-shape 1

667194 Silikone tubing, i. d. 7 x 1.5 mm, 1 m 1

500 422 Connecting lead, blue, 50 cm 1



522 621

575 451

675 3100

Thermodynamic cycle Heat

P 2.6.1Hot-air engine: qualitative experiments

P 2.6.1.1 Operating a hot-air engine as athermal engine

Operating a hot-air engine as a thermal engine (P 2.6.1.1)

The hot-air engine (invented by R. Stirling, 1816) is the oldestthermal engine, along with the steam engine. In greatly simplifiedterms, its thermodynamic cycle consists of an isothermic com-pression at low temperature, an isochoric application of heat, anisothermic expansion at high temperature and an isochoric emis-sion of heat. The displacement piston and the working piston areconnected to a crankshaft via tie rods, whereby the displacementpiston leads the working piston by 90°. When the working pistonis at top dead center (a), the displacement piston is movingdownwards, displacing the air into the electrically heated zone ofthe cylinder. Here, the air is heated, expands and forces theworking piston downward (b). The mechanical work is transferr-ed to the flywheel. When the working piston is at bottom deadcenter (c), the displacement piston is moving upwards, displac-ing the air into the water-cooled zone of the cylinder. The aircools and is compressed by the working cylinder (d). Theflywheel delivers the mechanical work required to execute thisprocess.

The experiment qualitatively investigates the operation of the hot-air engine as a thermal engine. Mechanical power is derived fromthe engine by braking at the brake hub. The voltage of the heat-ing filament is varied in order to demonstrate the relationshipbetween the thermal power supplied and the mechanical powerremoved from the system. The no-load speed of the motor foreach case is used as a measure of the mechanical power pro-duced in the system.

P2.

6.1.

1

84


388 182 Hot-air engine 1

562 11 U-core with yoke 1

562 12 Clamping device 1

562 21 Mains coil with 500 turns for 230 V 1

562 18 Extra-low-voltage coil, 50 turns 1

501 33 Connecting lead, Ø 2.5 mm2, 100 cm, black 2

388 181 Submersible pump, 12 V 1*

Low-voltage power supply 1*

667194 Silicone tubing, int. dia. 7 x 1.5 mm, 1 m


2*521 230

Operating the hot-air engine as a heat pump and a refrigerating machine (P 2.6.1.3)

P 2.6.1

P 2.6.1.3 Operating the hot-air engine as a heat pump and a refrige-rating machine

Hot-air engine: qualitative experiments

Depending on the direction of rotation of the crankshaft, the hot-air engine operates as either a heat pump or a refrigeratingmachine when its flywheel is externally driven. When the dis-placement piston is moving upwards while the working piston isat bottom dead center, it displaces the air in the top part of thecylinder. The air is then compressed by the working piston andtransfers its heat to the cylinder head, i.e. the hot-air motor ope-rates as a heat pump. When run in the opposite direction, the working piston causes the air to expand when it is in the toppart of the cylinder, so that the air draws heat from the cylinderhead; in this case the hot-air engine operates as a refrigeratingmachine.

The experiment qualitatively investigates the operation of the hot-air engine as a heat pump and a refrigerating machine. In orderto demonstrate the relationship between the externally suppliedmechanical power and the heating or refrigerating power,respectively, the speed of the electric motor is varied and thechange in temperature observed.

P2.

6.1.

3

Heat Thermodynamic cycle

85



388 19 Thermometer 1



388 181 Immersion pump 12 V 1*


667194 Silicone tubing, int. dia. 7 x 1.5 mm, 1 m 2*


Experiments to the hot-air engine can also be realized

with the hot-air engine P (388 176)

521 230


P 2.6.2Hot-air engine: quantitative experiments

P 2.6.2.1 Frictional losses in the hot-airengine (calorific determination)

P 2.6.2.2 Determining the efficiency ofthe hot-air engine as a heatengine

P 2.6.2.3 Determining the efficiency ofthe hot-air engine as a refrigerating machine

Frictional losses in the hot-air engine (calorific determination) (P 2.7.2.1)

When the hot-air engine is operated as a heat engine, each en-gine cycle withdraws the amount of heat Q1 from reservoir 1,generates the mechanical work W and transfers the difference Q2= Q1 – W to reservoir 2. The hot-air engine can also be made tofunction as a refrigerating machine while operated in the samerotational direction by externally applying the mechanical workW. In both cases, the work WF converted into heat in each cyclethrough the friction of the piston in the cylinder must be takeninto consideration.In order to determine the work of friction WF in the first experi-ment, the temperature increase DTF in the cooling water is meas-ured while the hot-air engine is driven using an electric motorand the cylinder head is open.The second experiment determines the efficiency

J = W

W + Q2

of the hot-air engine as a heat engine. The mechanical work Wexerted on the axle in each cycle can be calculated using theexternal torque N of a dynamometrical brake which brakes thehot-air engine to a speed f. The amount of heat Q2 given off cor-responds to a temperature increase DT in the cooling water.

The final experiment determines the efficiency

J = Q1

Q1 – Q2

of the hot-air engine as a refrigerating machine. Here, the hot-airengine with closed cylinder head is driven using an electric motorand Q1 is determined as the electrical heating energy required tomaintain the cylinder head at the ambient temperature.

P2.

6.2.

2

P2.

6.2.

1

P2.

6.2.

3

86


388 182 Hot-air engine 1 1 1

388 221 Accessories for hot-air engine 1 1 1

347 35 Experiment motor 1 1

347 36 Control unit for experiment motor 1 1




562 18 Extra-low voltage coil, 50 turns 1

521 35 Variable extra-low voltage transformer S 1

1 1 1

33746 Forked light barrier, infra-red 1 1 1

1 1 1

531 100 Multimeter METRAmax 2 1 1



382 36 Thermometer, -10° to + 40 °C 1 1 1




300 51 Stand rod, right-angled 1


590 06 Plastic beaker, 1000 ml 1 1 1




388 181 Immersion pump 12 V 1* 1* 1*

Low voltage power supply 1* 1* 1*

667194 Silicone tubing, int. dia. 7 x 1.5 mm, 1 m 2* 2* 2*


313 17 Stopclock II, 60 s/30 min 1 1 1

521 230

1 1

575 471 Counter S

501 16 Multi-core cable, 6-pole, 1.5 m

Hot-air engine as a heat engine: recording and evaluating the pV diagram with CASSY (P 2.6.2.4)

P 2.6.2

P 2.6.2.4 Hot-air engine as a heat engine:recording and evaluating thepV diagram with CASSY

Hot-air engine: quantitative experiments

Thermodynamic cycles are often described as a closed curve ina pV diagram (p: pressure, V: volume). The work added to or with-drawn from the system (depending on the direction of rotation)corresponds to the area enclosed by the curve.

In this experiment, the pV diagram of the hot air engine as a heatengine is recorded using the computer-assisted measured valuerecording system CASSY. The pressure sensor measures thepressure p in the cylinder and a displacement sensor measuresthe position s, from which the volume is calculated, as a functionof the time t. The measured values are displayed on the screendirectly in a pV diagram. In the further evaluation, the mechanicalwork performed as piston friction per cycle

W = – ∫ p · dV

and from this the mechanical power

P = W · ff: no-load speed

are calculated and plotted in a graph as a function of the no-loadspeed.

Heat Thermodynamic cycle

87

P2.

6.2.

4







529 031 Displacement transducer 1

524 031 Current supply box 1

1


524 200 CASSY Lab 1

309 48 Cord, 10 m 1

352 08 Helical spring, 5 N; 0.25 N/cm 1



388 181 Immersion pump 12 V 1*


667194 Silicone tubing, int. dia. 7 x 1.5 mm, 1 m



2*521 230



P 2.6.3Heat pump

P 2.6.3.1 Determining the efficiency ofthe heat pump as a function ofthe temperature differential

P 2.6.3.2 Investigating the function of the expansion valveof the heat pump

P 2.6.3.3 Analyzing the thermodynamiccycle of the heat pump usingthe Mollier diagram

Determining the efficiency of the heat pump as a function of the temperature differential (P 2.6.3.1)

The heat pump extracts heat from a reservoir with the tempera-ture T1 through vaporization of a coolant and transfers heat to areservoir with the temperature T2 through condensation of thecoolant. In the process, compression in the compressor (a-b)greatly heats the gaseous coolant. It condenses in the liquefier(c-d) and gives up the released condensation heat DQ2 to thereservoir T2. The liquefied coolant is filtered and fed to the expan-sion valve (e-f) free of bubbles. This regulates the supply of cool-ant to the vaporizer (g-h). In the vaporizer, the coolant once againbecomes a gas, withdrawing the necessary evaporation heat DQ1from the reservoir T1.

P2.

6.3.

2

P2.

6.3.

1

P2.

6.3.

3

88


389 521 Heat pump pT 1 1

531 83 Joule and wattmeter 1 1

666 209 Digital thermometer with four inputs 1 1 1

666 193 Temperature sensor NiCr-Ni 2 2 3

502 05 Measuring junction box 1 1

313 12 Digital stopwatch 1 1 1

Yt-recorder, 2 channels 1* 1* 1*

500 621 Safety connection lead, 50 cm, red 2 2

500 622 Safety connection lead, 50 cm, blue 2 2

501 46 Pair of cables, 50 cm, red and blue 2* 2* 2*


In the second experiment, the temperatures Tf and Th are record-ed at the outputs of the expansion valve and the vaporizer. If thedifference between these two temperatures falls below a specificlimit value, the expansion valve chokes off the supply of coolantto the vaporizer. This ensures that the coolant in the vaporizer isalways vaporized completely.

In the final experiment, a Mollier diagram, in which the pressurep is graphed as a function of the specific enthalpy h of the cool-ant, is used to trace the energy transformations of the heat pump.The pressures p1 and p2 in the vaporizer and liquefier, as well asthe temperatures Ta, Tb, Te and Tf of the coolant are used todetermine the corresponding enthalpy values ha, hb, he and hf.This experiment also measures the heat quantities DQ2 and DQ1released and absorbed per unit of time. This in turn is used todetermine the amount of coolant Dm circulated per unit of time.

The aim of the first experiment is to determine the efficiency

e =DQ2

DW

of the heat pump as a function of the temperature differential DT = T2 – T1. The heat quantity DQ2 released is determined fromthe heating of water reservoir T2, while the applied electricalenergy DW is measured using the joule and wattmeter.

1

575 713

Electricity

90

Table of contents Electricity

P3 ElectricityP 3.1 ElectrostaticsP 3.1.1 Basic electrostatics experiments 91–92

P 3.1.2 Coulomb's law 93–95

P 3.1.3 Lines of electric flux and isoelectric lines 96–97

P 3.1.4 Force effects in an electric field 98–99

P 3.1.5 Charge distributions on electrical conductors 100

P 3.1.6 Definition of capacitance 101

P 3.1.7 Plate capacitor 102–103

P 3.2 Principles of electricityP 3.2.1 Charge transfer with drops of water 104

P 3.2.2 Ohm's law 105

P 3.2.3 Kirchhoff's law 106–107

P 3.2.4 Circuits with electrical measuring instruments 108

P 3.2.5 Conducting electricityby means of electrolysis 109

P 3.2.6 Experiments on electrochemistry 110

P 3.3 MagnetostaticsP 3.3.1 Basic magnetostatics experiments 111

P 3.3.2 Magnetic dipole moment 112

P 3.3.3 Effects of force in a magnetic field 113

P 3.3.4 Biot-Savart's law 114

P 3.4 Electromagnetic inductionP 3.4.1 Voltage impulse 115

P 3.4.2 Induction in a moving conductor loop 116

P 3.4.3 Induction by means of a variable magnetic field 117

P 3.4.4 Eddy currents 118

P 3.4.5 Transformer 119–120

P 3.4.6 Measuring the earth’s magnetic field 121

P 3.5 Electrical machinesP 3.5.1 Basic experiments

on electrical machines 122

P 3.5.2 Electric generators 123

P 3.5.3 Electric motors 124

P 3.5.4 Three-phase machines 125

P 3.6 DC and AC circuitsP 3.6.1 Circuit with capacitor 126

P 3.6.2 Circuit with coil 127

P 3.6.3 Impedances 128

P 3.6.4 Measuring-bridge circuits 129

P 3.6.5 Measuring AC voltages and currents 130

P 3.6.6 Electrical work and power 131–132

P 3.6.7 Electromechanical devices 133

P 3.7 Electromagnetic oscillationsand waves

P 3.7.1 Electromagnetic oscillator circuit 134

P 3.7.2 Decimeter waves 135

P 3.7.3 Propagation ofdecimeter waves along lines 136

P 3.7.4 Microwaves 137

P 3.7.5 Propagation of microwaves along lines 138

P 3.7.6 Directional characteristic of dipole radiation 139

P 3.8 Moving charge carriers in a vacuum

P 3.8.1 Tube diode 140

P 3.8.2 Tube triode 141

P 3.8.3 Maltese-cross tube 142

P 3.8.4 Perrin tube 143

P 3.8.5 Thomson tube 144

P 3.9 Electrical conduction in gasesP 3.9.1 Self-maintained and

non-self-maintained discharge 145

P 3.9.2 Gas discharge at reduced pressure 146

P 3.9.3 Cathode and canal rays 147

Basic electrostatics experiments with the field electrometer (P 3.1.1.1)

P 3.1.1

P 3.1.1.1 Basic electrostatics experimentswith the field electrometer

Basic experiments on electrostatics

The field electrometer is a classic apparatus for demonstratingelectrical charges. Its metallized pointer, mounted on needlebearings, is conductively connected to a fixed metal support.When an electrical charge is transferred to the metal support viaa pluggable metal plate or a Faraday’s cup, part of the chargeflows onto the pointer. The pointer is thus repelled, indicating thecharge.

In this experiment, the electrical charges are generated by rub-bing two materials together (more precisely, by intensive contactfollowed by separation), and demonstrated using the field elec-trometer. This experiment proves that charges can be transferredbetween different bodies. Additional topics include charging ofan electrometer via induction, screening induction via a metalscreen and discharge in ionized air.

P3.

1.1.

1

Electricity Electrostatics

91


54010 Field electrometer 1

54011 Electrostatics demonstration set 1 1

54012 Electrostatics demonstration set 2 1




501 861 Set of 6 croc-clips, polished 1


Electrostatics Electricity

P 3.1.1Basic experiments on electrostatics

P 3.1.1.2 Basic electrostatics experi-ments with the electrometeramplifier

Basic electrostatics experiments with the electrometer amplifier (P 3.1.1.2)

The electrometer amplifier is an impedance converter with anextremely high-ohm voltage input (≥ 1013 Ö) and a low-ohm volt-age output (≤ 1 Ö). By means of capacitive connection of theinput and using a Faraday’s cup to collect charges, this device isideal for measuring extremely small charges. Experiments oncontact and friction electricity can be conducted with a highdegree of reliability.

This experiment investigates how charges can be separatedthrough rubbing two materials together. It shows that one ofthe materials carries positive charges, and the other negativecharges, and that the absolute values of the charges are equal. Ifwe measure the charges of both materials at the same time, theycancel each other out. The sign of the charge of a material doesnot depend on the material alone, but also on the properties ofthe other material.

P3.

1.1.

2 (a

)

P3.

1.1.

2 (b

)

92


532 14 Electrometer amplifier 1 1

562 791 Plug-in unit 230V/12 V AC/20 W; with female plug 1

522 27 Power supply 450 V AC 1

578 25 STE Capacitor 01 nF, 630 V 1 1

578 10 STE Capacitor 10 nF, 100 V 1 1

532 16 Connection rod 1 1

Voltmeter, DC, U ≤ ± 8 V, e.g.531 100 Multimeter METRAmax 2 1 1

541 00 Pair of friction rods 1 1

546 12 Faraday's cup 1 1

590 011 Clamping plug 1 1

542 51 Induction plate 1 1

664152 Watch glass dish, 40 mm dia. 1 1

340 89 Coupling plug 1 1


500 424 Connection lead, 50 cm, black 1 1

Measuring charges with the electrometer amplifier

Confirming Coulomb’s law – measuring with the torsion balance, Schürholz design (P 3.1.2.1)

P 3.1.2

P 3.1.2.1 Confirming Coulomb’s law –measuring with the torsionbalance, Schürholz design

Coulomb’s law

According to Coulomb’s law, the force acting between two point-shaped electrical charges Q1 and Q2 at a distance r from eachother can be determined using the formula

F =1

· Q1 · Q2

4Se0 r2

where e0 = 8.85 · 10-12 As/Vm (permittivity)

The same force acts between two charged fields when thedistance r between the sphere midpoints is significantly greaterthan the sphere diameter, so that the uniform charge distributionsof the spheres is undisturbed. In other words, the spheres in thisgeometry may be treated as points.

In this experiment, the coulomb force between two chargedspheres is measured using the torsion balance. The heart of thisextremely sensitive measuring instrument is a rotating body elas-tically mounted between two torsion wires, to which one of thetwo spheres is attached. When the second sphere is brought intoclose proximity with the first, the force acting between the twocharged spheres produces torsion of the wires; this can be indi-cated and measured using a light pointer. The balance must becalibrated if the force is to be measured in absolute terms.

The coulomb force is measured as a function of the distance r.For this purpose, the second sphere, mounted on a stand, isbrought close to the first one. Then, at a fixed distance, thecharge of one sphere is reduced by half. The measurement canalso be carried out using spheres with opposing charges. Thecharges are measured using an electrometer amplifier connect-ed as a coulomb meter. The aim of the evaluation is to verify theproportionalities

F “ 1and F “ Q1 · Q2r2

and to calculate the permittivity e0.

P3.

1.2.

1


93


516 01 Torsion balance after Schürholz 1

516 20 Accessories for Coulomb’s law of electrostatics 1

516 04 Scale, on stand, 1 m long 1

521 721 High voltage power supply 25 kV 1

501 05 High voltage cable, 1 m 1

59013 Insulated stand rod, 25 cm 1

30011 Saddle base 1

532 14 Electrometer amplifier 1


578 25 STE capacitor 1 nF, 630 V 1


Voltmeter, DC, U ≤ ± 8 V, e.g.531 100 Multimeter METRAmax 2 1

546 12 Faraday's cup 1

590 011 Clamping plug 1

532 16 Connection rod 1





313 07 Stopclock I, 30 s/15 min 1



500 414 Connection lead, 25 cm, black 1



501 43 Connection lead, 200 cm, yellow-green 1

471 830


P 3.1.2Coulomb’s law

P 3.1.2.2 Confirming Coulomb’s law –measuring with the force sensorand newton meter

Confirming Coulomb’s law with the force sensor and newton meter (P 3.1.2.2)

As an alternative to measuring with the torsion balance, the cou-lomb force between two spheres can also be determined usingthe force sensor. This device consists of two bending elementsconnected in parallel with four strain gauges in a bridge confi-guration; their electrical resistance changes when a load isapplied. The change in resistance is proportional to the forceacting on the instrument.

In this experiment, the force sensor is connected to a newtonmeter, which displays the measured force directly. No calibrationis necessary. The coulomb force is measured as a function of thedistance r between the sphere midpoints, the charge Q1 of thefirst sphere and the charge Q2 of the second sphere. Thecharges of the spheres are measured using an electrometeramplifier connected as a coulomb meter. The aim of the evalua-tion is to verify the proportionalities

F “ 1, F “ Q1 and F “ Q2r2

and to calculate the permittivity e0.

P3.

1.2.

2

94


314 263 Set of bodies for electric charge 1

337 00 Trolley 1, 85 g 1

460 82 Precision metal rail, 0.5 m 1

314 261 Force sensor 1

314 251 Newton meter 1





30011 Saddle base 1


562 791 Plug-in unit 230 V/12 V AC/20 W; with female plug 1



Voltmeter, DC, U ≤ ± 8 V, e. g.531 100 Multimeter METRAmax 2 1





300 41






501 43 Connection lead, 200 cm, yellow-green 1

Stand rod, 25 cm 1

Confirming Coulomb’s law with displacement sensor and CASSY (P 3.1.2.3)

P 3.1.2

P 3.1.2.3 Confirming Coulomb’s law –recording and evaluating withCASSY

Coulomb’s law

For computer-assisted measuring of the coulomb force betweentwo charged spheres, we can also connect the force sensor to aCASSY interface device via a bridge box. A displacement sensoris additionally required to measure the distance between thecharged spheres; this is connected to CASSY via a currentsource box.

This experiment utilizes the software CASSY Lab to record thevalues and evaluate them. The coulomb force is measured for dif-ferent charges Q1 and Q2 as a function of the distance r. Thecharges of the spheres are measured using an electrometeramplifier connected as a coulomb meter. The aim of the evalua-tion is to verify the proportionality

F “ 1

r2

and to calculate of the permittivity e0.

P3.

1.2.

3

P3.

1.2.

3


95



337 00 Trolley 1, 85 g 1

460 82 Precision metal rail, 0.5 m 1

460 95 Clamp rider 2

1

529 031 Displacement sensor 1


524 200 CASSY Lab 1





30011 Saddle base 1

532 14 Electrometer amplifier 1*

562 791 Plug-in unit 230 V/12 V AC/20 W; with female plug 1*

578 25 STE capacitor 1 nF, 630 V 1*

578 10 STE capacitor 10 nF, 100 V 1*

Voltmeter, DC, U ≤ ± 8 V, e. g.531 100 Multimeter METRAmax 2 1*


546 12 Faraday's cup 1*

590 011 Clamping plug 1*

532 16 Connection rod 1*



337 04 Set of driving weights 1



309 48 Cord, 10 m 1

501 46 Pair of cables, 100 cm, red and blue

500 424 Connection lead, 50 cm, black 1*

501 43 Connection lead, 200 cm, yellow-green 1*


*additionally recommended

524 060 Force sensor S, ± 1 N

1+1*


P 3.1.3Field lines and equipotential lines

P 3.1.3.1 Displaying lines of electric flux

Displaying lines of electric flux (P 3.1.3.1)

The space which surrounds an electric charge is in a state whichwe describe as an electric field. The electric field is also presenteven when it cannot be demonstrated through a force acting ona sample charge. A field is best described in terms of lines ofelectric flux, which follow the direction of electric field strength.The orientation of these lines of electric flux is determined by thespatial arrangement of the charges generating the field.In this experiment, small particles in an oil-filled cuvette are usedto illustrate the lines of electric flux. The particles align them-selves in the electric field to form chains which run along thelines of electric flux. Four different pairs of electrodes are provid-ed to enable electric fields with different spatial distributions tobe generated; these electrode pairs are mounted beneath thecuvette, and connected to a high voltage source of up to 10 kV.The resulting patterns can be interpreted as the cross-sectionsof two spheres, one sphere in front of a plate, a plate capacitorand a spherical capacitor.

P3.

1.3.

1

96


541 06 Equipment set E-field lines 1



452 111 Overhead projector Famulus alpha 250 1

Displaying the equipotential lines of electric fields (P 3.1.3.2)

P 3.1.3

P 3.1.3.2 Displaying the equipotentiallines of electric fields

Field lines and equipotential lines

In a two-dimensional cross-section of an electric field, points ofequal potential form a line. The direction of these isoelectriclines, just like the lines of electric flux, are determined by the spa-tial arrangement of the charges generating the field.

This experiment measures the isoelectric lines for bodies withdifferent charges. To do this, a voltage is applied to a pair of elec-trodes placed in an electrolytic tray filled with distilled water. AnAC voltage is used to avoid potential shifts due to electrolysis atthe electrodes. A voltmeter measures the potential difference be-tween the 0 V electrode and a steel needle immersed in thewater. To display the isoelectric lines, the points of equal poten-tial difference are localized and drawn on graph paper. In thisway, it is possible to observe and study two-dimensional sectionsthrough the electric field in a plate capacitor, a Faraday’s cup, adipole, an image charge and a slight curve.

P3.

1.3.

2


97


545 09 Electrolytic tank 1


Low-voltage power supply, 3, 6, 9, 12 V AC/3 A 1

Voltmeter, AC, U ≤ 3 V, e. g.531 100 Multimeter METRAmax 2 1

510 32 Set of 4 knitting needles 1





30011 Saddle base 1


Measurement example: equipotential lines around a needle tip

521 230


P 3.1.4Effects of force in an electric field

P 3.1.4.1 Measuring the force of an electric charge in a homogeneous electric field

Measuring the force of an electric charge in a homogeneous electric field (P 3.1.4.1)

In a homogeneous electric field, the force F acting on an elongat-ed charged body is proportional to the total charge Q and theelectric field strength E. Thus, the formula

F = Q · E

applies. In this experiment, the greatest possible charge Q istransferred to an electrostatic spoon from a plastic rod. The elec-trostatic spoon is within the electric field of a plate capacitor andis aligned parallel to the plates. To verify the proportional rela-tionship between the force and the field strength, the force Facting on the electrostatic spoon is measured at a known platedistance d as a function of the capacitor voltage U. The electricfield E is determined using the equation

E =Ud

The measuring instrument in this experiment is a current bal-ance, a differential balance with light-pointer read-out, in whichthe force to be measured is compensated by the spring force ofa precision dynamometer.

P3.

1.4.

1

98


516 32 Current balance with conductors 1

314 081 Precision dynamometer, 0.01 N 1


541 04 Plastic rod 1

541 21 Leather 1

544 22 Parallel plate capacitor 1

300 75 Laboratory stand I 1




441 53 Translucent screen 1



30011 Saddle base 1




471 830

Measuring the force between a charged sphere and a metal plate (P 3.1.4.3)

P 3.1.4

P 3.1.4.2 Kirchhoff’s voltage balance:Measuring the force between two charged plates of a plate capacitor

P 3.1.4.3 Measuring the force between a charged sphere anda metal plate

Effects of force in an electric field

As an alternative to measurement with the current balance, theforce in an electric field can also be measured using a force sen-sor connected to a newton meter. The force sensor consists oftwo bending elements connected in parallel with four straingauges in a bridge configuration; their electrical resistancechanges when a load is applied. The change in resistance is pro-portional to the force acting on the sensor. The newton meter dis-plays the measured force directly.

In the first experiment Kirchhoff’s voltage balance is set up inorder to measure the force

F = 1

· e0 · U2

· A2 d2

where e0 = 8.85 · 10-12 As/Vm (permittivity)

acting between the two charged plates of a plate capacitor. At agiven area A, the measurement is conducted as a function of theplate distance d and the voltage U. The aim of the evaluation isto confirm the proportionalities

F “ 1and F “ U2

d2

and to determine the permittivity e0.

The second experiment consists of a practical investigation ofthe principle of the image charge. Here, the attractive force actingon a charged sphere in front of a metal plate is measured. Thisforce is equivalent to the force of an equal, opposite charge attwice the distance 2d. Thus, it is described by the formula

F =1

· Q2

4Se0 (2d)2

First, the force for a given charge Q is measured as a function ofthe distance d. The measurement is then repeated with half thecharge. The aim of the evaluation is to confirm the proportionali-ties

F “ 1and F “ Q2.

d2

P3.

1.4.

2

P3.

1.4.

3


99


516 37 Electrostatic accessories 1 1

516 31 Vertically adjustable stand 1 1

314 251 Newton meter 1 1

314 261 Force sensor 1 1

314 265 Support for conductor loops 1




300 42 Stand rod, 47 cm 1 1



541 04 Plastic rod 1

541 21 Leather 1

500 410 Connection lead, 25 cm, yellow/green 1




P 3.1.5Charge distributions onelectrical conductors

P 3.1.5.1 Investigating the charge distri-bution on the surface of elec-trical conductors

P 3.1.5.2 Electrostatic induction with thehemispheres after Cavendish

Electrostatic induction with the hemispheres after Cavendish (P 3.1.5.2)

In static equilibrium, the interior of a metal conductor or a hollowbody contains neither electric fields nor free electron charges.On the outer surface of the conductor, the free charges are dis-tributed in such a way that the electric field strength is perpen-dicular to the surface at all points, and all points have equalpotential.

In the first experiment, an electric charge is collected from acharged hollow metal sphere using a charge spoon, and meas-ured using a coulomb meter. It becomes apparent that the chargedensity is greater, the smaller the bending radius of the surfaceis. This experiment also shows that no charge can be taken fromthe interior of the hollow body.

The second experiment reconstructs a historic experiment firstperformed by Cavendish. A metal sphere is mounted on an insu-lated base. Two hollow hemispheres surround the sphere com-pletely, but without touching it. When one of the hemispheres ischarged, the charge distributes itself uniformly over both hemi-spheres, while the inside sphere remains uncharged. If the insidesphere is charged and then surrounded by the hemispheres, thetwo hemispheres again show equal charges, and the insidesphere is uncharged.

P3.

1.5.

1

P3.

1.5.

2

100


543 07 Conical conductor on insulated rod 1

543 02 Sphere on insulated rod 1

543 05 Pair of hemispheres 1


542 52 Metal plate on insulating rod 1

521 70 High voltage power supply 10 kV 1 1

501 05 High voltage cable, 1 m 1 1


562 791 Plug-in unit 230 V/12 V AC/20 W; with female plug 1 1

578 25 STE capacitor 1 nF, 630 V 1 1


Voltmeter, DC, U ≤ ± 8 V, e. g.531 100 Multimeter METRAmax 2 1 1

340 89 Coupling plug 1



540 52 Demonstration insulator 1









501 43 Connection lead, 200 cm, yellow-green 1 1

Determining the capacitance of a sphere in free space (P 3.1.6.1)

P 3.1.6

P 3.1.6.1 Determining the capacitance ofa sphere in free space

P 3.1.6.2 Determining the capacitance ofa sphere in front of a metalplate

Definition of capacitance

The potential difference U of a charged conductor in an insulat-ed mounting in free space with reference to an infinitely distantreference point is proportional to the charge Q of the body. Wecan express this using the relationship

Q = C · U

and call C the capacitance of the body. Thus, for example, thecapacitance of a sphere with the radius r in a free space is

C = 4Se0 · r

because the potential difference of the charged sphere with re-spect to an infinitely distant reference point is

U =1

· Q

4Se0 r

where e0 = 8.85 · 10-12 As/Vm (permittivity).

The first experiment determines the capacitance of a sphere in afree space by charging the sphere with a known high voltage Uand measuring its charge Q using an electrometer amplifierconnected as a coulomb meter. The measurement is conductedfor different sphere radii r. The aim of the evaluation is to verifythe proportionalities

Q “ U and C “ r.

The second experiment shows that the capacitance of a bodyalso depends on its environment, e. g. the distance to otherearthed conductors. In this experiment, spheres with the radii rare arranged at a distance s from an earthed metal plate andcharged using a high voltage U. The capacitance of the arrange-ment is now

C = 4Se0 · r · ( 1 + r ).2s

The aim of the evaluation is to confirm the proportionality be-tween the charge Q and the potential difference U at any givendistance s between the sphere and the metal plate.

P3.

1.6.

1

P3.

1.6.

2


101


546 12 Faraday's cup 1 1

543 00 Set of 3 conducting spheres 1 1

587 66 Reflection plate, 50 cm x 50 cm 1


501 05 High voltage cable, 1 m 1 1


562 791 Plug-in unit 230 V/12 V AC/20 W; with female plug 1 1



Voltmeter, DC, U ≤ ± 8 V, e. g.531 100 Multimeter METRAmax 2 1 1










501 43 Connection lead, 200 cm, yellow-green 1 1

590 13 Insulated stand rod, 25 cm 1 1

300 42 I Stand rod, 47 cm I I 1


P 3.1.7Plate capacitor

P 3.1.7.1 Determining the capacitance ofa plate capacitor – measuring the charge with theelectrometer amplifier

P 3.1.7.2 Parallel and series connectionof capacitors – measuring the charge with theelectrometer amplifier

Determining the capacitance of a plate capacitor – measuring the charge with the electrometer amplifier (P 3.1.7.1)

A plate capacitor is the simplest form of a capacitor. Its capaci-tance depends on the plate area A and the plate spacing d. Thecapacitance increases when an insulator with the dielectric con-stant er is placed between the two plates. The total capacitanceis

C = ere0 ·A

d

where e0 = 8.85 · 10-12 As/Vm (permittivity).

In the first experiment, this relationship is investigated using ademountable capacitor assembly with variable geometry. Ca-pacitor plates with the areas A = 40 cm2 and A = 80 cm2 can beused, as well as various plate-type dielectrics. The distance canbe varied in steps of one millimeter.

The second experiment determines the total capacitance C of thedemountable capacitor with the two plate pairs arranged at afixed distance and connected first in parallel and then in series,compares these with the individual capacitances C1 and C2 ofthe two plate pairs. The evaluation confirms the relationship

C = C1 + C2

for parallel connection and

1=

1+

1

C C1 C2

for serial connection.

P3.

1.7.

1

P3.

1.7.

2

102


544 23 Demountable capacitor 1 1

522 27 Power supply 450 V AC 1 1

504 48 Two-way switch 1 1

Voltmeter, DC, U = ± 8 V, e. g.531 100 Multimeter METRAmax 2 1 1

Voltmeter, DC, U ≤ 300 V, e. g.531 100 Multimeter METRAmax 2 1 1







Determining the capacitance of a plate capacitor – measuring the charge with the I-measuring amplifier D (P 3.1.7.3)

P 3.1.7

P 3.1.7.3 Determining the capacitance ofa plate capacitor – measuring the charge with theI-measuring amplifier D

Plate capacitor

Calculation of the capacitance of a plate capacitor using the for-mula

C = e0 · A

d

A: plate aread: plate spacingwhere e0 = 8.85 · 10-12 As/Vm (permittivity)

ignores the fact that part of the electric field of the capacitorextends beyond the edge of the plate capacitor, and that conse-quently a greater charge is stored for a specific potential differ-ence between the two capacitors. For example, for a plate ca-pacitor grounded on one side and having the area

A = S · r2

the capacitance is given by the formula

C = e0 (S · r2+ 3.7724 · r + r · ln (Sr ) + . . .)d d

In this experiment, the capacitance C of a plate capacitor ismeasured as a function of the plate spacing d with the greatestpossible accuracy. This experiment uses a plate capacitor with aplate radius of 13 cm and a plate spacing which can be conti-nuously varied between 0 and 70 mm. The aim of the evaluationis to plot the measured values in the form

C = f ( 1)d

and compare them with the values to be expected according totheory.

P3.

1.7.

3


103


544 22 Parallel plate capacitor 1

521 65 DC power supply 0 ....500 V 1

504 48 Two-way switch 1

532 00 I-Measuring amplifier D 1

Voltmeter, DC , U ≤ 10 V, e. g.531 100 Multimeter METRAmax 2 1

Voltmeter, DC , U ≤ 500 V, e. g.531 712 Multimeter METRAmax 3 1

536 221 Measuring resister 100 MV 1

500 421 Connecting lead, 50 cm, red 1



Fundamentals of electricity Electricity

P 3.2.1Charge transfer with drops of water

P 3.2.1.1 Generating an electric current through the motion of charged drops of water

Generating an electric current through the motion of charged drops of water (P 3.2.1.1)

Each charge transport is an electric current. The electrical cur-rent strength (or more simply the “current”)

I =DQ

Dt

is the charge DQ transported per unit of time Dt. For example, ina metal conductor, DQ is given by the number DN of free elec-trons which flow through a specific conductor cross-section perunit of time Dt. We can illustrate this relationship using chargedwater droplets.

In the experiment, charged water drops drip out of a burette at aconstant rate

N. =

DN

Dt

N: number of water drops

into a Faraday’s cup, and gradually charge the latter. Each indi-vidual drop of water transports approximately the same charge q.The total charge Q in the Faraday’s cup is measured using anelectrometer amplifier connected as a coulomb meter. Thischarge shows a step-like curve as a function of the time t, as canbe recorded using a YT recorder. At a high drip rate N, a verygood approximation is

Q = N.· q · t.

The current is then

I = N.· q

P3.

2.1.

1

104


665 843 Burette, 10 ml: 0.05, with lateral stopcock, clear glass, Schellbach blue line 1


522 27 Power supply 450 V DC 1




578 26 STE capacitor 2.2 nF, 160 V 1


578 22 STE capacitor 100 pF, 630 V 1

Voltmeter, DC, U = ± 8 V, e. g.531 100 Multimeter METRAmax 2 1

YT-recorder, single channel 1*

664120 Beaker, 50 ml, ss, plastic 1

301 21 Stand base MF 2




666 555 Universal clamp, 0 ... 80 mm dia. 1

550 41 Constantan wire, 100 m, 0.25 mm Ø 1

501 641 Set of 6 two-way plug adapters, red 1








575 703

Verifying Ohm’s law (P 3.2.2.1)

P 3.2.2

P 3.2.2.1 Verifying Ohm’s law

Ohm’s law

In circuits consisting of metal conductors, Ohm’s law

U = R · I

represents a very close approximation of the actual circum-stances. In other words, the voltage drop U in a conductor isproportional to the current I through the conductor. The pro-portionality constant R is called the resistance of the conduc-tor. For the resistance, we can say

R = U ·s

A

r: resistivity of the conductor material,s: length of wire, A: cross-section of wire

This experiment verifies the proportionality between the currentand voltage for metal wires of different materials, thicknessesand lengths, and calculates the resistivity of each material.

P3.

2.2.

1

Electricity Fundamentals of electricity

105


550 57 Apparatus for resistance measurements 1

521 45 DC power supply 0....+/- 15 V 1

Ammeter, DC, I ≤ 3 A, e. g.531 100 Multimeter METRAmax 2 1






P 3.2.3Kirchhoff’s laws

P 3.2.3.1 Measuring current and voltageat resistors connected in parallel and in series

P 3.2.3.2 Voltage division with a potentiometer

P 3.2.3.3 Principle of a Wheatstone bridge

Measuring current and voltage at resistors connected in parallel and in series (P 3.2.3.1)

Kirchhoff’s laws are of fundamental importance in calculating thecomponent currents and voltages in branching circuits. The so-called “node rule” states that the sum of all currents flowing intoa particular junction point in a circuit is equal to the sum of allcurrents flowing away from this junction point. The “mesh rule”states that in a closed path the sum of all voltages through theloop in any arbitrary direction of flow is zero. Kirchhoff’s laws areused to derive a system of linear equations which can be solvedfor the unknown current and voltage components.

The first experiment examines the validity of Kirchhoff’s laws incircuits with resistors connected in parallel and in series. Theresult demonstrates that two resistors connected in series havea total resistance R

R = R1 + R2

while for parallel connection of resistors, the total resistance R is

1=

1+

1

R R1 R2

In the second experiment, a potentiometer is used as a voltagedivider in order to tap a lower voltage component U1 from a volt-age U. U is present at the total resistance of the potentiometer. Ina no-load, zero-current state, the voltage component

U1 =R1 · UR

can be tapped at the variable component resistor R1. The rela-tionship between U1 and R1 at the potentiometer under load is nolonger linear.

The third experiment examines the principle of a Wheatstonebridge, in which “unknown” resistances can be measuredthrough comparison with “known” resistances.

P3.

2.3.

3

P3.

2.3.

2

P3.

2.3.

1

106


Plug-in board A4 1 1 1

577 28 STE resistor 47 Ö, 2 W 1



577 36 STE resistor 220 Ö, 2 W 1 1

577 38 STE resistor 330 Ö, 2 W 1 2

57740 STE resistor 470 Ö, 2 W 1 1 1

57744 STE resistor 1 kÖ, 2 W 1 1

577 53 STE resistor 5.6 kÖ, 2 W 1

577 56 STE resistor 10 kÖ, 0.5 W 1

577 68 STE resistor 100 kÖ, 0.5 W 1

577 92 STE potentiometer 1 kÖ, 1 W 1

577 90 STE potentiometer 220 Ö, 3 W 1

501 48 Set of 10 bridging plugs 1 1 1

521 45 DC power supply 0 .... +/- 15 V 1 1 1

Ammeter, DC, I ≤ 1 A, e. g.531 100 Multimeter METRAmax 2

Voltmeter, DC, U ≤ 15 V, e. g.531 100 Multimeter METRAmax 2


1 1

1 1

Ammeter, DC, I <= 10 µA, cero point middle, e.g.531 100 Multimeter METRAmax 2 1

III

IIIIII

III

576 74

Determining resistances using a Wheatstone bridge (P 3.2.3.4)

P 3.2.3

P 3.2.3.4 Determining resistances usinga Wheatstone bridge

Kirchhoff’s laws

In modern measuring practice, the bridge configuration devel-oped in 1843 by Ch. Wheatstone is used almost exclusively.

In this experiment, a voltage U is applied to a 1 m long measu-ring wire with a constant cross-section. The ends of the wire areconnected to an unknown resistor Rx and a variable resistor Rarranged behind it, whose value is known precisely. A slidingcontact divides the measuring wire into two parts with the lengthss1 and s2. The slide contact is connected to the node between Rxand R via an ammeter which is used as a zero indicator. Once thecurrent has been regulated to zero, the relationship

Rx =s1 · Rs2

applies. Maximum accuracy is achieved by using a symmetricaexperiment setup, i. e. when the slide contact over the measuringwire is set in the middle position so that the two sections s1 ands2 are the same length.

P3.

2.3.

4


107

Cat. no. Description

536 02 Demonstration bridge, 1 m long 1

536 121 Measuring resistor 10 Ö, 4 W 1

536 131 Measuring resistor 100 Ö, 4 W 1

536 141 Measuring resistor 1 kÖ, 4 W 1

536 776 Resistance decade 0...1 kÖ 1

536 777 Resistance decade 0...100 Ö 1



521 45 DC power supply 0....+/- 15 V 1

Ammeter, DC, I ≤ 3 mA, D I = 1 mA531 13 Zero point center, Galvanometer C.A 403 1

501 28 Connecting lead, Ø 2,5 mm2, 50 cm, black 3


Circuit diagram of Wheatstone bridge

Principles of electricity Electricity

P 3.2.4Circuits with electrical measuring instruments

P 3.2.4.1 The ammeter as an ohmic resistor in a circuit

P 3.2.4.2 The voltmeter as an ohmic resistor in a circuit

The ammeter as an ohmic resistor in a circuit (P 3.2.4.1)

One important consequence of Kirchhoff’s laws is that the inter-nal resistance of an electrical measuring instrument affects therespective current or voltage measurement. Thus, an ammeterincreases the overall resistance of a circuit by the amount of itsown internal resistance and thus measures a current value whichis too low whenever the internal resistance is above a negligiblelevel. A voltmeter measures a voltage value which is too low whenits internal resistance is not great enough with respect to theresistance at which the voltage drop is to be measured.

In the first experiment, the internal resistance of an ammeter isdetermined by measuring the voltage which drops at the amme-ter during current measurement. It is subsequently shown thatthe deflection of the ammeter pointer is reduced by half, or thatthe current measuring range is correspondingly doubled, byconnecting a second resistor equal to the internal resistance inparallel to the ammeter.

The second experiment determines the internal resistance of avoltmeter by measuring the current flowing through it. In thisexperiment, the measuring range is extended by connecting asecond resistor with a value equal to the internal resistance tothe voltmeter in series.

P3.

2.4.

2

P3.

2.4.

1

108


576 74 Plug-in board A4 1 1


577 52 STE resistor 4.7 kV, 2 W 1 1

577 71 STE resistor 220 kV, 0.5 W 1

577 75 STE resistor 680 kV, 0.5 W 1

501 48 Set of 10 bridging plugs 1 1

521 45 DC power supply 0....+/- 15 V 1 1

531 51 Multimeter MA 1 H 2 2


Determining the Faraday constant (P 3.2.5.1)

P 3.2.5

P 3.2.5.1 Determining the Faraday constant

Conducting electricity by means of electrolysis

In electrolysis, the processes of electrical conduction entailsliberation of material. The quantity of liberated material isproportional to the transported charge Q flowing through theelectrolyte. This charge can be calculated using the Faradayconstant F, a universal constant which is related to the unitcharge e by means of Avogadro’s number NA.

F = NA · e

When we insert the molar mass n for the material quantity andtake the valence z of the separated ions into consideration, weobtain the relationship

Q = n · F · z

In this experiment, a specific quantity of hydrogen is produced inan electrolysis apparatus after Hofmann to determine the Fara-day constant. The valance of the hydrogen ions is z = 1. Themolar mass n of the liberated hydrogen atoms is calculated usingthe laws of ideal gas on the basis of the volume V of the hydro-gen collected at an external pressure p and room temperature T:

n = 2 · pVRT

where R = 8.314 J (universal gas constant)mol · K

At the same time, the electric work W is measured which isexpended for electrolysis at a constant voltage U0. The transport-ed charge quantity is then

Q = W .U0

P3.

2.5.

1


109


664 350 Water electrolysis unit 1

382 36 Thermometer, -10 to + 40 °C 1

531 83 Joule and wattmeter 1

521 45 DC power supply 0....+/- 15 V 1


649 45 Tray, 6 x 5 RE 1

674 792 Sulfuric acid, diluted, 500 ml 1




P 3.2.6Experiments on electrochemistry

P 3.2.6.1 Generating electric current witha Daniell cell

P 3.2.6.2 Measuring the voltage atsimple galvanic elements

P 3.2.6.2 Determining the standardpotentials of correspondingredox pairs

Measuring the voltage at galvanic elements (P 3.2.6.2)

In galvanic cells, electrical energy is generated using an electro-chemical process. The electrochemistry workplace enables youto investigate the physical principles which underlie such pro-cesses.

In the first experiment, a total of four Daniell cells are assembled.These consist of one half-cell containing a zinc electrode in aZnSO4 solution and one half-cell containing a copper electrodein a CuSO4 solution. The voltage produced by multiple cellsconnected in series is measured and compared with the voltagefrom a single cell. The current of a single cell is used to drive anelectric motor.

The second experiment combines half-cells of correspondingredox pairs of the type metal/metal cation to create simple gal-vanic cells. For each pair, the object is to determine which metalrepresents the positive and which one the negative pole, and to

P3.

2.6.

1-3

110


664 394 Electrochemistry workplace measuring unit 1

664 395 Electrochemistry working place 1

661 125 Set of chemicals for electrochemistry 1

measure the voltage between the half-cells. From this, a voltageseries for the corresponding redox pairs can be developed.

The third experiment uses a platinum electrode in 1-mol hydro-chloric acid as a simple standard hydrogen electrode in order topermit direct measurement of the standard potentials of corre-sponding redox pairs of the type metal/metal cation and non-metallic anion/non-metallic substance directly.

Displaying lines of magnetic flux (P 3.3.1.1)

P 3.3.1

P 3.3.1.1 Displaying lines of magneticflux

P 3.3.1.2 Basics of electromagnetism

Basic experiments onmagnetostatics

Magnetostatics studies the spatial distribution of magnetic fieldsin the vicinity of permanent magnets and stationary currents aswell as the force exerted by a magnetic field on magnets andcurrents. Basic experiments on this topic can be carried out with-out complex experiment setups.

In the first experiment, magnetic fields are observed by spread-ing iron filings over a smooth surface so that they align them-selves with the lines of magnetic flux. By this means it becomespossible to display the magnetic field of a straight conductor, themagnetic field of a conductor loop and the magnetic field of acoil.

The second topic combines a number of fundamental experi-ments on electromagnetic phenomena. First, the magnetic fieldsurrounding a current-carrying conductor is illustrated. Then theforce exerted by two current-carrying coils on each other and thedeflection of a current-carrying coil in the magnetic field of asecond coil are demonstrated.

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Electricity Magnetostatics

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560 70 Magnetic field demonstration set 1

56015 Equipment for electromagnetism 1

513 11 Magnetic needle 1

513 51 Base for magnetic needle 1

510 21 Horse-shoe magnet, with yoke 1

51012 Pair of round magnets 1

514 72 Shaker for iron filings 1

514 73 Iron filings 250 g 1

521 55 High current power supply 1 1





540 52 Demonstration insulator 2

30011 Saddle base 2

501 26 Connecting lead, Ø 2,5 mm2, 50 cm, blue 1





Deflection of a conductor by a permanent magnet (P 3.3.1.2)


Magnetostatics Electricity

P 3.3.2Magnetic dipole moment

P 3.3.2.1 Measuring the magnetic dipolemoments of long magneticneedles

Measuring the magnetic dipole moments of long magnetic needles (P 3.3.2.1)

Although only magnetic dipoles occur in nature, it is useful insome cases to work with the concept of highly localized “mag-netic charges”. Thus, we can assign pole strengths or “magneticcharges” qm to the pole ends of elongated magnetic needles onthe basis of their length d and their magnetic moment m:

qm =m

d

The pole strength is proportional to the magnetic flux F:

F = m0 · qm

where m0 = 4S · 10-7 Vs(permeability)

Am

Thus, for the spherical surface with a small radius r around thepole (assumed as a point source), the magnetic field is

B =1

· qm

4Sm0 r2

At the end of a second magnetic needle with the pole strengthq’m, the magnetic field exerts a force

F = q’m · B

and consequently

F =1

· qm · q’m

4Sm0 r2

In formal terms, this relationship is equivalent to Coulomb’s lawgoverning the force between two electrical charges.

This experiment measures the force F between the pole ends oftwo magnetized steel needles using the torsion balance. Theexperiment setup is similar to the one used to verify Coulomb’slaw. The measurement is initially carried out as a function of thedistance r of the pole ends. To vary the pole strength qm, the poleends are exchanged, and multiple steel needles are mountednext to each other in the holder.

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516 01 Torsion balance after Schürholz 1

510 50 Bar magnet 60 x 13 x 5 mm 1

516 21 Accessories for magnetostatics 1

516 04 Scale, on stand, 1 m long 1


450 51 Lamp, 6 V/30 W 1


Transformer, 6 V AC, 12 V AC / 30 W 1




521 210

Measuring the force acting on current-carrying conductors in a homogeneous magnetic field – Recording with CASSY(P 3.3.3.2)

P 3.3.3

P 3.3.3.1 Measuring the force acting oncurrent-carrying conductors in the field of a horseshoe magnet

P 3.3.3.2 Measuring the force acting oncurrent-carrying conductors ina homogeneous magnetic field– Recording with CASSY

P 3.3.3.3 Measuring the force acting oncurrent-carrying conductors inthe magnetic field of an air coil– Recording with CASSY

P 3.3.3.4 Basic measurements for the electrodynamic definitionof the ampere

Effects of force in a magnetic field

To measure the force acting on a current-carrying conductor in amagnetic field, conductor loops are attached to a force sensor.The force sensor contains two bending elements arranged inparallel with four strain gauges connected in a bridge configura-tion; their resistance changes in proportion to the force when astrain is applied. The force sensor is connected to a newtonmeter, or alternatively to the CASSY computer interface devicevia a bridge box. When using CASSY a 30 ampere box is recom-mended for current measurement.In the first experiment, the conductor loops are placed in themagnetic field of a horseshoe magnet. This experiment measuresthe force F as a function of the current I, the conductor length sand the angle a between the magnetic field and the conductor,and reveals the relationship

F = I · s · B sin aIn the second experiment, a homogeneous magnetic field isgenerated using an electromagnet with U-core and pole-pieceattachment. This experiment measures the force F as a functionof the current I. The measurement results for various conductorlengths s are compiled and evaluated in a graph.The third experiment uses an air coil to generate the magneticfield. The magnetic field is calculated from the coil parametersand compared with the values obtained from the force measure-ment.The object of the fourth experiment is the electrodynamic defini-tion of the ampere. Here, the current is defined on the basis ofthe force exerted between two parallel conductors of infinitelength which carry an identical current. When r represents thedistance between the two conductors, the force per unit of lengthof the conductor is:

F= m0 ·

l2s 2S · r

This experiment uses two conductors approx. 30 cm long, placedjust a few millimeters apart. The forces F are measured as a func-tion of the different current levels I and distances r.

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Electricity Magnetostatics

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1



562 25 Pole-shoe yoke 1

314 265 Support for conductor loops 1 1 1 1

516 34 Conductor loops for force measurement 1 1 1

516 244 Field coil, diameter 120 mm 1

516 249 Stand for coils and tubes 1

516 33 Set of conductors for Ampere definition 1

516 31 Vertically adjustable stand 1

Current source, DC, I ≤ 20 A, e. g.521 55 High current power supply 1 1 1 1

Current source, DC, I ≤ 5 A, e.g.521 50 AC/DC power supply 0....15 V 1 1

314 251 Newtonmeter 1 1

314 261 Force sensor 1


524 043 Sensor box - 30 Amperes 1 1

524 200 CASSY Lab 1 1



300 42 Stand rod, 47 cm 1 1 1 1

301 01 Leybold multiclamp 1 1 1 1

501 25 Connecting lead, Ø 2,5 mm2, 50 cm, red 1

501 26 Connecting lead, Ø 2,5 mm2, 50 cm, blue 2 1 1

501 30 Connecting lead, Ø 2.5 mm2, 100 cm, red 1 2 2 1

501 31 Connecting lead, Ø 2.5 mm2, 100 cm, blue 1 2 2 1

additionally required:PC with Windows 95/NT or higher 1 1

510 22 Large horse-shoe magnet, with yoke

1

1

524 060 Force sensor S, ± 1 N 1 1

Magnetostatics Electricity

P 3.3.4Biot-Savart’s law

P 3.3.4.1 Measuring the magnetic fieldfor a straight conductor and forcircular conductor loops

P 3.3.4.2 Measuring the magnetic field ofan air coil

P 3.3.4.3 Measuring the magnetic field ofa pair of coils in the Helmholtzconfiguration

Measuring the magnetic field for a straight conductor and for circular conductor loops (P 3.3.4.1)

In principle, it is possible to calculate the magnetic field of anycurrent-carrying conductor using Biot and Savart’s law. However,analytical solutions can only be derived for conductors with cer-tain symmetries, e. g. for an infinitely long straight wire, a circularconductor loop and a cylindrical coil. Biot and Savart’s law canbe verified easily using these types of conductors.

In the first experiment, the magnetic field of a long, straight con-ductor is measured for various currents I as a function of thedistance r from the conductor. The result is a quantitative confir-mation of the relationship

B =m0 ·

l2S r

In addition, the magnetic fields of circular coils with different radiiR are measured as a function of the distance x from the axisthrough the center of the coil. The measured values are com-pared with the values which are calculated using the equation

B =m0 ·

l · R2

2 (R2 + x2)32

All measurements can be carried out using an axial B-probe.This device contains a Hall sensor which is extremely sensitive tofields parallel to the probe axis. A tangential B-probe, in whichthe Hall sensor is sensitive perpendicular to the probe axis, isrecommended for further investigations.

The second experiment investigates the magnetic field of an aircoil in which the length L can be varied for a constant number ofturns N. For the magnetic field the relationship

B = m0 · l · NL

applies.

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The third experiment examines the homogeneity of the magneticfield in a pair of Helmholtz coils. The magnetic field along the axisthrough the coil centers is recorded in several measurementseries; the spacing a between the coils is varied from measure-ment series to measurement series. When a is equal to the coilradius, the magnetic field is essentially independent of the loca-tion x on the coil axis.


516 235 Set of 4 current conductors 1

516 242 Coil with variable number of turns per unit length 1


Pair of Helmholtz coils 1

516 62 Teslameter 1 1 1

516 61 Axial B-probe 1 1 1

516 60 Tangential B-probe 1*

501 16 Multicore cable, 6-pole, 1.5 m long 1 1 1



460 21 Holder for plug-in elements 1



30011 Saddle base 1

501 644 Set of 6 two-way plug adapters, black 1


501 30 Connecting lead, Ø 2.5 mm2, 100 cm, red 1 1 1

501 31 Connecting lead, Ø 2.5 mm2, 100 cm, blue 1 1 1


1

555 604

Generating a voltage surge in a conductor loop with a moving permanent magnet (P 3.4.1.1)

P 3.4.1

P 3.4.1.1 Generating a voltage surge in aconductor loop with a movingpermanent magnet

Voltage impulse

Each change in the magnetic flux F through a conductor loopinduces a voltage U, which has a level proportional to the changein the flux. Such a change in the flux is caused e. g. when a per-manent magnet is moved inside a fixed conductor loop. In thiscase, it is common to consider not only the time-dependent volt-age

U = dFdt

but also the voltage surge

t2

∫ U(t)dt = F(t1) – F(t2)t1

This corresponds to the difference in the magnetic flux densitiesbefore and after the change.In this experiment, the voltage surge is generated by manuallyinserting a bar magnet into an air coil, or pulling it out of a coil.The curve of the voltage U over time is measured and the areainside the curve is evaluated. This is always equal to the flux F ofthe permanent magnet inside the air coil independent of thespeed at which the magnet is moved, i. e. proportional to thenumber of turns of the coil for equal coil areas.

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Electricity Electromagnetic induction

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51011 Round magnet 3





524 200 CASSY Lab 1



Electromagnetic induction Electricity

P 3.4.2Induction in a moving conductor loop

P 3.4.2.1 Measuring the induction voltage in a conductor loopmoved through a magnetic field

Measuring the induction voltage in a conductor loop moved through a magnetic field (P 3.4.2.1)

When a conductor loop with the constant width b is withdrawnfrom a homogeneous magnetic field B with the speed

v =dxdt

the magnetic flux changes over the time dt by the value

dF = -B · b · dx

This change in flux induces the voltage

U = B · b · v

in the conductor loop. In this experiment, a slide on which induc-tion loops of various widths are mounted is moved between thetwo pole pieces of a magnet. The object is to measure the induc-tion voltage U as a function of the magnetic flux density B, thewidth b and the speed v of the induction loops. The aim of theevaluation is to verify the proportionalities

U “ B, U “ b and U “ v.

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516 40 Induction apparatus 1




532 13 Microvoltmeter 1

Induction voltage in a moved conductor loop

Measuring the induction voltage in a conductor loop for a variable magnetic field (P 3.4.3.1)

P 3.4.3

P 3.4.3.1 Measuring the induction voltage in a conductor loop fora variable magnetic field

Induction by means of a variable magnetic field

A change in the homogeneous magnetic field B inside a coil withN1 windings and the area A1 over time induces the voltage

U = N1 · A1 · dB

.dt

in the coil. In this experiment, induction coils with different areasand numbers of turns are arranged in a cylindrical field coilthrough which alternating currents of various frequencies, ampli-tudes and signal forms flow. In the field coil, the currents gener-ate the magnetic field

B = m0 · N2 · lL2

where m0 = 4S · 10–7 Vs (permeability)Am

and I(t) is the time-dependent current level, N2 the number ofturns and L2 the overall length of the coil. The curve over time U(t)of the voltages induced in the induction coils is recorded usingthe computer-based CASSY measuring system. This experimentexplores how the voltage is dependent on the area and the num-ber of turns of the induction coils, as well as on the frequency,amplitude and signal form of the exciter current.

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516 244 Field coil, diameter 120 mm 1

516 241 Set of induction coils 1

521 56 Triangular wave-form power supply 1

524 040 mV-Box 1


524 043 Sensor box - 30 Amperes 1

524 200 CASSY Lab 1


501 46 Pair of cables, 50 cm, black 2


Induction in a conduction loop for a variable magnetic field


P 3.4.4Eddy currents

P 3.4.4.1 Waltenhofen’s pendulum:demonstration of an eddy-current brake

P 3.4.4.2 Demonstrating the operatingprinciple of an AC power meter

Waltenhofen’s pendulum: demonstration of an eddy-current brake (P 3.4.4.1)

When a metal disk is moved into a magnetic field, eddy currentsare produced in the disk. The eddy currents generate a magnet-ic field which interacts with the inducing field to resist the motionof the disk. The energy of the eddy currents, which is liberatedby the Joule effect, results from the mechanical work which mustbe performed to overcome the magnetic force.

In the first experiment, the occurrence and suppression of eddycurrents is demonstrated using Waltenhofen’s pendulum. Thealuminum plate swings between the pole pieces of a strong elec-tromagnet. As soon as the magnetic field is switched on, the pen-dulum is arrested when it enters the field. The pendulum oscilla-tions of a slitted plate, on the other hand, are only slightlyattenuated, as only weak eddy currents can form.

The second experiment examines the workings of an alternatingcurrent meter. In principle, the AC meter functions much like anasynchronous motor with squirrel-cage rotor. A rotating alumi-num disk is mounted in the air gap between the poles of twomagnet systems. The current to be measured flows through thebottom magnet system, and the voltage to be measured isapplied to the top magnet system. A moving magnetic field isformed which generates eddy currents in the aluminum disk. Themoving magnetic field and the eddy currents produce an asyn-chronous angular momentum

N1 “ P

proportional to the electrical power P to be measured. The angu-lar momentum accelerates the aluminum disk until it attains equi-librium with its counter-torque

N2 “ CC: angular velocity of disk

generated by an additional permanent magnet embedded in theturning disk. Consequently, at equilibrium

N1 = N2

the angular velocity of the disk is proportional to the electricalpower P.

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560 34 Waltenhofen’s pendulum 1

342 07 Clamp with knife-edge bearings 1



560 31 Pair of bored pole pieces 1

537 32 Rheostat 10 V 1

Ammeter, AC, I ≤531 712 Multimeter METRAmax 3 1

Voltmeter, AC, U ≤531 100 Multimeter METRAmax 2 1

313 07 Stopclock I 30 s/15 min 1



300 51 Stand rod, right-angled 1


501 28 Connecting lead, Ø = 2,5 mm2, 50 cm, black

AC meter model, complete(593 20) for P 3.4.4.2

501 33 I Connecting lead, Ø = 2,5 mm2, 100 cm, black I I 9

521 545 DC Power supply 0...16 V, 5 A 1521 39 Variable extra-low voltage transformer 1

560 32 Rotatable aluminium disc 1562 34 Large coil holder 1



10 A, e.g.

25 V, e.g.



4

1

2

Voltage transformation with a transformer (P 3.4.5.1)

P 3.4.5

P 3.4.5.1 Voltage and current transfor-mation with a transformer

P 3.4.5.2 Voltage transformation with atransformer under load

P 3.4.5.3 Recording the voltage and cur-rent of a transformer underload as a function of time

Transformer

Regardless of the physical design of the transformer, the voltagetransformation of a transformer without load is determined by theratio of the respective number of turns

U2 =N2 (when I2 = 0)

U1 N1

The current transformation in short-circuit operation is inverselyproportional to the ratio of the number of turns

l2 =N2 (when U2 = 0)

l1 N1

The behavior of the transformer under load, on the other hand,depends on its particular physical design. This fact can bedemonstrated using the transformer for students’ experiments.

The aim of the first experiment is to measure the voltage trans-formation of a transformer without load and the current transfor-mation of a transformer in short-circuit mode. At the same time,the difference between an isolating transformer and an auto-transformer is demonstrated.

The second experiment examines the ratio between primary andsecondary voltage in a “hard” and a “soft” transformer underload. In both cases, the lines of magnetic flux of the transformerare revealed using iron filings on a glass plate placed on top ofthe transformer.

In the third experiment, the primary and secondary voltages andthe primary and secondary currents of a transformer under loadare recorded as time-dependent quantities using the computer-based CASSY measuring system. The CASSY software deter-mines the phase relationships between the four quantities direc-tly and additionally calculates the time-dependent power valuesof the primary and secondary circuits.

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562 801 Transformer for students experiments 1 1 1 1

521 35 Variable extra low voltage transformer S 1 1 1

537 32 Rheostat 10 V 1 1 1 1

Ammeter, AC, I ≤ 3 A, e.g.531 100 Multimeter METRAmax 2 1 1

Voltmeter, AC, U ≤ 20 V, e.g.531 100 Multimeter METRAmax 2 1 1


524 011 Power CASSY 1

524 200 CASSY Lab 1 1

459 23 Acryllic glass screen on rod 1

514 72 Shaker for iron filings 1

514 73 Iron filings 250 g 1

500 414 Connecting lead, 25 cm, black 2 1

500 444 Connecting lead, 100 cm, black 6 10 8


Recording the voltage and currentof a transformer under load as afunction of time (P 3.4.5.3b)

6


P 3.4.5Transformer

P 3.4.5.4 Power transmission of a transformer

P 3.4.5.5 Experiments with high currents

P 3.4.5.6 High-voltage experiments witha two-pronged lightning rod

Power transmission of a transformer (P 3.4.5.4a)

As an alternative to the transformer for students’ experiments, thedemountable transformer with a full range of coils is availablewhich simply slide over the arms of the U-core, making themeasily interchangeable. The experiments described for the trans-former for students’ experiments (P 3.4.5.1-3) can of course beperformed just as effectively using the demountable transformer,as well as a number of additional experiments.

The first experiment examines the power transmission of a trans-former. Here, the RMS values of the primary and secondary volt-age and the primary and secondary current are measured on avariable load resistor 0 – 110 Ö using the computer-basedCASSY measuring system. The phase shift between the voltageand current on the primary and secondary sides is determined atthe same time. In the evaluation, the primary power P1, thesecondary power P2 and the efficiency

J = P2

P1

are calculated and displayed in a graph as a function of the loadresistance R.

In the two other experiments, a transformer is assembled inwhich the primary side with 500 turns is connected directly to themains voltage. In a melting ring with one turn or a welding coilwith five turns on the secondary side, extremely high currents ofup to 100 A can flow, sufficient to melt metals or spot-weld wires.Using a secondary coil with 23,000 turns, high voltages of up to10 kV are generated, which can be used to produce electric arcsin horn-shaped spark electrodes.

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562 11 U-core with yoke 1 1 1 1

562 12 Clamping device 1 1 1 1

562 13 Coil with 250 turns 2 2

562 17 Coil with 23,000 turns 1

562 21 Mains coil with 500 turns for 230 V 1 1


562 31 Set of 5 sheet metal strips 1

562 20 Ring-shaped melting ladle 1

562 32 Melting ring 1


537 34 Rheostat 100 V 1 1

524 011 Power-CASSY 1


524 200 CASSY Lab 1 1




Measuring the earth’s magnetic field with a rotating induction coil (earth inductor) (P 3.4.6.1)

P 3.4.6

P 3.4.6.1 Measuring the earth’s magneticfield with a rotating inductioncoil (earth inductor)

Measuring the earth’smagnetic field

When a circular induction loop with N turns and a radius R ro-tates in a homogeneous magnetic field B around its diameter asits axis, it is permeated by a magnetic flux of

F(t) = N · S · R2 · n(t) · Bn(t) = normal vector of a rotating loop

If the angular velocity v is constant, we can say that

F(t) = N · S · R2 · Bb · cos vt

Where Bb is the effective component of the magnetic field per-pendicular to the axis of rotation. We can determine the magneticfield from the amplitude of the induced voltage

U0 = N · S · R2 · Bb · v

To achieve the maximum measuring accuracy, we need to usethe largest possible coil.

In this experiment the voltage U(t) induced in the earth’s magnet-ic field for various axes of rotation is measured using the com-puter-based CASSY measuring system. The amplitude andfrequency of the recorded signals and the respective activecomponent Bb are used to calculate the earth’s magnetic field.The aim of the evaluation is to determine the total value, the hori-zontal component and the angle of inclination of the earth’smagnetic field.

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347 35 Experiment motor 1*

347 36 Control unit for experiment motor 1*


524 040 mV-box 1

524 200 CASSY Lab 1

301 05 Bench clamp with pin 1*





555 604

Electrical machines Electricity

P 3.5.1Basic experiments on electrical machines

P 3.5.1.1 Investigating the interactions offorces of rotors and stators

P 3.5.1.2 Simple induction experimentswith electromagnetic rotors andstators

Simple induction experiments with electromagnetic rotors and stators (P 3.5.1.2)

The term “electrical machines” is used to refer to both motorsand generators. Both devices consist of a stationary stator and arotating armature or rotor. The function of the motors is due to theinteraction of the forces arising through the presence of a cur-rent-carrying conductor in a magnetic field, and that of the gene-rators is based on induction in a conductor loop moving within amagnetic field.

The action of forces between the magnetic field and the conduc-tor is demonstrated in the first experiment using permanent andelectromagnetic rotors and stators. A magnet model is used torepresent the magnetic fields. The object of the second experi-ment is to carry out qualitative measurements on electromagnet-ic induction in electromagnetic rotors and stators.

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563 480 Electrical motor and generator models, basic set 1 1

727 81 Basic machine unit 1

560 61 Cubical magnet model 1

521 48 AC/DC power supply 0....12 V, 230 V/50 Hz 1

Voltmeter, DC, |U| ≤ 3 V, e. g.531 100 Multimeter METRAmax 2




1

1

Generating AC voltage with a revolving-field generator (dynamo) and a revolving-armature generator (P 3.5.2.1)

P 3.5.2

P 3.5.2.1 Generating AC voltage with arevolving-field generator (dynamo) and a revolving-armature generator

P 3.5.2.2 Generating DC voltage with arevolving-armature generator

P 3.5.2.3 Generating AC voltage with apower-plant generator (generator with electromagneticrevolving field)

P 3.5.2.4 Generating voltage with an AC-DC generator (generator withelectromagnetic revolvingarmature)

P 3.5.2.5 Generating voltage with self-excited generators

Electric generators

Electric generators exploit the principle of electromagneticinduction discovered by Faraday to convert mechanical intoelectrical energy. We distinguish between revolving-armaturegenerators (excitation of the magnetic field in the stator, induc-tion in the rotor) and revolving-field generators (excitation of themagnetic field in the rotor, induction in the stator).

Both types of generators are assembled in the first experimentusing permanent magnets. The induced AC voltage U is meas-ured as a function of the speed f of the rotor. Also, the electricalpower P produced at a fixed speed is determined as a functionof the load resistance R.

The second experiment demonstrates the use of a commutator torectify the AC voltage generated in the rotor of a rotating-arma-ture generator. The number of rectified half-waves per rotor revo-lution increases when the two-pole rotor is replaced with a three-pole rotor.

The third and fourth experiments investigate generators whichuse electromagnets instead of permanent magnets. Here, theinduced voltage depends on the excitation current of the magne-tic field. The excitation current can be used to vary the generatedpower without changing the speed of the rotor or the frequencyof the AC voltage. This principle is used in power-plant genera-tors. In the AC/DC generator, the voltage can also be tapped viathe commutator in rectified form.

The final experiment examines generators in which the magneticfield of the stator is amplified by the generator current by meansof self-excitation. The stator and rotor windings are conductivelyconnected with each other. We distinguish between series-wound generators, in which the rotor, stator and load are allconnected in series, and shunt-wound generators, in which thestator and the load are connected in parallel to the rotor.

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Electricity Electrical machines

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563 480 Electrical motor and generator models, basic set 1 1 1 1 1 1 1 1

563 23 Three-pole rotor 1* 1* 1 1

727 81 Basic machine unit 1 1 1 1 1 1 1 1

563 302 Hand cranked gear 1 1 1 1 1 1 1 1

726 19 Panel frame, SL 85 1 1 1 1

301 300 Demonstration-experiment frame 1 1 1 1

Power supply, DC (stabilized), e.g.521 48 AC/DC power supply 0....12 V 1 1 1 1

537 36 Rheostat 1000 V 1 1

Multimeter, AC/DC, e.g.531 100 Multimeter METRAmax 2 2 1 1 1 2 2 1 1

Digital-analog multimeter 531 291 METRAHit 25 S 1

575 211 Two-channel oscilloscope 303 1* 1*

575 24 Screened cable BNC/4 mm 1* 1*

313 07 Stopclock I 30 s/15 min 1

500 422 Connection lead, 50 cm, blue 1 1


501 46 Pair of cables, 1 m, red and blue 2 2 1 1 2 2 2 2


Electrical machines Electricity

P 3.5.3Electric motors

P 3.5.3.1 Investigating a DC motor withtwo-pole rotor

P 3.5.3.2 Investigating a DC motor withthree-pole rotor

P 3.5.3.3 Investigating a series-woundand shunt-wound universalmotor

P 3.5.3.4 Principle of an AC synchronousmotor

Investigating a DC motor with two-pole rotor (P 3.5.3.1)

Electric motors exploit the force acting on current-carrying con-ductors in magnetic fields to convert electrical energy intomechanical energy. We distinguish between asynchronousmotors, in which the rotor is supplied with AC or DC voltage viaa commutator, and synchronous motors, which have no commu-tator, and whose frequencies are synchronized with the frequen-cy of the applied voltage.

The first experiment investigates the basic function of an electricmotor with commutator. The motor is assembled using a perma-nent magnet as stator and a two-pole rotor. The polarity of the rotorcurrent determines the direction in which the rotor turns. Thisexperiment measures the relationship between the applied voltageU and the no-load speed f0 as well as, at a fixed voltage, the cur-rent I consumed as a function of the load-dependent speed f.

The use of the three-pole rotor is the object of the second exper-iment. The rotor starts turning automatically, as an angularmomentum (torque) acts on the rotor for any position in themagnetic field. To record the torque curve M(f), the speed f of therotor is recorded as a function of a counter-torque M. In addition,the mechanical power produced is compared with the electricalpower consumed.

The third experiment takes a look at the so-called universalmotor, in which the stator and rotor fields are electrically excited.The stator and rotor coils are connected in series (“series-wound”) or in parallel (“shunt-wound”) to a common voltagesource. This motor can be driven both with DC and AC voltage,as the torque acting on the rotor remains unchanged when thepolarity is reversed. The torque curve M(f) is recorded for bothcircuits. The experiment shows that the speed of the shunt-wound motor is less dependent on the load than that of theseries-wound motor.

In the final experiment, the rotor coil of the AC synchronousmotor is synchronized with the frequency of the applied voltageusing a hand crank, so that the rotor subsequently continuesrunning by itself.

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2(b

)

P3.

5.3.

2(a)

P3.

5.3.

1(b

)

P3.

5.3.

1(a)

P3.

5.3.

4(b

)


563 480 Electrical motor and generator models, basic set 1 1 1 1 1 1 1 1

563 23 Three-pole rotor 1 1 1* 1*


563 302 Hand cranked gear 1 1

726 19 Panel frame, SL 85 1 1 1 1


Power supply, AC/DC, U ≤ 20 V, e. g.521 35 Variable low voltage transformer S 1 1 1 1 1 1 1 1

Ammeter, AC/DC, I ≤ 3 A, e. g.531 100 Multimeter METRAmax 2 1 1 1 1 1 1

Voltmeter, AC/DC, U ≤ 20 V, e. g.531 100 Multimeter METRAmax 2 1 1 1 1 1 1

451 281 Stroboscope, 230 V, 50 Hz 1 1 1 1 1 1 1 1

314161 Precision dynamometer, 5.0 N 1 1 1 1

314151 Precision dynamometer, 2.0 N 1 1 1 1

309 50 Demonstration cord, 20 m 1 1 1 1

576 71 Plug-in board section 1 1

579 13 STE toggle switch, single pole 1 1

579 06 STE lamp holder E 10, top 1 1

50518 Incandescent lamp E 10; 24.0 V/3.0 W 1 1

666 470 CPS-holder with bosshead, height adjustable 1 1 1 1

300 41 Stand rod, 25 cm 1 1 1 1

501 45 Pair of cables, 50 cm, red and blue 1 1 1 1 2 2

501 46 Pair of cables, 1 m, red and blue 2 2 2 2 2 2 2 2


Experiments with a three-phase revolving-armature generator (P 3.5.4.1)

P 3.5.4

P 3.5.4.1 Experiments with a three-phaserevolving-armature generator

P 3.5.4.2 Experiments with a three-phaserevolving-field generator

P 3.5.4.3 Comparing star and deltaconnections on a three-phasegenerator

P 3.5.4.4 Assembling synchronous andasynchronous three-phasemotors

Three-phase machines

In the real world, power is supplied mainly through the genera-tion of three-phase AC, usually referred to simply as “three-phase current”. Consequently, three-phase generators andmotors are extremely significant in actual practice. In principle,their function is analogous to that of AC machines. As with ACmachines, we differentiate between revolving-armature andrevolving-field generators, and between asynchronous and syn-chronous motors.

The simplest configuration for generating three-phase current, arevolving-armature generator which rotates in a permanentmagnetic field, is assembled in the first experiment using a three-pole rotor. The second experiment examines the more commonrevolving-field generator, in which the magnetic field of the rotorin the stator coils is induced by phase-shifted AC voltages. Inboth cases, instruments for measuring current and voltage, andfor observing the phase shift for a slowly turning rotor, areconnected between two taps. For faster rotor speeds, the phaseshift is measured using an oscilloscope.

In the third experiment, loads are connected to the three-phasegenerator in star and delta configuration. In the star configura-tion, the relationship

Uaa = öä3Ua0

is verified for the voltages Uaa between any two outer conductorsas well as Ua0 between the outer and neutral conductors. For thecurrents I1 flowing to the loads and the currents I2 flowingthrough the generator coils in delta configuration, the result is

I1 = öä3.I2

The final experiment examines the behavior of asynchronous andsynchronous machines when the direction of rotation is reversed.

Electricity Electrical machines

125

P3.

5.4.

4 (a

)

P3.

5.4.

3 (b

)

P3.

5.4.

3 (a

)

P3.

5.4.

2 (b

)

P3.

5.4.

2 (a

)

P3.

5.4.

1 (b

)

P3.

5.4.

1 (a

)

P3.

5.4.

4 (b

)


563 480 Electric motor and generator models, basic set 1 1 1 1 1 1 1 1

563 481 Electric motor and generator models, supplementary set 1 1 1 1 1 1 1 1

563 12 Short-circuit rotor 1 1


563 302 Hand cranked gear 1 1 1 1 1 1

726 50 Plug-in board 297 x 300 mm 1 1

579 06 STE lamp holder, E10, top 3 3

50514 Set of 10 lamps E 10; 6.0 V/3.0 W 3 3


AC/DC-power supply 521 48 0....12 V, 230 V/50 Hz 1 1 1 1

3-phase extra-low voltage 521 29 transformer 1 1

Multimeter, AC/DC, e.g.531 100 METRAmax 2 3 3 3 3 2 2 1 1

575 211 Two-channel oscilloscope 303 1* 1* 1* 1*

575 24 Screened cable BNC/4 mm 2* 2* 2* 2*

313 07 Stopclock I, 30s/15min 1* 1* 1* 1*

726 19 Panel frame, SL 85 1 1 1 1


500 414 Connecting lead, black, 25 cm 3 3 3 3

501 451 Pair of cables, 50 cm, black 3 3 4 4 6 6 2 2


DC and AC circuits Electricity

P 3.6.1Circuit with capacitor

P 3.6.1.1 Charging and discharging acapacitor when switching DCon and off

P 3.6.1.2 Determining the capacitivereactance of a capacitor in anAC circuit

Charging and discharging a capacitor when switching DC on and off (P 3.6.1.1)

To investigate the behavior of capacitors in DC and AC circuits,the voltage UC at a capacitor is measured using a two-channeloscilloscope, and the current IC through the capacitor isadditionally calculated from the voltage drop across a resistor Rconnected in series. The circuits for conducting these measure-ments are assembled on a plug-in board using the STE plug-insystem. A function generator is used as a voltage source withvariable amplitude and variable frequency.

In the first experiment, the function generator generates periodicsquare-wave signals which simulate switching a DC voltage onand off. The square-wave signals are displayed on channel I ofthe oscilloscope, and the capacitor voltage or capacitor currentis displayed on oscilloscope channel II. The aim of the experi-ment is to determine the time constant

t = R · C

for various capacitances C from the exponential curve of the re-spective charging or discharge current IC.

In the second experiment, an AC voltage with the amplitude U0and the frequency f is applied to a capacitor. The voltage UC(t)and the current IC(t) are displayed simultaneously on the oscil-loscope. The experiment shows that in this circuit the currentleads the voltage by 90°. In addition, the proportionality betweenthe voltage amplitude U0 and the current amplitude I0 is con-firmed, and for the proportionality constant

ZC =U0

I0

the relationship

ZC = – 1

2öf · Cis revealed.

P3.

6.1.

1

P3.

6.1.

2

126

Cat . No. Description





57744 STE resistor 0.1 kV, 2 W 1

57748 STE resistor 2.2 kV, 2 W 1

578 15 STE capacitor 1 µF, 100 V 3 3





Schematic circuit diagram

522 621

Measuring the current in a coil when switching DC on and off (P 3.6.2.1)

P 3.6.2

P 3.6.2.1 Measuring the current in a coilwhen switching DC on and off

P 3.6.2.2 Determining the inductive reac-tance of a coil in an AC circuit

Circuit with coil

To investigate the behavior of coils in DC and AC circuits, thevoltage UL at a coil is measured using a two-channel oscillo-scope, and the current IL through the coil is additionally calculat-ed from the voltage drop across a resistor R connected in series.The circuits for conducting these measurements are assembledon a plug-in board using the STE plug-in system for electrici-ty/electronics. A function generator is used as a voltage sourcewith variable amplitude and variable frequency.

In the first experiment, the function generator generates periodicsquare-wave signals which simulate switching a DC voltage onand off. The square-wave signals are displayed on channel I ofthe oscilloscope, and the coil voltage or coil current is displayedon oscilloscope channel II. The aim of the experiment is to deter-mine the time constant

t =L

R

for different inductances L from the exponential curve of the coilvoltage UL.

In the second experiment, an AC voltage with the amplitude U0and the frequency f is applied to a coil. The voltage UL(t) and thecurrent IL(t) are displayed simultaneously on the oscilloscope.The experiment shows that in this circuit the current lags behindthe voltage by 90°. In addition, the proportionality between thevoltage amplitude U0 and the current amplitude I0 is confirmed,and, for the proportionality constant

ZL =U0

I0

the relationship

ZL = 2π f · L

is revealed.

P3.

6.2.

2

Electricity DC and AC circuits

127




577 20 STE resistor 10 V, 2 W 1 1









Schematic circuit diagram

P3.

6.2.

1

522 621


P 3.6.3Impedance

P 3.6.3.1 Determining the impedance incircuits with capacitors andohmic resistors

P 3.6.3.2 Determining the impedance incircuits with coils and ohmicresistors

P 3.6.3.3 Determining the impedance incircuits with capacitors andcoils

Determining the impedance in circuits with capacitors and ohmic resistors (P 3.6.3.1)

The current I(t) and the voltage U(t) in an AC circuit are meas-ured as time-dependent quantities using a dual-channel oscillo-scope. A function generator is used as a voltage source withvariable amplitude U0 and variable frequency f. The measuredquantities are then used to determine the absolute value of thetotal impedance

Z =U0

I0

and the phase shift f between the current and the voltage.

A resistor R is combined with a capacitor C in the first exper-iment, and an inductor L in the second experiment. These exper-iments confirm the relationship

Zs = öR2 + Z2l and tanfs =

Zl

R

with Zl = –1

resp. Zl = 2öf · L2öf · C

for series connection and

1 1 1 R

ZP

= ö R2+

Zl2

and tanfp =Zl

for parallel connection. The third experiment examines the oscil-lator circuit as the series and parallel connection of capacitanceand inductance. The total impedance of the series circuit

Zs = 2öf · L – 1

2öf · Cdisappears at the resonance frequency

fr = 1

2ö · ßLC ,

P3.

6.3.

2

P3.

6.3.

1

P3.

6.3.

3

128


576 74 Plug-in board A4 1 1 1

57719 STE resistor 001 V, 2 W 1 1


577 32 STE resistor 100 V, 2 W 1 1 1

577 56 STE resistor 10 kV, 0.5 W 1 1



578 16 STE capacitor 4.7 µF, 63 V 1

578 31 STE capacitor 0.1µF, 100 V 1



Function generator S 12, 0.1 Hz to 20 kHz 1 1 1

575 211 Two-channel oscilloscope 303 1 1 1

575 24 Screened cable BNC/4 mm 2 2 2

501 46 Pair of cables, 1 m, red and blue 1 1 1

i.e. at a given current I the total voltage U at the capacitor and thecoil is zero, because the individual voltages UC and UL are equaland opposite. For parallel connection, we can say

1 = 1 – 2öf · C.ZP 2öf · L

At the resonance frequency, the impedance of this circuit is infi-nitely great; in other words, at a given voltage U the total currentI in the incumingine is zero, as the two individual currents IC andIL are equal and opposed.

522 621

Determining capacitive reactance with a Wien measuring bridge (P 3.6.4.1)

P 3.6.4

P 3.6.4.1 Determining capacitive reac-tance with a Wien measuringbridge

P 3.6.4.2 Determining inductive reactance with a Maxwell measuring bridge

Measuring-bridge circuits

The Wheatstone measuring bridge is one of the most effectivemeans of measuring ohmic resistance in DC and AC circuits.Capacitive and inductive reactance can also be determined bymeans of analogous circuits. These measuring bridges consist offour passive bridge arms which are connected to form a rec-tangle, an indicator arm with a null indicator and a supply armwith the voltage source. Inserting variable elements in the bridgearm compensates the current in the indicator arm to zero. Then,for the component resistance values, the fundamental compen-sation condition

Z1 = Z2 · Z3 ,Z4

applies, from which the measurement quantity Z1 is calculated.

The first experiment investigates the principle of a Wien measur-ing bridge for measuring a capacitive reactance Z1. In this confi-guration, Z2 is a fixed capacitive reactance, Z3 is a fixed ohmicresistance and Z4 is a variable ohmic resistance. For zero com-pensation, the following applies regardless of the frequency ofthe AC voltage:

1 =

1 ·

R3

C1 C2 R4

An oscilloscope or an earphone can alternatively be used as azero indicator.

In the second experiment, a Maxwell measuring bridge is assem-bled to determine the inductive reactance Z1. As the resistivecomponent of Z1 is also to be compensated, this circuit is some-what more complicated. Here, Z2 is a variable ohmic resistance,Z3 is a fixed ohmic resistance and Z4 is a parallel connectionconsisting of a capacitive reactance and a variable ohmic resis-tor. For the purely inductive component, the following applies withrespect to zero compensation:

2πf · L1 = R2 · R3 · 2πf · C4

f: AC voltage frequency.

P3.

6.4.

2 (a

)

P3.

6.4.

1 (b

)

P3.

6.4.

1 (a

)

P3.

6.4.

2 (b

)


129


576 74 Plug-in board A4 1 1 1 1

577 01 STE resistor 100 V, 0.5 W 1 1 1 1

577 93 STE 10-turn potentiometer 1 kV 1 1 2 2


578 16 STE capacitor 4.7 µF, 63 V 1 1 1 1

579 29 Earphone, 2 kV 1 1



501 48 Set of 10 bridging plugs 1 1 1 1

Function generator S 12, 0.1 Hz to 20 kHz 1 1 1 1




P 3.6.4.1 P 3.6.4.2

522 621


P 3.6.5Measuring AC voltages and currents

P 3.6.5.1 Frequency response and curveform factor of a multimeter

Frequency response and curve form factor of a multimeter (P 3.6.5.1)

When measuring voltages and currents in AC circuits at higherfrequencies, the indicator of the meter no longer responds inproportion to the voltage or current amplitude. The ratio of thereading value to the true value as a function of frequency is refer-red to as the “frequency response”. When measuring AC volta-ges or currents in which the shape of the signal deviates from thesinusoidal oscillation, a further problem occurs. Depending onthe signal form, the meter will display different current and volt-age values at the same frequency and amplitude. This phe-nomenon is described by the wave form factor.

This experiment determines the frequency response and waveform factor of a multimeter. Signals of a fixed amplitude and vary-ing frequencies are generated using a function generator andmeasured using the multimeter.

P3.

6.5.

1

130


531 100 Multimeter METRAmax 2 2

536 131 Measuring resistor 100 V, 4 W 1


575 211 Two-channel oscilloscope 303 1*

575 24 Screened cable BNC/4 mm 1*



522 621

Measuring the electrical work of an immersion heater using an AC power meter (P 3.6.6.2)

P 3.6.6

P 3.6.6.1 Determining the heating powerof an ohmic load in an AC circuit as a function of theapplied voltage

P 3.6.6.2 Measuring the electrical workof an immersion heater usingan AC power meter

Electrical work and power

The relationship between the power P at an ohmic resistance Rand the applied voltage U can be expressed with the relationship

P = U2.

R

The same applies for AC voltage when P is the power averagedover time and U is replaced by the RMS value

Urms =U0

ö2

U0: amplitude of AC voltage.

The relationship

P = U · I

can also be applied to ohmic resistors in AC circuits when thedirect current I is replaced by the RMS value of the AC

Irms =I0

ö2I0: amplitude of AC.

In the first experiment, the electrical power of an immersion heat-er for extra-low voltage is determined from the Joule heat emit-ted per unit of time and compared with the applied voltage Urms.This experiment confirms the relationship

P “ U 2rms.

In the second experiment, an AC power meter is used to deter-mine the electrical work W which must be performed to produceone liter of hot water using an immersion heater. For comparisonpurposes, the voltage Urms, the current Irms and the heating timet are measured and the relationship

W = Urms · Irms · t

is verified.

P3.

6.6.

1

P3.

6.6.

2


131


590 50 Lid with heater 1

384 52 Aluminium calorimeter 1

560 331 Alternating current meter 1

301 339 Pair of stand feet 1

303 25 Immersion heater 1




Ammeter, AC, I ≤ 6 A, e. g.531 712 Multimeter METRAmax 3 1 1


382 34 Thermometer, -10 to +110 °C 1 1

590 06 Plastic beaker, 1000 ml 1 1

500 624 Safety connection lead, 50 cm, black 4



Voltage source, AC 0...12 V, 6 A


P 3.6.6Electrical work and power

P 3.6.6.3 Quantitative comparison of DCpower and AC power using anincandescent lamp

P 3.6.6.4 Determining the crest factors ofvarious AC signal forms

P 3.6.6.5 Determining the active andreactive power in AC circuits

Determining the active and reactive power in AC circuits (P 3.6.6.5)

The electrical power of a time-dependent voltage U(t) at any loadresisance is also a function of time:

P(t) = U(t) · l(t)

I(t): time-dependent current through the load resistor.Thus, for periodic currents and voltages, we generally considerthe power averaged over one period T. This quantity is oftenreferred to as the active power PW. It can be measured electron-ically for any DC or AC voltages using the joule and wattmeter.

In the first experiment, two identical incandescent light bulbs areoperated with the same electrical power. One bulb is operatedwith DC voltage, the other with AC voltage. The equality of thepower values is determined directly using the joule and wattme-ter, and additionally by comparing the lamp brightness levels.This equality is reached when the DC voltage equals the RMSvalue of the AC voltage.

The object of the second experiment is to determine the crestfactors, i. e. the quotients of the amplitude U0 and the RMS valueUrms for different AC voltage signal forms generated using a func-tion generator by experimental means. The amplitude is meas-ured using an oscilloscope. The RMS value is calculated from thepower P measured at an ohmic resistor R using the joule andwattmeter according to the formula

Ueff = öP · R .

The third experiment measures the current Irms through a givenload and the active power PW for a fixed AC voltage Urms. To verifythe relationship

PW = Urms · Irms · cos f

the phase shift f between the voltage and the current is addition-ally determined using an oscilloscope. This experiment alsoshows that the active power for a purely inductive or capacitiveload is zero, because the phase shift is f = 90°. The apparentpower

Ps = Urms · Irms

is also referred to as reactive power in this case.

P3.

6.6.

4

P3.

6.6.

3

P3.

6.6.

5

132


531 83 Joule and Wattmeter 1 1 1

50514 Set of 10 lamps E 10; 6.0 V/3.0 W 2

576 71 Plug-in board section 2

579 06 STE lamp holder E 10, top 2


522 61 AC/DC amplifier, 30 W 1

536 101 Measuring resistor 1 V, 4 W 1

537 35 Rheostat 330 V 1

517 021 Capacitor, 40 µF, on plate 1




Voltage source, AC/DC, 0–12 V, 3 A, e. g.521 48 AC/DC power supply 0....12 V, 230 V/50 Hz 1

Voltage source, AC, 0–20 V, 1 A, e.g.521 35 Variable extra low voltage transformer S 1

Voltmeter, AC/DC, U ≤ 12 V, e.g.531 100 Multimeter METRAmax 2 1

Voltmeter, AC, U ≤ 20 V, e.g.531 100 Multimeter METRAmax 2 1



575 35 BNC/4 mm adapter, 2-pole 2

504 45 Single-pole cut-out switch 1

500 421 Connection lead, 50 cm, red 1



Demonstration of the function of a relay (P 3.6.7.2)

P 3.6.7

P 3.6.7.1 Demonstration of the functionof a bell

P 3.6.7.2 Demonstration of the functionof a relay

Electromechanical devices

In the first experiment, an electric bell is assembled using a ham-mer interrupter (Wagner interrupter). The hammer interrupterconsists of an electromagnet and an oscillating armature. In theresting state, the oscillating armature touches a contact, thusswitching the electromagnet on. The electromagnet attracts theoscillating armature, which strikes a bell. At the same time, thisaction interrupts the circuit, and the oscillating armature returnsto the resting position.

The second experiment demonstrates how a relay functions. Acontrol circuit operates an electromagnet which attracts thearmature of the relay. When the electromagnet is switched off, thearmature returns to the resting position. When the armaturetouches a contact, a second circuit is closed, which e.g. suppliespower to a lamp. When the contact is configured so that thearmature touches it in the resting state, we call this a breakcontact; the opposite case is termed a make contact.

P3.

6.7.

2 (a

)

P3.

6.7.

1

P3.

6.7.

2 (b

)


133


561 071 Bell/relay set, complete 1 1 1

301 339 Pair of stand feet 1 1 1

579 10 STE key switch n.o., single pole 1

579 13 STE toggle switch, single pole 1 1

579 30 STE adjustable contact 1

576 71 Plug-in board section 1 2

579 06 STE lamp holder E 10, top 1 2

50513 Lamp with socket, E 10; 6.0 V/5.0 W 1 2

Transformer, 6 V AC, 12 V AC / 30 W 1 1 1

500 444 Connection lead, 100 cm, black 2 5 7

Function principle of a relay (P 3.6.7.2)

521 210

Electromagnetic oscillations and waves Electricity

P 3.7.1Electromagnetic oscillator circuit

P 3.7.1.1 Free electromagnetic oscilla-tions

P 3.7.1.2 De-damping of electromagneticoscillations through inductivethree-point coupling after Hartley

Free electromagnetic oscillations (P 3.7.1.1a)

Electromagnetic oscillation usually occurs in a frequency rangein which the individual oscillations cannot be seen by the nakedeye. However, this is not the case in an oscillator circuit consist-ing of a high-capacity capacitor (C = 40 mF) and a high-induc-tance coil (L = 500 H). Here, the oscillation period is about 1 s,so that the voltage and current oscillations can be observeddirectly on a pointer instrument or Yt recorder.

The first experiment investigates the phenomenon of free elec-tromagnetic oscillations. The damping is so low that multipleoscillation periods can be observed and their duration measuredwith e. g. a stopclock. In the process, the deviations between theobserved oscillation periods and those calculated using Thom-son’s equation

T = 2ö · öL · C

are observed. These deviations can be explained by the current-dependency of the inductance, as the permeability of the ironcore of the coil depends on the magnetic field strength.

In the second experiment, an oscillator circuit after Hartley isused to “de-damp” the electromagnetic oscillations in the circuit,or in other words to compensate the ohmic energy losses in afeedback loop by supplying energy externally. Oscillator circuitsof this type are essential components in transmitter and receivercircuits used in radio and television technology. A coil with cen-ter tap is used, in which the connection points are connectedwith the emitter, base and collector of a transistor via AC. Thebase current controls the collector current synchronously withthe oscillation to compensate for energy losses.

P3.

7.1.

2 (b

)

P3.

7.1.

2 (a

)

P3.

7.1.

1 (c

)

P3.

7.1.

1 (b

)

P3.

7.1.

1 (a

)

P3.

7.1.

2 (c

)

134


517 011 Coil with high inductivity, on plate 1 1 1 1 1 1

517 021 Capacitor, 40 µF, on plate 1 1 1 1 1 1

301 339 Pair of stand feet 2 2 2 2 2 2

576 74 Plug-in board A4 1 1 1

576 86 STE mono cell holder 1 1 1

503 11 Set of 20 batteries 1.5 V (type MONO) 1 1 1

577 01 STE resistor 100 V, 0.5 W 1 1 1 1

57710 STE resistor 100 kV, 0.5 W 1 1 1

578 76 STE transistor BC 140, NPN, emitter bottom 1 1 1

579 13 STE toggle switch, single pole 1 1 1

501 48 Set of 10 bridging plugs 1 1 1 1 1 1

521 45 DC power supply 0....+/- 15 V 1 1 1

531 94 AV-meter 1 1

Yt-recorder, two channel 1 1


524 200 CASSY Lab 1 1


500 424 Connection lead, 50 cm, black 3 3 3

501 46 Pair of cables, 1 m, red and blue 2 3 3 1 2 2


575 713

Estimating the dielectric constant of water in the decimeter-wave range (P 3.7.2.4)

P 3.7.2

P 3.7.2.1 Radiation characteristic andpolarization of decimeter waves

P 3.7.2.2 Amplitude modulation of decimeter waves

P 3.7.2.4 Estimating the dielectric constant of water in the decimeter-wave range

Decimeter waves

It is possible to excite electromagnetic oscillations in a straightconductor in a manner analogous to an oscillator circuit. Anoscillator of this type emits electromagnetic waves, and theirradiated intensity is greatest when the conductor length is equiv-alent to exactly one half the wavelength (we call this a Ö/2 di-pole). Experiments on this topic are particularly successful withwavelengths in the decimeter range. We can best demonstratethe existence of such decimeter waves using a second dipolewhich also has the length Ö/2, and from which the voltage isapplied to an incandescent lamp or (via a high-frequency rec-tifier) to a measuring instrument.

The first experiment investigates the radiation characteristic of aÖ/2 dipole for decimeter waves. Here, the receiver is aligned par-allel to the transmitter and moved around the transmitter. In asecond step, the receiver is rotated with respect to the transmit-ter in order to demonstrate the polarization of the emitted deci-meter waves.

The next experiment deal with the transmission of audio-frequency signals using amplitude-modulated decimeter waves.In amplitude modulation a decimeter-wave signal

E(t) = E0 · cos(2S · f · t)

is modulated through superposing of an audio-frequency signalu(t) in the form

EAM(t) = E0 · (1 + kAM · u(t) ) · cos(2S · f · t)

kAM: coupling coefficient

The last experiment demonstrates the dielectric nature of water.In water, decimeter waves of the same frequency propagate witha shorter wavelength than in air. Therefore, a receiver dipoletuned for reception of the wavelength in air is no longer adequa-tely tuned when placed in water.

Electricity Electromagnetic oscillations and waves

135

P3.

7.2.

2

P3.

7.2.

1

P3.

7.2.

4


587 55 Decimeter wave transmitter 1 1 1

587 54 Set of dipoles in water tank 1

587 08 Broad-band speaker 1


522 61 AC/DC-amplifier 30 W 1


531 51 Multimeter MA 1H 1





P 3.7.3Propagation of decimeterwaves along lines

P 3.7.3.1 Determining the current andvoltage maxima on a Lecherline

P 3.7.3.2 Investigating the current andvoltage on a Lecher line withloop dipole

Determining the current and voltage maxima on a Lecher line (P 3.7.3.1)

E. Lecher (1890) was the first to suggest using two parallel wiresfor directional transmission of electromagnetic waves. Usingsuch Lecher lines, as they are known today, electromagneticwaves can be transmitted to any point in space. They are meas-ured along the line as a voltage U(x,t) propagating as a wave, oras a current I(x,t).

In the first experiment, a Lecher line open at the wire ends and ashorted Lecher line are investigated. The waves are reflected atthe ends of the wires, so that standing waves are formed. Thecurrent is zero at the open end, while the voltage is zero at theshorted end. The current and voltage are shifted by Ö/4 with re-spect to each other, i. e. the wave antinodes of the voltage coin-cide with the wave nodes of the current. The voltage maxima arelocated using a probe with an attached incandescent lamp. Aninduction loop with connected incandescent lamp is used todetect the current maxima. The wavelength Ö is determined fromfrom the intervals d between the current maxima or voltage maxi-ma. We can say

d =Ö2

In the second experiment, a transmitting dipole (Ö/2 folded di-pole) is attached to the end of the Lecher line. Subsequently, it isno longer possible to detect any voltage or current maxima onthe Lecher line itself. A current maximum is detectable in themiddle of the dipole, and voltage maxima at the dipole ends.

136

Current and voltage maxima on a Lecher line

P3.

7.3.

1-2


587 55 Decimeter wave transmitter 1

587 56 Lecher system with accessories 1


30011 Saddle base 3

Diffraction of microwaves at a double slit (P 3.7.4.4)

P 3.7.4

P 3.7.4.1 Field orientation and polariza-tion of microwaves in front of ahorn antenna

P 3.7.4.2 Absorption of microwaves

P 3.7.4.3 Determining the wavelength ofstanding microwaves

P 3.7.4.4 Diffraction of microwaves

P 3.7.4.5 Refraction of microwaves

P 3.7.4.6 Investigating total reflectionwith microwaves

Microwaves

grating made of thin metal strips is used; in this apparatus, theelectric field can only form perpendicular to the metal strips. Thepolarization grating is set up between the horn antenna and theE-field probe. This experiment shows that the electric field vectorof the radiated microwaves is perpendicular to the long side ofthe horn radiator.

The second experiment deals with the absorption of microwaves.Working on the assumption that reflections may be ignored, theabsorption in different materials is calculated using both the inci-dent and the transmitted intensity. This experiment reveals a factwhich has had a profound impact on modern cooking: micro-waves are absorbed particularly intensively by water.

In the third experiment, standing microwaves are generated byreflection at a metal plate. The intensity, measured at a fixed pointbetween the horn antenna and the metal plate, changes when themetal plate is shifted longitudinally. The distance between twointensity maxima corresponds to one half the wavelength. Insert-ing a dielectric in the beam path shortens the wavelength.

The next two experiments show that many of the properties ofmicrowaves are comparable to those of visible light. The diffrac-tion of microwaves at an edge, a single slit, a double slit and anobstacle are investigated. Additionally, the refraction of micro-waves is demonstrated and the validity of Snell’s law of refractionis confirmed.

The final experiment investigates total reflection of microwaves atmedia with lower refractive indices. We know from wave mechan-ics that the reflected wave penetrates about three to four wave-lengths deep into the medium with the lower refractive index,before traveling along the boundary surface in the form of sur-face waves. This is verified in an experiment by placing an ab-sorber (e.g. a hand) on the side of the medium with the lowerrefractive index close to the boundary surface and observing thedecrease in the reflected intensity.

P3.

7.4.

5

P3.

7.4.

4

P3.

7.4.

3

P3.

7.4.

2

P3.

7.4.

1

P3.

7.4.

6


137


737 01 Gunn oscillator 1 1 1 1 1 1

737 020 Gunn power supply 1 1 1 1 1 1

309 06 578 Stand rod 245 mm, with thread 1 1 1 1 1 1

737 21 Large horn antenna 1 1 1 1 1 1

737 27 Physics microwave accessories I 1 1 1 1

737 275 Physics microwave accessories II 1 1 1 1

737 35 E-field probe 1 1 1 1 1 1

737 390 Set of absorbers

Voltmeter, DC, U ≤ 10 V, 1 1 1 1 1 1

300 02 Stand base, V-shape, 20 cm

30011 Saddle base

501 022 BNC cable, 2 m long 2 2 2 2 2 2

501 461 Pair of cables, 1 m, black 1 1 1 1 1 1

Microwaves are electromagnetic waves in the wavelength rangebetween 0.1 mm and 100 mm. They are generated e.g. in a cavi-ty resonator, whereby the frequency is determined by the volumeof the cavity resonator. An E-field probe is used to detect themicrowaves; this device measures the parallel component of theelectric field. The output signal of the probe is proportional to thesquare of the field strength, and thus to the intensity.

The first experiment investigates the orientation and polarizationof the microwave field in front of a radiating horn antenna. Here,the field in front of the horn antenna is measured point by pointin both the longitudinal and transverse directions using the E-field probe. To determine the polarization, a rotating polarization


1 * 1* 1* 1* 1* 1*

531 100 e.g. Multimeter METRAmax2

2 2 3 4 2 2

1


P 3.7.5Propagation of microwavesalong lines

P 3.7.5.1 Guiding of microwaves along a Lecher line

P 3.7.5.2 Qualitative demonstration ofguiding of microwaves througha flexible metal waveguide

P 3.7.5.3 Determining the standing-waveratio of a rectangular wave-guide for a variable reflectionfactor

Guiding of microwaves along a Lecher line (P 3.7.5.1)

To minimize transmission losses over long distances, microwavescan also be transmitted along lines. For this application, metalwaveguides are most commonly used; Lecher lines, consisting oftwo parallel wires, are less common.

Despite this, the first experiment investigates the guiding ofmicrowaves along a Lecher line. The voltage along the line ismeasured using the E-field probe. The wavelengths are deter-mined from the spacing of the maxima.

The second experiment demonstrates the guiding of microwavesalong a hollow metal waveguide. First, the E-field probe is usedto verify that the radiated intensity at a position beside the hornantenna is very low. Next, a flexible metal waveguide is set upand bent so that the microwaves are guided to the E-field probe,where they are measured at a greater intensity.

Quantitative investigations on guiding microwaves in a rectangu-lar waveguide are conducted in the third experiment. Here,standing microwaves are generated by reflection at a shortingplate in a waveguide, and the intensity of these standing wavesis measured as a function of the location in a measuring line withmovable measuring probe. The wavelength in the waveguide iscalculated from the distance between two intensity maxima orminima. A variable attenuator is set up between the measuringline and the short which can be used to attenuate the intensity ofthe returning wave by a specific factor, and thus vary the stand-ing-wave ratio.

P3.

7.5.

3 (a

)

P3.

7.5.

2

P3.

7.5.

1

P3.

7.5.

3 (b

)

138


737 01 Gunn oscillator 1 1 1 1

737 020 Gunn power supply 1 1

737 021 Gunn power supply with SWR meter 1 1

737 03 Coax detector 1 1

737 06 Isolator 1

737 09 Variable attenuator 1 1

737 095 Fixed attenuator 1

73710 Moveable short 1 1

737111 Slotted measuring line 1 1

73714 Waveguide termination 1 1

73715 Support for waveguide components

737 21 Large horn antenna 1 1

737 275 Physics microwave accessories II 1

737 35 E-field probe 1 1

737 399 Set of 10 thumb srcews M4 1 1

Voltmeter, DC, U ≤ 10 V, e. g.



501 01 BNC cable, 0.25 m long 1 1

501 02 BNC cable, 1 m long 2 2


501 461 Pair of cables, 1 m, black 1 1


737 390 I Set of absorbers I 1* I I 1* I 1*

531 100 Multimeter METRAmax2 1 1

1 1

309 06 578 Stand rod 245 mm, with thread 1 1

737 27 Physics microwave accessories I 1

Directional characteristic of a helical antenna – manual recording (P 3.7.6.1)

P 3.7.6

P 3.7.6.1 Directional characteristic of ahelical antenna – manualrecording

P 3.7.6.2 Directional characteristic of aYagi antenna – manual recor-ding

P 3.7.6.3 Directional characteristic of a helical antenna – recording with a computer

P 3.7.6.4 Directional characteristic of aYagi antenna – recording with a computer

Directional characteristic of dipole radiation

Directional antennas radiate the greater part of their electromag-netic energy in a particular direction and/or are most sensitive toreception from this direction. All directional antennas requiredimensions which are equivalent to multiple wavelengths. In themicrowave range, this requirement can be fulfilled with an ex-tremely modest amount of cost and effort. Thus, microwaves areparticularly suitable for experiments on the directional character-istics of antennas.

In the first experiment, the directional characteristic of a helicalantenna is recorded. As the microwave signal is excited with alinearly polarizing horn antenna, the rotational orientation of thehelical antenna (clockwise or counterclockwise) is irrelevant. Themeasurement results are represented in the form of a polar dia-gram, from which the unmistakable directional characteristic ofthe helical antenna can be clearly seen.

In the second experiment, a dipole antenna is expanded usingparasitic elements to create a Yagi antenna, to improve the direc-tional properties of the dipole arrangement. Here, a total of fourshorter elements are placed in front of the dipole as directors,and a slightly longer element placed behind the dipole serves asa reflector. The directional factor of this arrangement is deter-mined from the polar diagram.

In the third and fourth experiment, the antennas are placed on aturntable which is driven by an electric motor; the angular turn-table position is transmitted to a computer. The antennas receivethe amplitude-modulated microwave signals, and frequency-sel-ective and phase-selective detection are applied to suppressnoise. The received signals are preamplified in the turntable.After filtering and amplification, they are passed on to the com-puter. For each measurement, the included software displays thereceiving power logarithmically in a polar diagram.

P3.

7.6.

3

P3.

7.6.

2

P3.

7.6.

1

P3.

7.6.

4


139


737 01 Gunn oscillator 1 1 1 1

737 020 Gunn power supply 1 1

737 03 Coax detector 1 1

737 05 PIN modulator 1* 1*

737 06 Isolator 1* 1*

73715 Support for waveguide components

737 21 Large horn antenna 1 1 1 1

737 390 Set of absorbers 1 1 1 1

737405 Rotating antenna platform 1 1

1 1

Dipole antenna kit 1 1

Yagi antenna kit 1 1

737440 Helical antenna kit 1 1

Voltmeter, DC, U ≤ 10 V, e. g.1 1



501 02 BNC cable, 1 m long 1



501 461 Pair of cables, 1 m, black 2 2


1

309 06 578 I Stand rod 245 mm, with thread I 2 I 2 I I*additionally recommended

737 412

737 432

737 407 Antenna stand with amplifier

531 100 Multimeter METRAmax2

Free charge carriers in a vacuum Electricity

P 3.8.1Tube diode

P 3.8.1.1 Recording the characteristic ofa tube diode

P 3.8.1.2 Half-wave rectification using atube diode

Recording the characteristic of a tube diode (P 3.8.1.1)

A tube diode contains two electrodes: a heated cathode, whichemits electrons due to thermionic emission, and an anode. Apositive potential between the anode and the cathode generatesan emission current to the anode, carried by the free electrons. Ifthis potential is too low, the emission current is prevented by thespace charge of the emitted electrons, which screen out theelectrical field in front of the cathode. When the potential be-tween the anode and the cathode is increased, the isoelectriclines penetrate deeper into the space in front of the cathode, andthe emission current increases. This increase of the current withthe potential is described by the Schottky-Langmuir law:

I å U32

This current increases until the space charge in front of thecathode has been overcome and the saturation value of theemission current has been reached. On the other hand, if thenegative potential applied to the anode is sufficient, the electronscannot flow to the anode and the emission current is zero.

In the first experiment, the characteristic of a tube diode is re-corded, i.e. the emission current is measured as the function ofthe anode potential. By varying the heating voltage, it can bedemonstrated that the saturation current depends on the tem-perature of the cathode.

The second experiment demonstrates half-wave rectification ofthe AC voltage signal using a tube diode. For this experiment, anAC voltage is applied between the cathode and the anode via anisolating transformer, and the voltage drop is measured at aresistor connected in series. This experiment reveals that thediode blocks when the current is reversed.

P3.

8.1.

2

P3.

8.1.

1

140


Demonstration diode tube 1 1

Stand for electron tubes 1 1

521 65 Tube power supply 0 .... 500 V 1 1

521 40 Variable low voltage transformer 0 .... 250 V 1

Ammeter, AC, I ≤ 10 mA, e.g.531 100 Multimeter METRAmax 2 1

Voltmeter, DC, U ≤ 500 V, e.g.531 712 Multimeter METRAmax 3 1


575 231 Probe, 100 MHz, 1:1 or 10:1 1


500 641 Safety connection lead, 100 cm, red 3

500 642 Safety connection lead, 100 cm, blue

555 610

555 600

536 251 Measuring resistor 100 kOhm, 2 W 1

2

4 3

Recording the characteristic field of a tube triode (P 3.8.2.1)

P 3.8.2

P 3.8.2.1 Recording the characteristicfield of a tube triode

P 3.8.2.2 Amplifying voltages with a tubetriode

Tube triode

In a tube triode, the electrons pass through the mesh of a grid ontheir way from the cathode to the anode. When a negative volt-age UG is applied to the grid, the emission current IA to the anodeis reduced; a positive grid voltage increases the anode current.In other words, the anode current can be controlled by the gridvoltage.

The first experiment records the family of characteristics of thetriode, i.e. the anode current IA as a function of the grid voltageUG and the anode voltage UA.

The second experiment demonstrates how a tube triode can beused as an amplifier. A suitable negative voltage UG is used to setthe working point of the triode on the characteristic curve IA(UA)so that the characteristic is as linear as possible in the vicinity ofthe working point. Once this has been set, small changes in thegrid voltage FUG cause a change in the anode voltage FUA bymeans of a proportional change in the anode current FIA. Theratio:

V =dUA

dUG

is known as the gain.

P3.

8.2.

1

P3.

8.2.

2

Electricity Free charge carriers in a vacuum

141

Characteristic field of a tube triode


Demonstration triode tube 1 1


536 251 Measuring resistor 100 kV, 2 W 1

521 65 Tube power supply 0....500 V 1 1

Ammeter, AC, I ≤ 1 mA, e. g.531 100 Multimeter METRAmax 2 1



575211 Two-channel oscilloscope 303 1

575 231 Probe, 100 MHz, 1:1 or 10:1 1



500 641 Safety connection lead, 100 cm, red

500 642 Safety connection lead, 100 cm, blue 5

555 612

555 600

522 621 Function generator, S12, 0.1 Hz to 20 kHz 1

1 25 3

3


P 3.8.3Maltese-cross tube

P 3.8.3.1 Demonstrating the linear pro-pagation of electrons in a field-free space

P 3.8.3.2 Deflection of electrons in anaxial magnetic field

Deflection of electrons in an axial magnetic field (P 3.8.3.2)

In the Maltese cross tube, the electrons are accelerated by theanode to a fluorescent screen, where they can be observed asluminescent phenomena. A Maltese cross is arranged betweenthe anode and the fluorescent screen, and its shadow can beseen on the screen. The Maltese cross has its own separate lead,so that it can be connected to any desired potential.

The first experiment confirms the linear propagation of electronsin a field-free space. In this experiment, the Maltese cross isconnected to the anode potential and the shadow of the Maltesecross in the electron beam is compared with the light shadow. Wecan conclude from the observed coincidence of the shadowsthat electrons propagate in a straight line. The Maltese cross isthen disconnected from any potential. The resulting spacecharges around the Maltese cross give rise to a repulsive poten-tial, so that the image on the fluorescent screen becomes larger.

In the second experiment an axial magnetic field is applied usingan electromagnet. The shadow cross turns and shrinks as afunction of the coil current. When a suitable relationship betweenthe high voltage and the coil current is set, the cross is focusedalmost to a point, and becomes larger again when the current isincreased further. The explanation for this magnetic focusing maybe found in the helical path of the electrons in the magnetic field.

P3.

8.3.

1

P3.

8.3.

2

142

Cat. no. Description

Maltese cross tube 1 1





Schematic diagram of Maltese cross tube

555 620

555 600

555 604

500 621 Safety connectin lead, 50 cm, red 1 2

500 642 Safety connectin lead, 100 cm, blue 1 2


521 545 DC power supply 0...16 V, 5 A 1

500 622 Safety connectin lead, 50 cm, blue 1


500 644 Safety connectin lead, 100 cm, black 2 2

P 3.8.4

P 3.8.4.1 Hot-cathode emission in avacuum: determining the polar-ity and estimating the specificcharge of the emitted chargecarriers

P 3.8.4.2 Generating Lissajou figuresthrough electron deflection incrossed alternating magneticfields

Perrin tube

In the Perrin tube, the electrons are accelerated through ananode with iris diaphragm onto a fluorescent screen. Deflectionplates are mounted at the opening of the iris diaphragm for hori-zontal electrostatic deflection of the electron beam. A Faraday’scup, which is set up at an angle of 45° to the electron beam, canbe charged by the electrons deflected vertically upward. Thecharge current can be measured using a separate connection.

In the first experiment, the current through a pair of Helmholtzcoils is set so that the electron beam is incident on the Faraday’scup of the Perrin tube. The Faraday’s cup is connected to anelectroscope which has been pre-charged with a known polarity.The polarity of the electron charge can be recognized by thedirection of electroscope deflection when the Faraday’s cup isstruck by the electron beam. At the same time, the specific elec-tron charge can be estimated. The following relationship applies:

e=

2UA

m (B · r)2UA: anode voltage

The bending radius r of the orbit is predetermined by the geo-metry of the tube. The magnetic field B is calculated from the cur-rent I through the Helmholtz coils.

In the second experiment, the deflection of electrons in crossedalternating magnetic fields and in coaxial alternating electric andmagnetic fields is used to produce Lissajou figures on thefluorescent screen. This experiment demonstrates that the elec-trons respond to a change in the electromagnetic fields withvirtually no lag.

P3.

8.4.

2

P3.

8.4.

1

Electricity Free charge carriers in a vacuum

143


Perrin tube 1 1


Pair of Helmholtz coils 1 1

1


540 091 Electroscope 1

30011 Saddle base 1



522 621 Function generator S 12, 0.1 Hz to 20 kHz 1

500 600

500 622

562 14 Coil with 500 turns

521 35 Variable extra low-voltage transformer S 1

521 545 DC power supply 0 ... 16 V, 5 A 1

300 761 Support blocks, set of 6 pcs 1




4 3

2 3

500 644 Safety connection lead, 100 cm, black 2 2

500 604

Hot-cathode emission in a vacuum: determining the polarity and estimating the specific charge of emitted charge carriers (P 3.8.4.1)


P 3.8.5Thomson tube

P 3.8.5.1 Investigating the deflection ofelectrons in electrical andmagnetic fields

P 3.8.5.2 Assembling a velocity filter(Wien filter) to determine thespecific electron charge

Investigating the deflection of electrons in electrical fields (P 3.8.5.1)

In the Thomson tube, the electrons pass through a slit iris behindthe anode and fall glancingly on a fluorescent screen placed inthe beam path at an angle. A plate capacitor is mounted at theopening of the slit diaphragm which can electrostatically deflectthe electron beam vertically. In addition, Helmholtz coils can beused to generate an external magnetic field which can alsodeflect the electron beam.

The first experiment investigates the deflection of electrons inelectric and magnetic fields. For different anode voltages UA, thebeam path of the electrons is observed when the deflection volt-age UP at the plate capacitor is varied. Additionally, the electronsare deflected in the magnetic field of the Helmholtz coils by var-ying the coil current I. The point at which the electron beamemerges from the fluorescent screen gives us the radius R of theorbit. When we insert the anode voltage in the following equation,we can obtain an experimental value for the specific electroncharge

e=

2UA ,

m (B · r)2

whereby the magnetic field B is calculated from the current I.

In the second experiment, a velocity filter (Wien filter) is con-structed using crossed electrical and magnetic fields. Amongother things, this configuration permits a more precise determi-nation of the specific electron charge. At a fixed anode voltageUA, the current I of the Helmholtz coils and the deflection voltageUP are set so that the effects of the electric field and the magnet-ic field just compensate each other. The path of the beam is thenvirtually linear, and we can say:

e=

1·

UP 2

m 2UA( B · d )

d: plate spacing of the plate capacitor

P3.

8.5.

1-2

144


Electron beam deflection tube 1

Stand for electron tubes 1


521 70 High voltage power supply 10 kV

Deflection of electrons in magnetic fields

2

555 624

555 600

555 604








Non-self-maintained discharge: comparing the charge transport in a gas triode and high-vacuum triode (P 3.9.1.1)

P 3.9.1

P 3.9.1.1 Non-self-maintained discharge:comparing the charge transportin a gas triode and high-vacu-um triode

P 3.9.1.2 Ignition and extinction of self-maintained gas discharge

Self-maintained and non-self-maintained discharge

A gas becomes electrically conductive, i. e. gas dischargeoccurs, when a sufficient number of ions or free electrons ascharge carriers are present in the gas. As the charge carriersrecombine with each other, new ones must be produced con-stantly. We speak of self-maintained gas discharge when theexisting charge carriers produce a sufficient number of newcharge carriers through the process of collision ionization. Innon-self-maintained gas discharge, free charge carriers are pro-duced by external effects, e. g. by the emission of electrons froma hot cathode.

The first experiment looks at non-self-maintained gas discharge.The comparison of the current-voltage characteristics of a high-vacuum triode and an He gas triode shows that additional chargecarriers are created in a gas triode. Some of the charge carrierstravel to the grid of the gas triode, where they are measuredusing a sensitive ammeter to determine their polarity.

The second experiment investigates self-maintained discharge inan He gas triode. Without cathode heating, gas discharge occursat an energizing voltage UZ which depends on the type of gas.This gas discharge also maintains itself at lower voltages, andonly goes out when the voltage falls below the extinction voltageUL. Below the energizing voltage UZ, non-self-maintaineddischarge can be triggered, e. g. by switching on the cathodeheating.

P3.

9.1.

1

P3.

9.1.

2

Electricity Electrical conduction in gases

145


Gas-filled triode 1 1

Demonstration triode tube 1


521 65 Tube power supply 0....500 V 1 1



Ammeter, AC, I ≤ 50 mA, e. g.



555 600

500 614

500 612

531 57 Multimeter METRAport 3E 1 1

6 5 54 3 3

2 1

(a) (b)

1

11

1

Electrical conduction in gases Electricity

P 3.9.2Gas discharge at reduced pressure

P 3.9.2.1 Investigating self-maintaineddischarge in air as a functionof air pressure

Investigating self-maintained discharge in air as a function of air pressure (P 3.9.2.1)

Glow discharge is a special form of gas discharge. It maintainsitself at low pressures with a relatively low current density, and isconnected with spectacular luminous phenomena. Research intothese phenomena provided fundamental insights into the struc-ture of the atom.

In this experiment, a cylindrical glass tube is connected to avacuum pump and slowly evacuated. A high voltage is applied tothe electrodes at the end of the glass tube. No discharge occursat standard pressure. However, when the pressure is reduced toa certain level, current flows, and a luminosity is visible. When thegas pressure is further reduced, multiple phases can be ob-served: First, a luminous “thread” joins the anode and the catho-de. Then, a column of light extends from the anode until it occu-pies almost the entire space. A glowing layer forms on the catho-de. The column gradually becomes shorter and breaks down intomultiple layers, while the glowing layer becomes larger. Thelayering of the luminous zone occurs because after collisionexcitation, the exciting electrons must traverse an accelerationdistance in order to acquire enough energy to re-excite theatoms. The spacing of the layers thus illustrates the free pathlength.

P3.

9.2.

1

146


554161 Discharge tube, open 1

378 752 Rotary-vane vacuum pump D 2.5 E 1

378 764 Exhaust filter 1*

378 015 Cross DN 16 KF 1

378 023 Male ground joint NS 19/26 1



378 776 Variable leak valve DN 16 KF 1

378 777 Ball valve with 2 flanges DN 16 KF 1

378 500 Vacuum meter THERMOVAC TM 21 1

378 501 Gauge tube TR 211 1

378 502 Gauge head cable, 3 m 1

378 701 High-vacuum grease P, 50 g 1




Magnetic deflection of cathode and canal rays (P 3.9.3.1)

P 3.9.3

P 3.9.3.1 Magnetic deflection of cathodeand canal rays

Cathode and canal rays

Cathode and canal rays can be observed in a gas discharge tubewhich contains only a residual pressure of less than 0.1 mbar.When a high voltage is applied, more and more electrons areliberated from the residual gas on collision with the cathode. Theelectrons travel to the anode virtually unhindered, and some ofthem manage to pass through a hole to the glass wall behind it.Here they are observed as fluorescence phenomena. The lumi-nousity also appears behind the cathode, which is also providedwith a hole. A tightly restricted canal ray consisting of positiveions passes straight through the hole until it hits the glass wall.

In this experiment, the cathode rays, i. e. the electrons, and thecanal rays are deflected using a magnet. From the observationthat the deflection of the canal rays is significantly less, we canconclude that the ions have a lower specific charge.

P3.

9.3.

1

Electricity Electrical conduction in gases

147


554161 Discharge tube, open 1

378 752 Rotary-vane vacuum pump D 2.5 E 1

378 764 Exhaust filter 1*

378 015 Cross DN 16 KF 1

378 023 Male grount joint NS 19/26 1



378 776 Variable leak valve DN 16 KF 1

378 777 Ball valve with 2 flanges DN 16 KF 1

378 500 Vacuum meter THERMOVAC TM 21 1

378 501 Gauge tube TR 211 1

378 502 Gauge head cable, 3 m 1

378 701 High-vacuum grease P, 50 g 1





Electronics

Table of contents Electronics

150

P4 ElectronicsP 4.1 Components

and basic circuitsP 4.1.1 Current and voltage sources 151–152

P 4.1.2 Special resistors 153

P 4.1.3 Diodes 154

P 4.1.4 Diode circuits 155

P 4.1.5 Transistors 156

P 4.1.6 Transistor circuits 157

P 4.1.7 Optoelectronics 158

P 4.2 Operational amplifierP 4.2.1 Internal design

of an operational amplifier 159

P 4.2.2 Operational amplifier circuits 160

P 4.3 Open- and closed-loop controlP 4.3.1 Open-loop control 161

P 4.3.2 Closed-loop control 162

P 4.4 Digital technologyP 4.4.1 Basic logical operations 163

P 4.4.2 Switching networks and units 164

P 4.4.3 Serial and parallel arithmetic units 165

P 4.4.4 Digital control systems 166

P 4.4.5 Structure of a central processing unit (CPU) 167

P 4.4.6 Microprocessor 168

Determining the internal resistance of a battery (P 4.1.1.1)

P 4.1.1

P 4.1.1.1 Determining the internal resistance of a battery

P 4.1.1.2 Operating a DC power supplyas a constant-current and constant-voltage source

Current and voltage sources

The voltage U0 generated in a voltage source generally differsfrom the terminal voltage U measured at the connections as soonas a current I is drawn from the voltage source. A resistance Rimust therefore exist within the voltage source, across which apart of the generated voltage drops. This resistance is called theinternal resistance of the voltage source.

In the first experiment, a rheostat as an ohmic load is connectedto a battery to determine the internal resistance. The terminalvoltage U of the battery is measured for different loads, and thevoltage values are plotted over the current I through the rheostat.The internal resistance Ri is determined using the formula

U = U0 – Ri · I

by drawing a best-fit straight line through the measured values.A second diagram illustrates the power

P = U · I

as a function of the load resistance. The power is greatest whenthe load resistance has the value of the internal resistance Ri.

The second experiment demonstrates the difference between aconstant-voltage source and a constant-current source using aDC power supply in which both modes are implemented. Thevoltage and current of the power supply are limited to the re-spective values U0 and I0. The terminal voltage U and the currentI consumed are measured for various load resistances R. Whenthe load resistance R is reduced, the terminal voltage retains aconstant value U0 as long as the current I remains below the setlimit value I0. The DC power supply operates as a constant-volt-age source with an internal resistance of zero. When the loadresistance R is increased, the current consumed remains con-stant at I0 as long as the terminal voltage does not exceed thelimit value U0. The DC power supply operates as a constant-cur-rent source with infinite internal resistance.

P4.

1.1.

1

P4.

1.1.

2

Electronics Components and basic circuits

151


576 89 Battery case 2 x 4.5 Volt 1

503 11 Set of 20 batteries 1.5 V (type MONO) 1

521 50 AC/DC power supply 0....15 V 1



Ammeter, DC, I ≤ 6 A, e. g.531 712 Multimeter METRAmax 3 1*

537 32 Rheostat 10 V 1 1


501 25 Connecting lead, Ø 2,5 mm2, 50 cm, red 1*

501 26 Connecting lead, Ø 2,5 mm2, 50 cm, blue 1*




Components and basic circuits Electronics

P 4.1.1Current and voltage sources

P 4.1.1.3 Recording the current-voltagecharacteristics of a solar batteryas a function of the irradiance

Recording the curent-voltage characteristics of a solar battery as a function of the irradiance (P 4.1.1.3)

The solar cell is a semiconductor photoelement in which irradi-ance is converted directly to electrical energy at the p-n junction.Often, multiple solar cells are combined to create a solar battery.

In this experiment the current-voltage characteristics of a solarbattery are recorded for different irradiance levels. The irradianceis varied by changing the distance of the light source. Thecharacteristic curves reveal the characteristic behavior. At a lowload resistance, the solar battery supplies an approximately con-stant current. When it exceeds a critical voltage (which dependson the irradiance), the solar battery functions increasingly as aconstant-voltage source.

P4.

1.1.

3

152


578 63 STE solar battery 2 V / 0.3 A 1

576 74 Plug-in board, DIN A4 1

576 77 Pair of holders for rastered socket panel 1

577 90 STE potentiometer 220 V, 3 W 1

501 48 Set of 10 bridging plugs 1


Ammeter, DC, I ≤ 200 mA, e. g.531 100 Multimeter METRAmax 2 1

450 64 Halogen lamp housing 12 V, 50/100W 1

450 63 Halogen lamp, 12 V/100 W 1

521 25 Transformer 2 ....12 V 1

30011 Saddle base 1



Current-voltage characteristics for different illuminance levels

Recording the current-voltage characteristic of an incandescent lamp (P 4.1.2.1)

P 4.1.2

P 4.1.2.1 Recording the current-voltagecharacteristic of an incandescent lamp

P 4.1.2.2 Recording the current-voltagecharacteristic of a varistor

P 4.1.2.3 Measuring the temperature-dependency of PTC and NTCresistors

P 4.1.2.4 Measuring the light-dependencyof photoresistors

Special resistors

Many materials do not conduct voltage and current in proportionto one another. Their resistance depends on the current level. Intechnical applications, elements in which the resistance dependssignificantly on the temperature, the luminous intensity or an-other physical quantity are increasingly important.

In the first experiment, the computer-assisted measured-valuerecording system CASSY is used to record the current-voltagecharacteristic of an incandescent lamp. As the incandescent fila-ment heats up when current is applied, and its resistancedepends on the temperature, different characteristic curves aregenerated when the current is switched on and off. The charac-teristic also depends on the rate of increase dU/dt of the voltage.

The second experiment records the current-voltage characteris-tic of a varistor (voltage dependent resistor). Its characteristic isnon-linear in its operating range. At higher currents, it enters theso-called “rise range", in which the ohmic component of the totalresistance increases.

The aim of the third experiment is to measure the temperaturecharacteristics of an NTC thermistor resistor and a PTC thermis-tor resistor. The respective measured values can be describedusing empirical equations in which only the rated value R0, thereference temperature T0 and a material constant appear asparameters.

The subject of the final experiment is the characteristic of a CdSlight-dependent resistor. Its resistance varies from approx. 100 Vto approx. 10 MV, depending on the brightness. The resistanceis measured as a function of the distance from an incandescentlamp which illuminates the light-dependent resistor.

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153


505 08 Set of 10 lamps E 10; 12 V/3 W 1

50513 Lamp with socket E 10; 6.0 V/5.0 W 1

576 71 Plug-in board section 1 1 2

577 98 STE Resistor 1 E, 0.5 W 1

578 00 STE VDR-resistor 1

578 02 STE photoresistor LDR 05 1

578 04 STE NTC probe 4.7 kE 1

578 06 STE PTC probe 30 E 1

579 05 STE lamp holder, E10, lateral 1

DC power supply 0....16 V, 5A 1 1 1


Voltmeter, DC, U ≤ 20 V, e.g.531 100 Multimeter METRAmax 2 1 1 1

Ammeter, DC, I ≤ 3 A, e.g.531 100 Multimeter METRAmax 2 1 1 1


524 200 CASSY Lab 1


382 34 Thermometer, -10° to + 110 °C 1

666 767 Hot plate, 150 mm dia., 1500 W 1


500 441 Connecting lead, red 100 cm 1 1 1




2 2 2

579 06 I Lamp holder E10, top, STE I 1 I I I

521 210

521 545


P 4.1.3Diodes

P 4.1.3.1 Recording the current-voltage characteristicsof diodes

P 4.1.3.2 Recording the current-voltage characteristicsof zener diodes

P 4.1.3.3 Recording the current-voltage characteristicsof light-emitting diodes (LEDs)

Recording the current-voltage characteristics of light-emitting diodes (LEDs) (P 4.1.3.3)

Virtually all aspects of electronic circuit technology rely on semi-conductor components. The semiconductor diodes are amongthe simplest of these. They consist of a semiconductor crystal inwhich an n-conducting zone is adjacent to a p-conducting zone.Capture of the charge carriers, i.e. the electrons in the n-con-ducting and the “holes” in the p-conducting zones, forms a low-conductivity zone at the junction called the depletion layer. Thesize of this zone is increased when electrons or holes are re-moved from the depletion layer by an external electric field witha certain orientation. The direction of this electric field is calledthe reverse direction. Reversing the electric field drives the re-spective charge carriers into the depletion layer, allowing currentto flow more easily through the diode.

In the first experiment, the current-voltage characteristics of anSi-diode (silicon diode) and a Ge-diode (germanium diode)diode are measured and graphed manually point by point. Theaim is to compare the current in the reverse direction and thethreshold voltage as the most important specifications of the twodiodes.

The objective of the second experiment is to measure the cur-rent-voltage characteristic of a zener or Z-diode. Here, specialattention is paid to the breakdown voltage in the reverse direc-tion, as when this voltage level is reached the current risesabruptly. The current is due to charge carriers in the depletionlayer, which, when accelerated by the applied voltage, ionizeadditional atoms of the semiconductor through collision.

The final experiment compares the characteristics of infrared,red, yellow and green light-emitting diodes. The threshold voltageU is inserted in the formula

e · U = h · cÖ

e: electron charge, c: velocity of light,h: Planck’s constant,

to estimate the wavelength Ö of the emitted light.

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2

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1.3.

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3

154


576 74 Rastered socket panel, DIN A4 1 1 1

577 32 STE Resistor 100 E, 2 W 1 1 1

578 57 STE light emitting diode LD 57 C, green 1

578 47 STE light emitting diode yellow, LED 3, top 1

578 48 STE light emitting diode red, LED 2, top 1

578 49 STE light emitting diode LD 271 H, infrared 1

578 50 STE Ge-diode AA 118 1

578 51 STE Si-diode 1 N 4007 1

578 54 STE Z-diode ZPD 9.1 1


521 48 AC/DC-Power supply, 0....12 V, 230 V/50 Hz 1 1 1

531 100 Voltmeter, DC, U ≤ 10 V, e.g.Multimeter METRAmax 2 1 1 1

Ammeter, DC, I ≤ 150 mA, e.g. 531 100 Multimeter METRAmax 2 1 1 1

500 441 Connecting lead, red 100 cm 1 1 1


Rectification of AC voltages with diodes (P 4.1.4.1)

P 4.1.4

P 4.1.4.1 Rectification of AC voltageswith diodes

P 4.1.4.2 Limiting voltages with a Z-diode

P 4.1.4.3 Testing polarity with light emitting diodes.

Diode circuits

Diodes, zener diodes (or Z-diodes) and light-emitting diodes areused today in virtually every electronic circuit.

The first experiment explores the function of half-wave and full-wave rectifiers in the rectification of AC voltages. The half-waverectifier assembled using a single diode blocks the first half-waveof every AC cycle and conducts only the second half-wave(assuming the diode is connected with the corresponding polar-ity). The full-wave rectifier, assembled using four diodes in abridge configuration, uses both half-waves of the AC voltage.

The second experiment demonstrates how a Z-diode can beused to protect against voltage surges. As long as the appliedvoltage is below the breakdown voltage UZ of the Z-diode, the Z-diode acts as an insulator and the voltage U is unchanged. Atvoltages above UZ, the current flowing through the Z-diode is sohigh that U is limited to UZ.

The aim of the last experiment is to assemble a circuit for testingthe polarity of a voltage using a green and a red light emittingdiode (LED). The circuit is tested with both DC and AC voltage.

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155


576 74 Plug-in board, DIN A4 1 1 1

57742 STE resistor 680 E, 2 W 1 1

578 48 STE light emitting diode red, LED 2, top 1

578 57 STE light emitting diode LD 57 C, green 1

578 51 STE Si-diode 1 N 4007 4


579 06 STE lamp holder, E10, top 1 1

501 48 Set of 10 bridging plubs 1

505 08 Set of 10 lamps E 10; 12 V/3.0 W 1 1

521 48 AC/DC power supply 0....12 V, 230 V/50 Hz 1 1 1

575 211 Two channel oscilloscope 303 1


Voltmeter, AC/DC, U ≤ 12 V, e. g.531 100 Multimeter METRAmax 2 1




P 4.1.5Transistors

P 4.1.5.1 Investigating the diode characteristics of transistorjunctions

P 4.1.5.2 Recording the characteristics ofa transistor

P 4.1.5.3 Recording the characteristics ofa field-effect transistor

Recording the characteristics of a transistor (P 4.1.5.2)

Transistors are among the most important semiconductor com-ponents in electronic circuit technology. We distinguish betweenbipolar transistors, in which the electrons and holes are bothinvolved in conducting current, and field-effect transistors, inwhich the current is carried solely by electrons. The electrodesof a bipolar transistor are called the emitter, the base and thecollector. The transistor consists of a total of three n-conductingand p-conducting layers, in the order npn or pnp. The base layer,located in the middle, is so thin that charge carriers originating atone junction can cross to the other junction. In field-effect tran-sistors, the conductivity of the current-carrying channel is chan-ged using an electrical field, without applying power. The elementwhich generates this field is called the gate. The input electrodeof a field-effect transistor is known as the source, and the outputelectrode is called the drain.

The first experiment examines the principle of the bipolar tran-sistor and compares it with a diode. Here, the difference betweenan npn and a pnp transistor is explicitly investigated.

The second experiment examines the properties of an npn tran-sistor on the basis of its characteristics. This experiment mea-sures the input characteristic, i. e. the base current IB as a func-tion of the base-emitter voltage UBE, the output characteristic, i. e.the collector current IC as a function of the collector-emitter vol-tage UCE at a constant base current IB and the collector currentIC as a function of the base current IB at a constant collector-emitter voltage UCE .

In the final experiment, the characteristic of a field-effect tran-sistor, i. e. the drain current ID, is recorded and diagrammed as afunction of the voltage UDS between the drain and source at aconstant gate voltage UG.

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156


576 74 Plug-in board, DIN A4 1 1 1

577 32 STE resistor 100 Ω, 2 W 1 1

57744 STE resistor 1 kΩ, 2 W 1 1

577 64 STE resistor 47 kΩ, 0,5 W 1 1

577 90 STE potentiometer 220 Ω, 3 W 1 1

577 92 STE potentiometer 1 kΩ, 1 W 1 1

578 67 STE transistor BD 137, NPN, emitter bottom 1 1

578 68 STE transistor BD 138, PNP, emitter bottom 1

578 77 STE transistor BF 244 (FET) 1

578 51 STE Si-diode 1 N 4007 1


521 48 AC/DC power supply 0....12 V, 230 V/50 Hz 1 1

521 45 DC power supply 0 ... ± 15 V 1

Transformer, 6 V ~, 12 V ~/ 30 W 1

Ammeter, DC, I ≤ 100 mA, e.g.531 100 Multimeter METRAmax 2 1 2 1

Voltmeter, DC, U ≤ 12 V, e.g.531 100 Multimeter METRAmax 2 1 1 1



500 422 Connecting lead, blue, 50 cm 1 1


1

521 210

Transistor as amplifier (P 4.1.6.1)

P 4.1.6

P 4.1.6.1 Transistor as amplifier

P 4.1.6.2 Transistor as switch

P 4.1.6.3 Transistor as sine-wave generator (oscillator)

P 4.1.6.4 Transistor as function generator

P 4.1.6.5 Field-effect transistor as amplifier

P 4.1.6.6 Field-effect transistor as switch

Transistor circuits


157

Transistor circuits are investigated on the basis of a number ofexamples. These include the basic connections of a transistor asan amplifier, the transistor as a light-dependent or temperature-dependent electronic switch, the Wien bridge oscillator as anexample of a sine-wave generator, the astable multivibrator,basic circuits with field-effect transistors as amplifiers as well asthe field-effect transistor as a low-frequency switch.

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3

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2

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1(b

)

P4.

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1(a)

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6


576 74 Rastered socket panel DIN A4 1 1 1 1 1 1

578 67 STE transistor BD 137, NPN, emitter bottom 1 1 1

578 76 STE transistor BC 140, NPN, emitter bottom 2 1

578 762 STE transistor BC 140, NPN, emitter top 1

578 77 STE FET transistor BF 244 1

57744 STE resistor 1 kE, 2 W 1 1 1 2

57746 STE resistor 1.5 kE, 2 W 2

577 56 STE resistor 10 kE, 0.5 W 1 1 3 1 1

577 58 STE resistor 15 kE, 0.5 W 2 2 1

577 61 STE resistor 33 kE, 0.5 W 1

577 64 STE resistor 47 kE, 0.5 W 1 1 2 1


577 68 STE resistor 100 kE, 0.5 W 2 1

577 76 STE resistor 1 ME, 0.5 W 1

577 80 STE regulation resistor 10 kE, 1 W 1 1 1

577 81 STE regulation resistor 4.7 kE, 1 W 2

577 82 STE regulation resistor 47 kE, 1 W 1 1

577 92 STE regulation resistor 1 kE, 1 W 1


578 06 STE PTC probe 30 W 1





578 33 STE capacitor 0.47µF, 100 V 1



578 38 STE electrolytic capacitor 47 µF, 40 V 1 1 1

P4.

1.6.

5

P4.

1.6.

4

P4.

1.6.

3

P4.

1.6.

2

P4.

1.6.

1(b

)

P4.

1.6.

1(a)

P4.

1.6.

6


578 39 STE electrolytic capacitor 100 µF, 35 V 1 1

578 40 STE electrolytic capacitor 470 µF, 16 V 1 1 1

578 41 STE electrolytic capacitor 220 µF, 35 V 1

578 51 STE Si-diode 1 N 4007 2

579 06 STE Lamp holder E10, top 1 2

579 13 STE toggle switch, single-pole 1

579 38 STE heating element, 100 W, 2 W 1

501 48 Set of 10 bridging plugs 1 1 1 1 1 1 1

505 08 Set of 10 lamps E 10; 12 V/3 W 1

50519 Glow lamp E 10; 15 V/2.0 W 2



521 45 DC power supply 0....+/- 15 V 1 1 1 1 1 1

575 211 Two-channel oscilloscope 303 1 1 1 1 1 1

575 24 Screened cable BNC/4 mm 2 2 2 2 2 2

531 100 Multimeter METRAmax 2 2 1 1 1 1

501 28 Connecting lead, Ø 2.5 mm2, 50 cm, black 1 3 1 1

501 45 Pair of cables, 50 cm, red and blue 1 1 4 2 1 2 2

501 451 Pair of cables, 50 cm, black 1 1

1

1

522 621


P 4.1.7Optoelectronics

P 4.1.7.1 Recording the characteristicsof a phototransistor connectedas a photodiode

P 4.1.7.2 Assembling a purely opticaltransmission line

Assembling a purely optical transmission line (P 4.1.7.2)

Optoelectronics deals with the application of the interactionsbetween light and electrical charge carriers in optical and elec-tronic devices. Optoelectronic arrangements consist of a light-emitting, a light-transmitting and a light-sensitive element. Thelight beam is controlled electrically.

The subject of the first experiment is a phototransistor withoutbase terminal connection used as a photodiode. The current-voltage characteristics are displayed on an oscilloscope for theunilluminated, weakly illuminated and fully illuminated states. It isrevealed that the characteristic of the fully illuminated photodiodeis comparable with that of a Z-diode, while no conducting-statebehavior can be observed in the unilluminated state.

The second experiment demonstrates optical transmission of theelectrical signals of a function generator to a loudspeaker. Thesignals modulate the light intensity of an LED by varying the on-state current; the light is transmitted to the base of a phototran-sistor via a flexible light waveguide. The phototransistor isconnected in series to the speaker, so that the signals are trans-mitted to the loudspeaker.

158

P4.

1.7.

1 (b

)

P4.

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1 (a

)

P4.

1.7.

2



578 57 STE light emitting diode LD 57C, green 1

578 58 STE light emitting diode CQV 51J, red 1

578 61 STE photodiode BPX 43 1

P4.

1.7.

1 (b

)

P4.

1.7.

1 (a

)

P4.

1.7.

2


578 68 STE transistor BD 138, PNP, emitter bottom 1

578 85 STE operational amplifier LM 741 1

577 28 STE resistor 47 E, 2 W 1

577 32 STE resistor 100 E, 2 W 1 1

57740 STE resistor 470 E, 2 W 1

57744 STE resistor 1 kE 2 W 1


577 56 STE resistor 10 kE, 0.5 W 1 1 3





579 05 STE lamp holder E 10, lateral 1 1

505 08 Set of 10 lamps E 10, 12 V/3 W 1 1


521 45 DC power supply 0....+/- 15 V 1 1




Ammeter, DC, I ≤ 150 mA, e.g.531 100 Multimeter METRAmax 2 1 1

579 29 Earphone, 2 kE 1






521 210

522 621

Discrete assembly of an operational amplifier as a transistor circuit (P 4.2.1.1)

P 4.2.1

P 4.2.1.1 Discrete assembly of an operational amplifier as a transistor circuit

Internal design of an operational amplifier

Many electronics applications place great demands on theamplifier. The ideal characteristics include an infinite input resis-tance, an infinitely high voltage gain and an output voltage whichis independent of load and temperature. These requirements canbe satisfactorily met using an operational amplifier.

In this experiment, an operational amplifier is assembled fromdiscrete elements as a transistor circuit. The key components ofthe circuit are a difference amplifier on the input side and anemitter-follower stage on the output side. The gain and the phaserelation of the output signals are determined with respect to theinput signals in inverting and non-inverting operation. This ex-periment additionally investigates the frequency characteristic ofthe circuit.

Electronics Operational amplifier

159

P4.

2.1.

1


576 75 Rastered socket panel, DIN A3 2



57710 STE resistor 100 kE, 0.5 W 1





57744 STE resistor 1 kE, 2 W 4

577 52 STE resistor 4.7 kE, 2 W 2

577 93 STE 10-turn potentiometer 1 kE, 2 W 1



578 51 STE Si-diode 1 N 4007 4


578 69 STE transistor BC 550, NPN, emitter bottom 3

578 71 STE transistor BC 550, NPN, emitter top 1

578 72 STE transistor BC 560, PNP, emitter top 1


521 45 DC power supply 0....+/- 15 V 1




500 414 Connecting lead, black, 25 cm 5





Multimeter with diode tester, e.g.531 181 Analog-digital multimeter C.A 5011 1*

Circuit diagram of an operational amplifier assembled from discrete components


1+1*

522 621

Operational amplifier Electronics

P 4.2.2Operational amplifier circuits

P 4.2.2.1 Unconnected operationalamplifier (comparator)

P 4.2.2.2 Inverting operational amplifier

P 4.2.2.3 Non-inverting operationalamplifier

P 4.2.2.4 Adder and subtracter

P 4.2.2.5 Differentiator and integrator

Adder and subtracter (P 4.2.2.4)

160

The first experiment shows that the unconnected operationalamplifier overdrives for even the slightest voltage differential atthe inputs. It generates a maximum output signal with a sign cor-responding to that of the input-voltage differential.

In the second and third experiments, the output of the operation-al amplifier is fed back to the inverting and non-inverting inputsvia resistor R2. The initial input signal applied via resistor R1 isamplified in the inverting operational amplifier by the factor

V = – R2

R1

and in the non-inverting module by the factor

V =R2 + 1R1

The fourth experiment demonstrates the addition of multiple inputsignals and the subtraction of input signals.

The aim of the final experiment is to use the operational amplifieras a differentiator and an integrator. For this purpose, a capacitoris connected to the input resp. the feedback loop of the opera-tional amplifier. The output signals of the differentiator areproportional to the change in the input signals, and those of theintegrator are proportional to the integral of the input signals.

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576 74 Plug-in board, DIN A4 1 1 1 1 1

578 85 STE operational amplifier LM 741 1 1 1 1 1



57740 STE resistor 470 E, 2 W 1 1

57744 STE resistor 1 kE, 2 W 1 1 1

57746 STE resistor 1.5 kE, 2 W 1 1


577 50 STE resistor 3.3 kE, 2 W 1

577 52 STE resistor 4.7 kE, 2 W 1 1 1

577 56 STE resistor 10 kE, 0.5 W 1 2 2 2 1



577 61 STE resistor 33 kE, 0.5 W 2 1 1



577 68 STE resistor 100 kE, 0.5 W 1 1 4 1


577 76 STE resistor 1 ME, 0.5 W 1

577 80 STE regulation resistor 10 kE, 1 W 1 1

577 96 STE potentiometer 100 kE, 1 W 2 1 1



578 26 STE capacitor 2.2 nF, 160 V 2 1


578 51 STE Si diode 1 N 4007 1

578 76 STE transistor BC 140, NPN, emitter bottom 1

501 48 Set of 10 bridging plugs 1 1 1 1 1

521 45 DC power supply 0....+/- 15 V 1 1 1 1 1

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4

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3

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2

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575 211 Two-channel oscilloscope 303 1 1 1 1

575 24 Screened cable BNC/4 mm 2 2 2 2

531 57 Multimeter METRAport 3E 1 1 1

500 424 Connection lead, 50 cm, black 8 8 9 8 7

522 621

Assembling a traffic-light control system (P 4.3.1.1)

P 4.3.1

P 4.3.1.1 Assembling a traffic-light con-trol system

P 4.3.1.2 Assembling a model for controlof stairway illumination

Open-loop control

“Control” is the term for any process in which the input variablesof a system influence the output variables. The type of influencedepends on the individual system.

In the first experiment, the red, yellow and green phases of a traf-fic light are controlled cyclically by means of three cam disksdriven by a common shaft. Here, the elastic switching tabs areactuated as the on and off switches for the individual lights. Whenthe cam disks are provided with the appropriate pluggable cams,the three phases of the traffic light are controlled in a sensiblesequence.

The second experiment examines how a stairway illuminationsystem is controlled. Pressing a pushbutton switches on thelighting and the drive motor of the cam disk at the same time.Both remain on for a period which is determined by the numberof cams attached to the disk.

P4.

3.1.

1

P4.

3.1.

2

Electronics Open- and closed-loop control

161


576 74 Rastered socket panel, DIN A4 1 1

579 06 STE lamp socket E 10, top 3 1

579 10 STE key switch n.o. single-pole 1

579 18 STE dual program disk with cams 2 1

579 36 STE motor 12 V /4 W, with gear 1 1


505 08 Set of 10 lamps E 10; 12 V/3 W 1

505 07 Set of 10 lamps E 10; 4.0 V/0.16 W 1

521 48 AC/DC power supply 0....12 V, 230 V/50 Hz 1 1



Open- and closed-loop control Electronics

P 4.3.2Closed-loop control

P 4.3.2.1 Assembling a model for servocontrol

P 4.3.2.2 Brightness control with CASSY

P 4.3.2.3 Voltage control with CASSY

Voltage control with CASSY (P 4.3.2.3)

162

In the first experiment, a model of a servo control is assembledwhich consists of a P-controller with downstream operatingamplifier as power controller, a set-point potentiometer and amotor potentiometer as servo drive.

The aim of the two other experiments is the computer-aided rea-lization of closed control loops. In the one case, a PI controller isassembled and used to control an incandescent lamp whosebrightness is measured using a photoresistor. The other configu-ration controls a generator which supplies a constant voltageindependently of the load.

P4.

3.2.

2

P4.

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1(b

)

P4.

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1(a)

P4.

3.2.

3Cat. No. Description

578 31 STE capacitor 0.1 µF, 100 V 2 2


578 86 STE power OP amp TCA 365 1 1

579 05 STE lamp socket E 10, side 1

579 06 STE lamp socket E 10, top 3

579 13 STE toggle switch, single pole 1

579 43 STE motor and tachogenerator 2

581 43 STE potentiometer 4.7 kΩ, 2 W 1 1

581 49 STE motor potentiometer 4.7 kΩ, 2 W 1 1


50510 Set of 10 lamps E 10; 3.8 V/0.27 W 1

50513 Lamp with socket, E 10; 6.0 V/5.0 W 1

524 011 Power CASSY 1 1



524 200 CASSY Lab 1 1



307 641 Plastic tubing, 6 mm int. dia. 1


501 532 Set 30 connecting leads 1 1

501 45 Pair of cables, 50 cm, red and blue 1*

522 56 Function generator S 12, 0.1 Hz to 20 kHz 1*

additionally required:1 PC with Windows 95/NT or higher 1 1


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3.2.

2

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3.2.

1(b

)

P4.

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1(a)

P4.

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3Cat. No. Description



577 07 STE resistor 10 kΩ, 0.5 W 1 1

57715 STE resistor 0.1 Ω, 2 W 1

57719 STE resistor 1 Ω, 2 W 1

577 20 STE resistor 10 Ω, 2 W 1

57748 STE resistor 2.2 kΩ, 2 W 3 3

577 68 STE resistor 100 kΩ, 0.5 W 3 3

577 76 STE resistor 1 MΩ, 0.5 W 1 1

577 78 STE resistor 10 MΩ, 0.5 W 1 1

577 79 STE regulation resistor 1 kΩ, 1 W 1 1

577 81 STE regulation resistor 4.7 kΩ, 1 W 1 1



521 45 I DC power supply 0...+/-15 V I 1 I 1 I I

AND, OR, XOR, NOT, NAND and NOR operations with two variables (P 4.4.1.1)

P 4.4.1

P 4.4.1.1 AND, OR, XOR, NOT, NANDand NOR operations with twovariables

P 4.4.1.2 De Morgan's laws

P 4.4.1.3 Operations with three variables

Basic logical operations

Digital devices are built on the simple concept of repeated appli-cation of just a few basic circuits. Operations using these circuitsare governed by the rules of Boolean algebra, sometimes alsocalled “logic algebra” when applied to digital circuit technology.

The first experiment introduces all operations with one or twovariables used in digital technology. The aim is to verify the lawswhich apply in Boolean algebra, i. e. those describing commuta-tion, idempotents, absorption and negation.

The second experiment demonstrates de Morgan's laws in prac-tical application. The object of the final experiment is to verify theassociative and distributive laws through experiment when oper-ating three variables.

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4.1.

1-3

Electronics Digital technology

163


571 011 SIMULOG LS-TTL, P 1 Basic logic circuits 1

571 29 Base plate DIN A 4 for SIMULOG LS-TTL 1

522 33 Regulated power supply, 2 x 5 V DC/1.0 A 1

571 21 Set of 5 connecting leads, 4 cm 1



Digital technology Electronics

P 4.4.2Combinatorial and sequential circuits

P 4.4.2.1 AND, NAND, OR and NOR operations with four variables

P 4.4.2.2 Coders, decoders and codeconverters

P 4.4.2.3 Multiplexers and demultiplexers

P 4.4.2.4 Adders

P 4.4.2.5 Flipflops

P 4.4.2.6 Counters

P 4.4.2.7 Shift registers

4-bit digital counter (P 4.4.2.6)

164

A combinatorial circuit performs operations on multiple digitalcircuits such that the output variables are uniquely determinedby the input variables. A sequential circuit is additionally able tostore the states of individual variables. The output variables alsodepend on the result of preceding events, which is representedby the switching state of flipflops.

As an approach to the structure of complex combinatorial cir-cuits, the first experiment applies the understanding of basicoperations previously learned to the logical operation of fourinputs.

Combinatorial circuits for coding and decoding signals are thetheme of the second experiment. In this experiment, the object isto assemble a coder for coding decimal numbers in binary form,a corresponding decoder and a code converter for convertingbinary to Gray code.

The third experiment demonstrates how a multiplexer is used toswitch multiple inputs onto a single output and a demultiplexerdistributes the signals of a single input line to multiple outputlines.

The fourth experiment investigates half adders, full adders andparallel adders as key components of a computer.

The aim of the fifth experiment is to study the function of flipflops.It deals with the various demands on the behavior of these fun-damental components of sequential circuits, which are requiredfor assembling RS, D and JK flipflops.

The sixth experiment gives the students an opportunity to assem-ble various synchronous and asynchronous counters. Specifical-ly, these include a binary counter, a BCD counter, a 4-bit count-er, a forward-reverse counter and a counter with parallel datainput.

The final experiment investigates the shift register as a furtherimportant function group in data-processing systems. This ex-periment shows how these components can be used to realizemultiplication and division of binary numbers in an extremelyeasy fashion.

P4.

4.2.

1-7


571 011 SIMULOG LS-TTL, P 1 basic logic circuits 1

571 022 SIMULOG LS-TTL, extension P 2 switching networks and units 1







Serial and parallel adders and subtracters (P 4.4.3.3)

P 4.4.3

P 4.4.3.1 Data transfer between registers

P 4.4.3.2 Serial and parallel logic elements

P 4.4.3.3 Serial and parallel adders andsubtracters

P 4.4.3.4 Functions of the buffer, latchand accumulator

Serial and parallel arithmetic units

In information technology, the hardware executes arithmetic,Boolean and other operations using arithmetic units. The opera-tions can be performed either serially or in parallel.

The first three experiments investigate the serial and parallel pro-cessing of data in registers, logic elements and adders and sub-tracters.

The final experiment demonstrates the function of the buffer as abus driver, the latch as a small intermediate storage element andthe accumulator as a register which supports arithmetic opera-tions.

P4.

4.3.

1-4


165



571 022 SIMULOG LS-TTL extension P 2 switching networks and units 1

571 044 SIMULOG LS-TTL extension E 4 serial and parallel arithmetic units 1

571 29 Base plate DIN A4 for SIMULOG LS-TTL 1







P 4.4.4Digital control systems

P 4.4.4.1 Structure of functional circuits

P 4.4.4.2 DA and AD converter

Setup for measuring reaction times (P 4.4.4.1)

Digital control units are used increasingly in industrial applica-tions in order to realize periodic processes reliably and withoutthe need for a great deal of complex circuitry.

In the first experiment, the object is to assemble functional digi-tal circuits for controlling a traffic light, an LED display with hexa-decimal display, a digital clock with decimal display of secondsand an alarm system.

The second experiment investigates the function of an analog-digital and a digital-analog converter which allow digital and ana-log units to be integrated in an industrial open control loop.

166

P4.

4.4.

1-2



571 022 SIMULOG LS-TTL, extension P 2 switching networks and units 1

571 033 SIMULOG LS-TTL, extension E 3, digital measurements and control circuits 1


571 98 IC-socket, 14 pin, top 1

571 99 IC-socket, 16 pin, top 1







Structure of a central processing unit (CPU) (P 4.4.5.1)

P 4.4.5

P 4.4.5.1 Function of the ALU, CPU timer,RAM und I/O components

P 4.4.5.2 Address bus and data bus

P 4.4.5.3 Indirect, direct and immediateaddressing

P 4.4.5.4 Conditional and unconditionaljump instructions

P 4.4.5.5 Program memory

P 4.4.5.6 Examples of programs

Structure of a central processing unit (CPU)

The heart of every information processing system is the centralprocessing unit (CPU). This consists of an arithmetic and logicunit (ALU), a control unit, the registers and the working memory(RAM), as well as the input and output modules. These elementsare linked via the bus system. The structure of the CPU is deter-mined mainly by the requirements of the software.

The first experiment explores the functions of the individual hard-ware components of a CPU, while the second experiment inves-tigates the organization of the address and data buses.

The aim of the third experiment is to illustrate the difference be-tween indirect, direct and immediate addressing of storage loca-tions in arithmetic and logic operations.

The fourth experiment shows how a predefined program se-quence can be altered using conditional and unconditional jumpinstructions.

The fifth experiment looks at how to assemble and expand theprogram memory. Finally, simple program examples are realizedin the last experiment.


167

P4.

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571 099 SIMULOG LS-TTL, kit C 9 (complete kit) assembly of a central unit 1









P 4.4.6Microprocessor

P 4.4.6.1 Signal transmission via theaddress, data and controlbuses

P 4.4.6.2 Program counter and addressstructure, zero page

P 4.4.6.3 Data-transfer instructions

P 4.4.6.4 Rotation and shift instructions

P 4.4.6.5 Arithmetic and logic operations

P 4.4.6.6 Program control using jumps,branches, subprogram callsand interrupt processing

P 4.4.6.7 Application examples

Assembly with microprocessor (P 4.4.6.7)

The microprocessor BP 6502 is used as the basis for the step-by-step investigation of the main structures and functions of areal microprocessor with input/output units, address-bus displayand working memory. Here, the special properties of micropro-cessors are of course taken into account.

The first experiment comprises introductory demonstrations onsignal transmission via the address, data and control buses.

The second experiment illustrates the function of the programcounter, which counts one address further each time an instruc-tion is read. In addition, the division of the 16-bit wide addressesinto pages and the storage capacity of each page are examined,as well as the special importance of the zero page.

The third experiment focuses on the various data-transferinstructions of the processor and demonstrates how each one isused. This is followed in the fourth experiment by the investiga-tion of processing instructions which shift the content of a regis-ter one bit to the right or the left, so that a ninth bit, the carry flag,is required to accommodate the carry digit. The aim of the fifthexperiment is to perform arithmetic and logic operations on tworegister contents.

The final two experiments illustrate the control of complex pro-grams. Jump instructions enable the creation of a program loopas well as the subsequent return. Branching instructions make itpossible to make the program dependent on a condition. Sub-program calls, as the name implies, permit special subprogramsto be activated repeatedly from various points in the main pro-gram. Interrupt processing enables a defined interruption of theprogram flow in such a way that the program can be resumed atthe same point.

168

P4.

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571 088 SIMULOG LS-TTL, kit M 8 (complete kit) microprocessor circuits 1








Optics

170

Table of contents Optics

P5 OpticsP 5.1 Geometrical opticsP 5.1.1 Reflection and diffraction 171

P 5.1.2 Laws of imaging 172

P 5.1.3 Image distortion 173

P 5.1.4 Optical instruments 174

P 5.2 Dispersion and chromaticsP 5.2.1 Refractive index and dispersion 175

P 5.2.2 Decomposition of white light 176

P 5.2.3 Color mixing 177

P 5.2.4 Absorption spectra 178

P 5.3 Wave opticsP 5.3.1 Diffraction 179–180

P 5.3.2 Two-beam interference 182

P 5.3.3 Newton's rings 183

P 5.3.4 Michelson interferometer 184

P 5.3.5 Mach-Zehnder interferometer 185

P 5.3.6 White-light reflection holography 186

P 5.3.7 Transmission holography 187

P 5.4 PolarizationP 5.4.1 Basic experiments 188

P 5.4.2 Birefringence 189

P 5.4.3 Optical activity, polarimetry 190

P 5.4.4 Kerr effect 191

P 5.4.5 Pockels effect 192

P 5.4.6 Faraday effect 193

P 5.5 Light intensityP 5.5.1 Quantities and measuring methods

of lighting engineering 194

P 5.5.2 Laws of radiation 195

P 5.6 Velocity of lightP 5.6.1 Measurement according to

Foucault and Michelson 196

P 5.6.2 Measuring with short light pulses 197

P 5.6.3 Measuring withan electronically modulated signal 198

P 5.7 SpectrometerP 5.7.1 Prism spectrometer 199

P 5.7.2 Grating spectrometer 200–201

Optics Geometrical optics

171

Refraction (reflection) of light (P 5.1.1.1, P 5.1.1.2)

Reflection, refraction

P 5.1.1.1 Reflection of light at straightand curved mirrors

P 5.1.1.2 Refraction of light at straightsurfaces and investigation ofray paths in prisms and lenses

Frequently, the propagation of light can be adequately describedsimply by defining the ray path. Examples of this are the raypaths of light in mirrors, in lenses and in prisms using sectionalmodels.

The first experiment examines how a mirror image is formed byreflection at a plane mirror and demonstrates the reversibility ofthe ray path. The law of reflection is experimentally validated:

a = ba: angle of incidence, b: angle of reflection

Further experiment objectives deal with the reflection of a parallellight beam in the focal point of a concave mirror, the existence ofa virtual focal point for reflection in a convex mirror, the relation-ship between focal length and bending radius of the curved mir-ror and the creation of real and virtual images for reflection at acurved mirror.

The second experiment deals with the change of direction whenlight passes from one medium into another. The law of refractiondiscovered by W. Snell is quantitatively verified:

sina=

n2sinb n1

a: angle of incidence, b: = angle of refraction, n1: refractive index of medium 1 (here air), n2: refractive index of medium 2 (here glass)

This experiment topic also studies total reflection at the transitionfrom a medium with a greater refractive index to one with a lesserrefractive index, the concentration of a parallel light beam at thefocal point of a collecting lens, the existence of a virtual focalpoint when a parallel light beam passes through a dispersinglens, the creation of real and virtual images when imaging withlenses and the ray path through a prism.


463 52 Optical disk with 8 model objects 1


450 51 Lamp, 6 V/30 W 1

Transformer, 6 V AC, 12 V AC/30 VA 1


463 51 Diaphragm with 5 slits 1

460 08 Lens f = + 150 mm 1




P5.

1.1.

1–2

P 5.1.1

521 210

Geometrical optics Optics

172

Determining the focal lengths at collecting lenses using Bessel’s method (P 5.1.2.3)

Laws of imaging

P 5.1.2.1 Determining the focal lengthsat collecting and dispersinglenses using collimated light

P 5.1.2.2 Determining the focal lengthsat collecting lenses throughautocollimation

P 5.1.2.3 Determining the focal lengthsat collecting lenses using Bes-sel’s method

P 5.1.2.4 Verifying the imaging laws witha collecting lens

The focal lengths of lenses are determined by a variety of means.The basis for these are the laws of imaging.

In the first experiment, an observation screen is set up parallel tothe optical axis so that the path of a parallel light beam can beobserved on the screen after passing through a collecting or dis-persing lens. The focal length is determined directly as the dis-tance between the lens and the focal point.

In autocollimation, a parallel light beam is reflected by a mirrorbehind a lens so that the image of an object is viewed right nextto that object. The distance d between the object and the lens isvaried until the object and its image are exactly the same size. Atthis point, the focal length is:

f = d

In the Bessel method, the object and the observation screen areset up at a fixed overall distance s apart. Between these pointsthere are two lens positions x1 and x2 at which a sharply focusedimage of the object is produced on the observation screen. Fromthe lens laws, we can derive the following relationship for thefocal length:

f =1

· s –(x1 – x2)2

4 s )(In the final experiment, the object height G, the object width g, theimage height B and the image width b are measured directly fora collecting lens in order to confirm the lens laws. The focallength can be calculated using the formula:

f =g · b g + b


450 51 Lamp, 6 V/30 W 1 1 1

450 60 Lamp housing 1 1 1

460 20 Aspherical condenser 1 1 1

Transformer, 6 V AC, 12 V AC/30 W 1 1 1

460 02 Lens f = + 50 mm 1 1

460 03 Lens f = + 100 mm 1 1

460 08 Lens f = + 150 mm 1

460 04 Lens f = + 200 mm 1

460 09 Lens f = + 300 mm 1

460 06 Lens f = - 100 mm 1

46166 Set of two transparencies 1 1

460 28 Plane mirror with ball joint 1

44153 Translucent screen 1 1

460 43 Small optical bench 1 1 1


30101 Leybold multiclamp 3 3 3

31177 Steel tape measure, 2 m 1 1 1

P5.

1.2.

1

P5.

1.2.

2

P5.

1.2.

3–4

P 5.1.2

521 210

Spherical aberration and coma in lens imaging (P 5.1.3.1)

P 5.1.3

P 5.1.3.1 Spherical aberration and comain lens imaging

P 5.1.3.2 Astigmatism and curvature ofimage field in lens imaging

P 5.1.3.3 Lens imaging distortions (barreland cushion)

P 5.1.3.4 Chromatic aberration in lensimaging

Image distortion

A spherical lens only images a point in an ideal point when theimaging ray traces intersect the optical axis at small angles, andthe angle of incidence and angle of refraction are also smallwhen the ray passes through the lens. As this condition is onlyfulfilled to a limited extent in practice, aberrations (image de-fects) are unavoidable.

The first two experiments deal with aberrations of image sharp-ness. In a ray path parallel to the optical axis, paraxial rays areunited at a different distance from abaxial rays. This effect,known as “spherical aberration”, is particularly apparent in len-ses with sharp curvatures. “Coma” is the term for one-sided,plume-like or blob-like distortion of the image when imaged by abeam of light passing through the lens at an oblique angle. Astig-matism and curvature of field may be observed when imaginglong objects with narrow light beams. The focal plane is in reali-ty a curved surface, so that the image on the observation screenbecomes increasingly fuzzy toward the edges when the middle issharply focused. Astigmatism is the phenomenon whereby atightly restricted light beam does not produce a point-type image,but rather two lines which are perpendicular to each other with afinite spacing with respect to the axis.

The third experiment explores aberrations of scale. An iris dia-phragm directly in front of or behind the imaging lenses causesdistortions of the image. Blocking light rays in front of the lenscauses a barrel-shaped distortion, i. e. a reduction in the imagingscale with increasing object size. Screening behind the lensresults in cushion-type aberrations.

The fourth experiment examines chromatic aberrations. Theseare caused by a change in the refractive index with the wave-length, and are thus unavoidable when not working with non-monochromatic light.

P5.

1.3.

3

P5.

1.3.

2

P5.

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P5.

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4

Optics Geometrical optics

173


461 61 Pair of stops for spherical aberration 1

461 66 Set of 2 transparencies 1

467 95 Filter set red, green, blue 1

450 60 Lamp housing 1 1 1 1

450 51 Lamp, 6 V/30 W 1 1 1 1

460 20 Aspherical condensor 1* 1* 1 1

Transformer, 6 V AC, 12 V AC / 30 W 1 1 1 1

460 08 Lens, f = + 150 mm 1 1 1 1

460 26 Iris diaphragm 1 1 1 1

441 53 Translucent screen 1 1 1 1





Intersections of paraxial and abaxial rays

521 210

Geometrical optics Optics

P 5.1.4Optical instruments

P 5.1.4.1 Magnifier and microscope

P 5.1.4.2 Kepler’s telescope and Galileo’s telescope

Kepler’s telescope (P 5.1.4.2)

The magnifier, the microscope and the telescope are introducedas optical instruments which primarily increase the angle of vi-sion. The design principle of each of these instruments is repro-duced on the optical bench. For quantitative conclusions, thecommon definition of magnification is used:

V =tanc c: angle of vision with instrument

tanG G: angle of vision without instrument

In the first experiment, small objects are observed from a shortdistance. First, a collecting lens is used as a magnifier. Then, amicroscope in its simplest form is assembled using two collect-ing lenses. The first lens, the objective, produces a real, mag-nified and inverted intermediate image. The second lens, theocular (or eyepiece) is used as a magnifier to view this inter-mediate image. For the total magnification of the microscope, thefollowing applies:

VM = Vob · VocVob: imaging scale of objective,Voc: imaging scale of ocular.

Here, Voc corresponds to the magnification of the magnifier.

Voc = s0 s0: clear field of vision,foc foc: focal length of ocular.

The aim of the second experiment is to observe distant objectsusing a telescope. The objective and the ocular of a telescopeare arranged so that the back focal point of the objective coin-cides with the front focal point of the ocular. A distinction is madebetween the Galilean telescope, which uses a dispersing lens asan ocular and produces an erect image, and the Kepler tele-scope, which produces an inverted image because its ocular isa collecting lens. In both cases, the total magnification can bedetermined as:

VT = fob fob: focal length of objective,foc foc: focal length of ocular.

P5.

1.4.

1

P5.

1.4.

2

174



450 51 Lamp, 6 V/30 W 1




311 09 Glass scale, 5 cm long 1

460 02 Lens, f = + 50 mm 1 1

460 03 Lens, f = + 100 mm 1 1

460 08 Lens, f = + 150 mm 1

460 04 Lens, f = + 200 mm 1 1

460 05 Lens, f = + 500 mm 1

460 06 Lens, f = – 100 mm 1


460 353 Optics rider, H = 60 mm/W = 36 mm 3




30011 Saddle base 1

Ray path through the Kepler telescope

521 210

Determining the refractive index and dispersion of liquids (P 5.2.1.2)

P 5.2.1

P 5.2.1.1 Determining the refractive indexand dispersion of flint glassand crown glass

P 5.2.1.2 Determining the refractive indexand dispersion of liquids

Refractive index and dispersion

Dispersion is the term for the fact that the refractive index n is dif-ferent for different-colored light. Often, dispersion also refers tothe quantity dn/dl, i. e. the quotient of the change in the refrac-tive index dn and the change in the wavelength dl.

In the first experiment, the angle of minimum deviation G is deter-mined for a flint glass and a crown glass prism at the samerefracting angle Z. This enables determination of the refractiveindex of the respective prism material according to the formula

sin 1 (e + f)2

n = sin 1 e

2

The measurement is conducted for several different wavelengths,so that the dispersion can also be quantitatively measured.

In the second experiment, an analogous setup is used to investi-gate dispersion in liquids. Toluol, turpentine oil, cinnamic ether,alcohol and water are each filled into a hollow prism in turn, andthe differences in the refractive index and dispersion are ob-served.

P5.

2.1.

1

P5.

2.1.

2

Optics Dispersion, chromatics

175


465 22 Crown glass prism 1

465 32 Flint glass prism 1

465 51 Hollow prism 1

460 25 Prism table 1 1

460 22 Holder with spring clips 1 1


450 51 Lamp, 6 V/30 W 1 1


Transformator, 6 V AC,12 V AC /30 VA 1 1

468 03 Monochromatic light filter, red 1 1

468 07 Monochromatic light filter, yellow/green 1 1

468 11 Monochromatic light filter, blue with violet 1 1

460 08 Lens, f = + 150 mm 1 1




311 77 Steel tape measure, 2m 1 1

Toluol, 250 ml 1

Terpentine oil, rectified, 250 ml 1

Cinnamil ether, 100 ml 1

665 003 Funnel, 50 mm dia., glass 1

521 210

675 2100

675 0410

675 4760

Dispersion, chromatics Optics

P 5.2.2Dispersion of white light

P 5.2.2.1 Newton’s experiments ondispersion and recombinationof white light

P 5.2.2.2 Adding complementary colorsto create white light

Newton’s experiment on the non-dispersable nature of spectral colors (P 5.2.2.1)

The discovery that white sunlight is made up of light of differentcolors was one of the great milestones toward understanding theperception of color. Isaac Newton, in particular, conductednumerous experiments on this topic.

The first experiment topic looks at Newton’s experiments on thedecomposition of a beam of white light using the light of anincandescent light bulb. In the first step, the white light is brokendown into its spectral components in a glass prism. The secondstep shows that the dispersed light cannot be broken down fur-ther by a second prism. If only one spectral component is al-lowed to pass through a slit behind the first prism, the secondprism will deviate this light, but will not break it down further.Using an assembly of two crossed prisms with the refractingedges perpendicular to each other provides additional confirma-tion of this principle. The vertical spectrum behind the first prismis deviated obliquely by the second prism, as the spectral colorsare not broken down further by the second prism. The fourth stepdemonstrates the recombination of spectral colors to createwhite light by viewing the spectrum behind the first prism througha second prism arranged parallel to the first.

P5.

2.2.

1

P5.

2.2.

2

176


465 32 Flint glass prism 2 1

465 25 Narrow prism on base 1


450 51 Lamp, 6 V/30 W 1 1



Transformer, 6 V AC, 12 V AC / 30 W 1 1

460 03 Lens, f = + 100 mm 1






301 03 Rotatable clamp 2

300 51 Stand rod, right-angled 1 1


The second experiment also uses the color spectrum of anincandescent light bulb. This experiment starts with the recombi-nation of the spectrum in a collecting lens to create white light.Subsequent screening of individual spectral ranges using anextremely narrow prism produces two images of different colors,which partially overlap on the observation screen. The colors canbe varied by laterally shifting the narrow prism. The overlap fieldis white, which means that the respective complementary colorsare projected next to each other on the screen.

521 210

Optics Dispersion, chromatics

177

Additive and subtractive color mixing (P 5.2.3.1)

Color mixing

P 5.2.3.1 Additive and subtractive colormixing

The apparatus for additive color mixing contains three color fil-ters with the primary colors red, green and yellow. The coloredlight is made to overlap either partially or completely using mir-rors. In the areas of overlap, additive color mixing creates thecolors cyan (green + blue), magenta (blue + red) and yellow (red+ green), and in the middle white (red + blue + green).

The apparatus for subtractive color mixing contains three colorfilters with the colors cyan, magenta and yellow. The filters par-tially overlap; in the overlap zones, the three primary colors blue,red and green, and in the middle, black, are formed.


46616 Apparatus for additive color mixing 1

46615 Apparatus for subtractive color mixing 1



Additive color mixing Subtractive color mixing

P5.

2.3.

1

P 5.2.3


Dispersion, chromatics Optics

178

Absorption spectra of tinted glass samples (P 5.2.4.1)

Absorption spectra

P 5.2.4.1 Absorption spectra of tintedglass samples

P 5.2.4.2 Absorption spectra of coloredliquids

The colors we perceive when looking through colored glass orliquids are created by the transmitted component of the spectralcolors.

In both experiments, the light passing through colored pieces ofglass or colored liquids from an incandescent light bulb is viewedthrough a direct-vision prism and compared with the continuousspectrum of the lamp light. The original, continuous spectrum withthe continuum of spectral colors disappears. All that remains isa band with the color components of the filter or liquid.


466 050 Direct vision prism 1 1

477140 Plate glass cell 50 x 50 x 20 mm 1

467960 Filter set yellow, cyan, magenta 1

468 010 Monochromatic light filter, dark red 1

468 090 Monochromatic light filter, blue/green 1

468110 Monochromatic light filter, blue with violet 1




450 510 Lamp, 6 V/30 W 1 1

460 200 Aspherical condenser 1 1

ransformer, 6 V AC, 12 V AC/30 VA 1 1


460 030 Lens f = + 100 mm 1 1


301010 Leybold multilamp 5 5


Potassium permanganate, 250 g 1

P5.

2.4.

1

P5.

2.4.

2

Absorption spectra of tinted glass samples (without filter set yellow, cyan, magenta)

P 5.2.4

521 210 T

672 7010

Diffraction at a double slit (P 5.3.1.2)

P 5.3.1

P 5.3.1.1 Diffraction at a slit, at a postand at a circular iris diaphragm

P 5.3.1.2 Diffraction at a double slit andat multiple slits

P 5.3.1.3 Diffraction at one- and two-dimensional gratings

Diffraction

The first experiment looks at the intensity minima for diffractionat a slit. Their angles Gk with respect to the optical axis for a slitof the width b is given by the relationship

sin Gk = k · Ö

(k = 1; 2; 3; . . . )b

Ö: wavelength of the light

In accordance with Babinet’s theorem, diffraction at a post pro-duces similar results. In the case of diffraction at a circular irisdiaphragm with the radius r, concentric diffraction rings may beobserved; their intensity minima can be found at the angles Gkusing the relationship

sin Gk = k · Ö

(k = 0.610; 1.116; 1.619; . . . )r

The second experiment explores diffraction at a double slit. Theconstructive interference of secondary waves from the first slit withsecondary waves from the second slit produces intensity maxima;at a given distance d between slit midpoints, the angles Gn of thesemaxima are specified by

sin Gn = n · Ö

(n = 0; 1; 2; . . . )d

The intensities of the various maxima are not constant, as theeffect of diffraction at a single slit is superimposed on the dif-fraction at a double slit. In the case of diffraction at more than twoslits with equal spacings d, the positions of the interference maxi-ma remain the same. Between any two maxima, we can alsodetect N-2 secondary maxima; their intensities decrease for afixed slit width b and increasing number of slits N.

The third experiment investigates diffraction at a line grating anda crossed grating. We can consider the crossed grating as con-sisting of two line gratings arranged at right angles to each other.The diffraction maxima are points at the “nodes” of a straight,square matrix pattern.

P5.

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P5.

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P5.

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Optics Wave optics

179

Cat. No Description

469 91 Diaphragm with 3 single slits 1

469 96 Diaphragm with 3 circular holes 1

469 97 Diaphragm with 3 fine lines 1

469 84 Diaphragm with 3 double slits 1


469 86 Diaphragm with 5 multiple slits 1

469 87 Diaphragm with 3 gratings 1

469 88 Diaphragm with 2 wire-mesh gratings 1

He-Ne laser 0.2 /1 mW max., linearly polarized 1 1 1

460 22 Holder with spring clips 1 1 1

460 01 Lens, f = + 5 mm 1 1 1

460 02 Lens, f = + 50 mm 1 1 1

460 32 Precision optical bench, standardized cross section, 1 m 1 1 1

460 353 Optics rider, H = 60 mm/W = 36 mm 4 4 4

441 53 Translucent screen 1 1 1

300 11 Saddle base 1 1 1

471 830

Wave optics Optics

P 5.3.1Diffraction

P 5.3.1.4 Diffraction at a single slit –measuring and evaluating withCASSY

P 5.3.1.5 Diffraction at multiple slits –measuring and evaluating withCASSY

Diffraction at a single slit – measuring and evaluating with CASSY (P 5.3.1.4)

P5.

3.1.

4

P5.

3.1.

5

180

A photoelement with a narrow light opening is used to measurethe diffraction intensities; this sensor can be moved perpendicu-larly to the optical axis on the optical bench, and its lateral posi-tion can be measured using a displacement transducer. Themeasured values are recorded and evaluated using the softwareUniversal Data Acquisition.

The first experiment investigates diffraction at slit of variablewidth. The recorded measured values for the intensity I are com-pared with the results of a model calculation for small diffractionangles G which uses the slit width b as a parameter:

l: wavelength of the light,s: lateral shift of photoelement, L: distance between diffraction object and photoelement.

The second experiment explores diffraction at multiple slits. Inthe model calculation performed for comparison purposes, theslit width b and the slit spacing d are both used as parameters.

N: number of illuminated slits.

I a sin öb f) 2( l

öb fl

( ) where f = sL

l a sin öb f) 2

l( löb fl

( ) · l asin Nöd f) 2( l

sin öd f ( l )( )


460 14 Adjustable slit 1

He-Ne laser 0.2/1 mW max., linearly polarized 1 1

460 01 Lens, f = + 5 mm 1 1

460 02 Lens, f = + 50 mm 1 1





578 62 STE photoelement 1 1

460 21 Holder for plug-in elements 1 1


460 34 Auxiliary bench w. swivel joint, protractor and index bench, 0.5 m 1 1

460 352

460 355 Sliding rider 1 1


524 040 mV-box 1 1

524 031 Current supply box 1 1

529 031 Displacement sensor 1 1

524 200 CASSY Lab 1 1


309 48 Cord, 10 m 1 1




Rider 90/50 4 4

471 830

Diffraction at a single slit (P 5.3.1.6, top) and at a half-plane (P 5.3.1.8, bottom)

P 5.3.1

P 5.3.1.6 Diffraction at a single slit –measuring and evaluating withVideoCom

P 5.3.1.7 Diffraction at multiple slits –measuring and evaluating withVideoCom

P 5.3.1.8 Diffraction at a half-plane –measuring and evaluating withVideoCom

Diffraction

Diffraction at a single slit or multiple slits can also be measured asa one-dimensional spatial intensity distribution using the single-line CCD camera VideoCom (here used without the camera lens).The VideoCom software enables fast, direct comparison of themeasured intensity distributions with model calculations in whichthe wavelength Ö, the focal length f of the imaging lens, the slitwidth b and the slit spacing d are all used as parameters. Theseparameters agree closely with the values arrived at through exper-iment.

It is also possible to investigate diffraction at a half-plane. Thanksto the high-resolution CCD camera, it becomes easy to follow theintensity distribution over more than 20 maxima and minima andcompare it with the result of a model calculation. The model cal-culation is based on Kirchhoff’s formulation of Huygens’ principle.The intensity I at point x in the plane of observation is calculatedfrom the amplitude of the electric field strength E at this point usingthe formula

l (x) = |E(x) |2

The field strength is obtained through the phase-correct additionof all secondary waves originating from various points x’ in the dif-fraction plane, from the half-plane boundary x’ = 0 to x’ = ∞

∞E(x) Ù ∫ exp( i · G (x, x’) ) · dx’

0

Here,

G(x, x’) = 2S

· (x – x’)2

Ö 2L

is the phase shift of the secondary wave which travels from pointx’ in the diffraction plane to point x in the observation plane as afunction of the direct wave. The parameters in the model calcula-tion are the wavelength Ö and the distance L between the diffrac-tion plane and the observation plane. Here too, the agreement withthe values obtained in the experiment is close.

P5.

3.1.

7

P5.

3.1.

6

P5.

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8

Optics Wave optics

181

Measured (black) and calculated (red) intensity distributions (P 5.3.1.6, P 5.3.1.8)


460 14 Adjustable slit 1




He-Ne laser 0.2/1 mW max., linearly polarized 1 1 1

472 401 Polarization filter 1 1 1

460 01 Lens, f = + 5 mm 1 1 1

460 02 Lens, f = + 50 mm 1 1

460 11 Lens, f = + 500 mm 1 1 1


460 32 Precision optical bench, standardized cross section, 1 m 1 1 1


33747 VideoCom 1 1 1

additionally required:PC with Windows 95 or Windows NT 1 1 1

471 830

Wave optics Optics

182

Interference at a Fresnel’s mirror with an He-Ne laser (P 5.3.2.1)

Two-beam interference

P 5.3.2.1 Interference at a Fresnel’s mir-ror with an He-Ne laser

P 5.3.2.2 Lloyd’s mirror experiment withan He-Ne laser

P 5.3.2.3 Interference at Fresnel’s bi-prism with an He-Ne laser

In these experiments, two coherent light sources are generatedby recreating three experiments of great historical significance.In 1821, A. Fresnel used two mirrors inclined with respect to oneanother to create two virtual light sources positioned close to-gether, which, being coherent, interfered with each other.

In 1839, H. Lloyd demonstrated that a second, virtual light sourcecoherent with the first can be created by reflection in a mirror. Heobserved interference phenomena between direct and reflectedlight. Coherent light sources can also be produced using aFresnel biprism, first demonstrated in 1826. Refraction in bothhalves of the prism results in two virtual images, which are closertogether the smaller the prism angle is.

In each of these experiments, the respective wavelength Ö of thelight used is determined by the distance d between two inter-ference lines and the distance a of the (virtual) light sources. Ata sufficiently great distance L between the (virtual) light sourcesand the projection screen, the relationship

Ö = a · dL

obtains. The determination of the quantity a depends on the res-pective experiment setup.


He-Ne laser , linearly polarized 1 1 1

471050 Fresnel’s mirror, adjustable 1 1

662 093 Microscope slides 76 x 26 mm, 50 pcs. 1

471090 Fresnel biprism 1

460 250 Prism table 1

460 010 Lens f = +05 mm 1 1 1

460 040 Lens f = + 200 mm 1 1 1

460 320 Precision optical bench, standardized cross-section, 1 m 1 1 1



441530 Translucent screen 1 1 1


311520 Vernier calipers, plastic 1 1 1

311770 Steel tape measure, 2 m 1 1 1

P5.

3.2.

3

P5.

3.2.

1

P5.

3.2.

2

P 5.3.2

P 5.3.2.1 P 5.3.2.2 P 5.3.2.3

471 830

Optics Wave optics

183

Newton’s rings in transmitted and reflected white light (P 5.3.3.2)

Newton’s rings

P 5.3.3.1 Newton’s rings in transmittedmonochromatic light

P 5.3.3.2 Newton’s rings in transmittedand reflected white light

Newton’s rings are produced using an arrangement in which aconvex lens with an extremely slight curvature is touching a glassplate, so that an air wedge with a spherically curved boundarysurface is formed. When this configuration is illuminated with avertically incident, parallel light beam, concentric interferencerings (the Newton’s rings) are formed around the point of contactbetween the two glass surfaces both in reflection and in transmit-ted light. For the path difference of the interfering partial beams,the thickness d of the air wedge is the defining factor; this dis-tance is not in a linear relation to the distance r from the point ofcontact:

d = r 2

2R

R: bending radius of convex lens

In the first experiment, the Newton’s rings are investigated withmonochromatic, transmitted light. At a known wavelength Ö, thebending radius R is determined from the radii rn of the inter-ference rings. Here, the relationship for constructive interferenceis:

d = n · l

2 where n = 0, 1, 2, ...

Thus, for the radii of the bright interference rings, we can say:

r 2n = n · R · l where n = 0, 1, 2 , ...

In the second experiment, the Newton’s rings are studied both inreflection and in transmitted light. As the partial beams in the airwedge are shifted in phase by Ö/2 for each reflection at the glasssurfaces, the interference conditions for reflection and transmit-ted light are complementary. The radii rn of the bright interferencelines calculated for transmitted light using the equations abovecorrespond precisely to the radii of the dark rings in reflection. Inparticular, the center of the Newton’s rings is bright in transmittedlight and dark in reflection. As white light is used, the interferencerings are bordered by colored fringes.


471111 Glass plates for Newton’s rings 1 1

460 03 Lens f = + 100 mm 2

460 04 Lens f = + 200 mm 2


47188 Beam divider 2


460 32 Precision optical bench, standardized cross-section, 1 m 1 1



460 356 Cantilever arm 100 1

451111 Spectral lamp Na 1

451062 Spectral lamp Hg 100 1

45116 Housing for spectral lamps 1

45130 Universal choke 230 V, 50 Hz 1

450 64 Halogen lamp housing 12 V, 50/100 W 1

450 63 Halogen lamp, 12 V/100 W 1

52125 Transformer 2 ... 12 V 1

468 30 Mercury light filter, yellow 1

468 31 Mercury light filter, green 1

468 32 Mercury light filter, blue 1

44153 Translucent screen 1

30011 Saddle base 1

50133 Connecting lead, dia. 2.5 mm2, 100 cm, black 2

P5.

3.3.

1

P5.

3.3.

2

P 5.3.3

5

Wave optics Optics

184

Setting up a Michelson interferometer on the laser optics base plate (P 5.3.4.1)

Michelson interferometer

P 5.3.4.1 Setting up a Michelson interferometer on the laser op-tics base plate

P 5.3.4.2 Determining the wavelength ofthe light of an He-Ne laserusing a Michelson interferometer

In a Michelson interferometer, an optical element divides a coher-ent light beam into two parts. The component beams travel differ-ent paths, are reflected into each other and finally recombined.As the two component beams have a fixed phase relationshipwith respect to each other, interference patterns can occur whenthey are superposed on each other. A change in the optical pathlength of one component beam alters the phase relation, andthus the interference pattern as well.

Thus, given a constant refractive index, a change in the inter-ference pattern can be used to determine a change in the geo-metric path, e.g. changes in length due to heat expansion or theeffects of electric or magnetic fields. When the geometric path isunchanged, then this configuration can be used to investigatechanges in the refractive index due to variations e.g. in pressure,temperature and density.

In the first experiment, the Michelson interferometer is assembledon the vibration-proof laser optics base plate. This setup is idealfor demonstrating the effects of mechanical shocks and airstreaking.

In the second experiment, the wavelength of an He-Ne laser isdetermined from the change in the interference pattern whenmoving an interferometer mirror using the shifting distance Ws ofthe mirror. During this shift, the interference lines on the observa-tion screen move. In evaluation, either the interference maxima orinterference minima passing a fixed point on the screen while theplane mirror is shifted are counted. For the wavelength Ö, the fol-lowing equation applies:

Ö = 2 ·Ds

Z

Z: number of intensity maxima or minima counted


473 400 Laser optics base plate 1 1

He-Ne laser 0.2/1 mW max, linearly polarized 1 1

0 Laser mount 1 1

473 420 Optics base 4 5

473 432 Beam divider 50 % 1 1

473 430 Holder for beam divider 1 1

473 460 Planar mirror with fine adjustment 2 2

473 470 Spherical lens, f + 2.7 mm 1 1

473 480 Fine adjustment mechanism 1



311030 Wooden ruler, 1 m long 1 1

P5.

3.4.

1

P5.

3.4.

2

P 5.3.4

471 830

473 411

Optics Wave optics

185

Measuring the refractive index of air with a Mach-Zehnder interferometer (P 5.3.5.2)

Mach-Zehnder- interferometer

P 5.3.5.1 Setting up a Mach-Zehnderinterferometer on the laseroptics base plate

P 5.3.5.2 Measuring the refractive indexof air with a Mach-Zehnderinterferometer

In a Mach-Zehnder interferometer, an optical element divides acoherent light beam into two parts. The component beams aredeflected by mirrors and finally recombined. As the two partialbeams have a fixed phase relationship with respect to each other,interference patterns can occur when they are superposed oneach other. A change in the optical path length of one componentbeam alters the phase relation, and consequently the interferen-ce pattern as well. As the component beams are not reflectedinto each other, but rather travel separate paths, these experi-ments are easier to comprehend and didactically more effectivethan experiments with the Michelson interferometer. However, theMach-Zehnder interferometer is more difficult to adjust.

In the first experiment, the Mach-Zehnder interferometer isassembled on the vibration-proof laser optics base plate. In thesecond experiment, the refractive index of air is determined. Toachieve this, an evacuable chamber is placed in the path of onecomponent beam of the Mach-Zehnder interferometer. Slowlyevacuating the chamber alters the optical path length of therespective component beam.

Setting up a Michelson interferometer is recommended beforeusing a Mach-Zehnder interferometer for the first time.


473 400 Laser optics base plate 1 1


0 Laser mount 1 1

473 420 Optics base 5 6

473 430 Holder for beam divider 2 2

473 432 Beam divider 50 % 2 2

473 460 Planar mirror with fine adjustment 2 2

473 470 Spherical lens, f + 2.7 mm 1 1

473 485 Evacuable chamber 1




311030 Wooden ruler, 1 m long 1 1



P5.

3.5.

1

P5.

3.5.

2

P 5.3.5

Setting up a Mach-Zehnder interferometer on the laser optics base plate (P 5.3.5.1)

471 830

473 411

Wave optics Optics

186

Creating white-light reflection holograms on the laser optics base plate (P 5.3.6.1)

White-light reflection holography

P 5.3.6.1 Creating white-light reflectionholograms on the laser opticsbase plate

In creating white-light reflection holograms, a broadened laserbeam passes through a film and illuminates an object placedbehind the film. Light is reflected from the surface of the objectback onto the film, where it is superposed with the light waves ofthe original laser beam. The film consists of a light-sensitive emul-sion of sufficient thickness. Interference creates standing waveswithin the film, i.e. a series of numerous nodes and antinodes at adistance of Ö/4 apart. The film is exposed in the planes of the anti-nodes but not in the nodes. Semitransparent layers of metallicsilver are formed at the exposed areas.

To reconstruct the image, the finished hologram is illuminatedwith white light – the laser is not required. The light wavesreflected by the semitransparent layers are superposed on eachother in such a way that they have the same properties as thewaves originally reflected by the object. The observer sees athree-dimensional image of the object. Light beams originating atdifferent layers only reinforce each other when they are in phase.

The in-phase condition is only fulfilled for a certain wavelength,which allows the image to be reconstructed using white light.

The object of this experiment is to create white-light reflectionholograms. This process uses a protection class 2 laser, so as tominimize the risk of eye damage for the experimenter. Both ampli-tude and phase holograms can be created simply by varying thephotochemical processing of the exposed film.

Recommendation: the Michelson interferometer on the laser op-tics base plate is ideal for demonstrating the effects of disturb-ances due to mechanical shocks or air streaking in unsuitablerooms, which can prevent creation of satisfactory holograms.


473 40 Laser optics base plate 1

He-Ne laser 0.2/1 mW max, linearly polarized 1

Laser mount 1

473 42 Optics base 3

473 44 Film holder 1

473 45 Object holder 1

473 47 Spherical lens f = 2.7 mm 1

31103 Wooden ruler, 1 m long 1

473 448 Holography film 1

473 446 Darkroom accessories 1

663 615 Schuko socket strip, 5 sockets (safety mains sockets) 1

31317 Stopclock II, 60 s/30 min 1

64911 Set of 6 small trays, 1 x 1 RE 1

661234 Polyethylene bottle, 1000 ml, wn with screw cap 3

667016 Scissors, 200 mm, pointed 1

473 444 Photographic chemicals 1

Iron(III) nitrate nonahydrate, 250 g 1

Potassium bromide (KBr), 100 g 1

P5.

3.6.

1

P 5.3.6

671 8910

672 4910

471 830

473 411

Optics Wave optics

187

Creating transmission holograms on the laser optics base plate (P 5.3.7.1)

Transmission holography

P 5.3.7.1 Creating transmission holograms on the laser opticsbase plate

In creating transmission holograms, a laser beam is split into anobject beam and a reference beam, and then broadened. Theobject beam illuminates an object and is reflected. The reflectedlight is focused onto a film together with the reference beam,which is coherent with the object beam. The film records an irreg-ular interference pattern which shows no apparent similarity withthe object in question.

To reconstruct the hologram, a light beam which corresponds tothe reference beam is diffracted at the amplitude hologram insuch a way that the diffracted waves are practically identical tothe object waves. In reconstructing a phase hologram the phaseshift of the reference waves is exploited. In both cases, the ob-server sees a three-dimensional image of the object.

The object of this experiment is to create transmission hologramsand subsequently reconstruct them. This process uses a protec-tion class 2 laser, so as to minimize the risk of eye damage for theexperimenter. Both amplitude and phase holograms can becreated simply by varying the photochemical processing of theexposed film.

Recommendation: the Michelson interferometer on the laser op-tics base plate is ideal for demonstrating the effects of disturb-ances due to mechanical shocks or air streaking in unsuitablerooms, which can prevent creation of satisfactory holograms.


473 40 Laser optics base plate 1

He-Ne laser 0.2/1 mW max, linearly polarized 1

Laser mount 1

473 42 Optics base 5

473 435 Variable beam divider 1

473 43 Holder for beam divider 1

473 44 Film holder 1

473 45 Object holder 1

473 47 Spherical lens f = 2.7 mm 2

473 448 Holography film 1

473 446 Darkroom accessories 1

31103 Wooden ruler, 1 m long 1

663 615 Schuko socket strip, 5 sockets (safety mains sockets) 1

31317 Stopclock II, 60 s/30 min 1

64911 Set of 6 small trays, 1 x 1 RE 1

661234 Polyethylene bottle, 1000 ml, wn with screw cap 3

667016 Scissors, 200 mm, pointed 1

473 444 Photographic chemicals 1

Iron(III) nitrate nonahydrate, 250 g 1

Potassium bromide (KBr), 100 g 1

P5.

3.7.1

P 5.3.7

671 8910

672 4910

471 830

473 411

Polarization Optics

P 5.4.1Basic experiments

P 5.4.1.1 Polarization of light throughreflection at a glass plate

P 5.4.1.2 Fresnel’s laws of reflection

P 5.4.1.3 Polarization of light throughscattering in an emulsion

P 5.4.1.4 Malus’ law

Fresnel’s laws of reflection (P 5.4.1.2)

The fact that light can be polarized is important evidence of thetransversal nature of light waves. Natural light is unpolarized. Itconsists of mutually independent, unordered waves, each ofwhich has a specific polarization state. Polarization of light is theselection of waves having a specific polarization state.

In the first experiment, unpolarized light is reflected at a glasssurface. When we view this through an analyzer, we see that thereflected light as at least partially polarized. The greatest polar-ization is observed when reflection occurs at the polarizing angle(Brewster angle) ar. The relationship

tanar = n

gives us the refractive index n of the glass.

Closer observation leads to Fresnel’s laws of reflection, whichdescribe the ratio of reflected to incident amplitude for differentdirections of polarization. These laws are quantitatively verified inthe second experiment.

The third experiment demonstrates that unpolarized light canalso be polarized through scattering in an emulsion, e. g. dilutedmilk, and that polarized light is not scattered uniformly in alldirections.

The aim of the fourth experiment is to derive Malus’s law: whenlinearly polarized light falls on an analyzer, the intensity of thetransmitted light is

I = I0 · cos2GI0: intensity of incident lightG: angle between direction of polarization and analyzer

P5.

4.1.

3

P5.

4.1.

2

P5.

4.1.

1

P5.

4.1.

4

188


477 20 Plate glass cell, 100 x 100 x 10 mm 1 1 1

460 25 Prism table 1 1 1

450 64 Halogen lamp housing W/100 W 1 1 1

450 63 Halogen lampe, 12 V/100 W 1 1 1

450 66 Picture slider for halogen lamp housing 1 1 1

521 25 Transformer 2....12 V 1 1 1


450 51 Lamp, 6 V/30 W 1



460 26 Iris diaphragm 1 1 1 1

472 401 Polarization filter 2 2 2 2

460 03 Lens, f = + 100 mm 1 1 1

460 08 Lens, f = + 150 mm 1

460 04 Lens, f = + 200 mm 1


578 62 STE Photoelement

460 21 Holder for plug-in elements 1 1

Ammeter*, DC, I ≤ 1 mA, DI = 2 mA, Ri ≤ 50 V, e. g.531 281 Digital-analog multimeter METRAHit 24 S 1 1


460 40 Swivel joint with angle scale 1 1





* Readable in darkened room

1 1

521 210

6

1

Optics Polarization

189

Quarter-wavelength and half-wavelength plate (P 5.4.2.2)

Birefringence

P 5.4.2.1 Birefringence and polarizationwith calcite (Iceland spar)

P 5.4.2.2 Quarter-wavelength and half-wavelength plate

P 5.4.2.3 Photoelasticity: Investigatingthe distribution of strains inmechanically stressed bodies

The validity of Snell’s law of refraction is based on the premisethat light propagates in the refracting medium at the same velo-city in all directions. In birefringent media, this condition is onlyfulfilled for the ordinary component of the light beam (the ordinaryray); the law of refraction does not apply for the extraordinary ray.

The first experiment looks at birefringence of calcite (Icelandspar). We can observe that the two component rays formed in thecrystal are linearly polarized, and that the directions of polariza-tion are perpendicular to each other.

The second experiment investigates the properties of Ö/4 and Ö/2plates and explains these in terms of their birefringence; it furt-her demonstrates that the names for these plates refer to the pathdifference between the ordinary and the extraordinary raysthrough the plates.

In the third experiment, the magnitude and direction of mechani-cal stresses in transparent plastic models are determined.

The plastic models become optically birefringent when subjected tomechanical stress. Thus, the stresses in the models can be revea-led using polarization-optical methods. For example, the plasticmodels are illuminated in a setup consisting of a polarizer and ana-lyzer arranged at right angles. The stressed points in the plasticmodels polarize the light elliptically. Thus, the stressed points appe-ar as bright spots in the field of view. In another configuration, theplastic models are illuminated with circularly polarized light andobserved using a quarter-wavelength plate and an analyzer. Heretoo, the stressed points appear as bright spots in the field of view.


472 02 Iceland spar crystal 1

47195 Set of photoelastic models 1


460 26 Iris diaphragm 1 1

472 401 Polarization filter 2 2 2

472 601 Quarter-wavelength plate 2 2

472 59 Half-wavelength plate 1

468 30 Mercury light filter, yellow 1

578 62 STE photoelement 1


460 02 Lens f = + 50 mm 1

460 08 Lens f = + 150 mm 2

460 06 Lens f = – 100 mm 1


460 32 Precision optical bench, standardized cross-section, 1 m 1 1 1



450 63 Halogen lamp, 12 V/100 W 1 1 1


52125 Transformer 2 ... 12 V 1 1 1

531281 Ammeter, DC, I ≤ 1 mA, W I = 2 BA, Ri ≤ 50 E e.g. Digital-analog multimeter METRAHit 24 S 1

30011 Saddle base 1

50146 Pair of cables, 100 cm, red and blue 1 2 1

P5.

4.2.

1

P5.

4.2.

2

P5.

4.2.

3

P 5.4.2

Photoelasticity: Investigating the distribution of strains in mechanically stressed bodies(P 5.4.2.3)

Polarization Optics

190

Rotation of the plane of polarization with sugar solutions (P 5.4.3.2)

Optical activity,polarimetry

P 5.4.3.1 Rotation of the plane of polarization with quartz

P 5.4.3.2 Rotation of the plane of polarization with sugar solutions

P 5.4.3.3 Building a half-shadow polarimeter with discrete elements

P 5.4.3.4 Determining the concentrationof sugar solutions with a standard commercial polari-meter

Optical activity is the property of some substances of rotating theplane of linearly polarized light as it passes through the material.The angle of optical rotation is measured using a device called apolarimeter.

The first experiment studies the optical activity of crystals, in thiscase a quartz crystal. Depending on the direction of intersectionwith respect to the optical axis, the quartz rotates the light clock-wise (“right-handed”), counterclockwise (“left-handed”) or isoptically inactive. The angle of optical rotation is closely depen-dent on the wavelength of the light; therefore a yellow filter isused.

The second experiment investigates the optical activity of a sugarsolution. For a given cuvette length d, the angles of optical rota-tion R of optically active solutions are proportional to the concen-tration c of the solution.

a = [a] · c · d

[a]: rotational effect of the optically active solution

The object of the third experiment is to assemble a half-shadowpolarimeter from discrete components. The two main elementsare a polarizer and an analyzer, between which the opticallyactive substance is placed. Half the field of view is covered by anadditional, polarizing foil, of which the direction of polarization isrotated slightly with respect to the first. This facilitates measuringthe angle of optical rotation.

In the fourth experiment, the concentrations of sugar solutionsare measured using a standard commercial polarimeter andcompared with the values determined by weighing.


472 62 Quartz, parallel 1

472 64 Quartz, right-handed 1

472 65 Quartz, left-handed 1



450 63 Halogen lamp, 12 V/100 W 1 1 1


52125 Transformer 2 ... 12 V 1 1 1

468 30 Mercury light filter, yellow 1 1


468 07 Monochromatic light filter, yellow-green 1


472 401 Polarization filters 2 2 2

460 03 Lens f = + 100 mm 1 1 1

47720 Plate glass cell, 100 x 100 x 10 mm 1


520 51108 Polarization film 1

D(+)-saccharose, 100 g 1 1 1




30101 Leybold multiclamp

300 01 Stand base, V-shape, 28 mm 1 1 1

657590 Polarimeter P1000 1

664111 Beaker 100 ml, ts, hard glass 1

667793 Electronic balance LS 200, 200 g : 0.1 g 1

50133 Connecting lead, dia. 2.5 mm2, 100 cm, black 2 2 2

P5.

4.3.

1

P5.

4.3.

2

P5.

4.3.

3

P5.

4.3.

4

P 5.4.3

Determining the concentration of sugarsolutions with a standard commercialpolarimeter (P 5.4.3.4)

1

6 6 7

463 80 111 Slide cover slip 5 x 5 cm 2

666 963 Spatula with spoon end, 120 x 20 mm 1 1 1

674 6050

Optics Polarization

191

Investigating the Kerr effect in nitrobenzol (P 5.4.4.1)

Kerr effect

P 5.4.4.1 Investigating the Kerr effect innitrobenzol

In 1875, J. Kerr discovered that electrical fields cause birefrin-gence in isotropic substances. The birefringence increasesquadratically with the electric field strength. For reasons of sym-metry, the optical axis of birefringence lies in the direction of theelectric field. The normal refractive index of the substance ischanged to ne for the direction of oscillation parallel to theapplied field, and to no for the direction of oscillation perpendic-ular to it. The experiment results in the relationship

ne – no = K · Ö · E2

K: Kerr constant, l: wavelength of light used, E: electric field strength

The experiment demonstrates the Kerr effect for nitrobenzol, asthe Kerr constant is particularly great for this material. The liquidis filled into a small glass vessel in which a suitable plate capaci-tor is mounted. The arrangement is placed between two polariza-tion filters arranged at right angles, and illuminated with a linearlypolarized light beam. The field of view is dark when no electricfield is applied. When an electric field is applied, the field of viewbrightens, as the light beam is elliptically polarized when passingthrough the birefringent liquid.


473 31 Kerr cell 1

Nitrobenzol 1

52170 High voltage power supply 10 kV 1

50105 High voltage cables 2

450 64 Lamp housing 12 V, 50/100 W 1

450 63 Halogen lamp, 12 V/100 W 1




468 05 Monochromatic light filter, yellow 1

468 07 Monochromatic light filter, yellow-green 1


472 401 Polarization filter 2

460 03 Lens f = + 100 mm 1

460 25 Prism table 1


460 32 Precision optical bench, standardized cross-section, 1 m 1

460 351 Optics rider H = 60 mm/W = 50 mm 6

50133 Connecting lead, dia. 2.5 mm2, 100 cm, black 2

P5.

4.4.

1

P 5.4.4

673 9410

Polarization Optics

192

Demonstrating the Pockels effect in a conoscopic beam path (P 5.4.5.1)

Pockels effect

P 5.4.5.1 Demonstrating the Pockels effect in a conoscopic beam path

P 5.4.5.2 Pockels effect:transmitting informationusing modulated light

The occurrence of birefringence and the alteration of existingbirefringence in an electrical field as a linear function of the elec-tric field strength is known as the Pockels effect. In terms of thevisible phenomena, it is related to the Kerr effect. However, due toits linear dependency on the electric field strength, the Pockelseffect can only occur in crystals without an inversion center, forreasons of symmetry.

The first experiment demonstrates the Pockels effect in a lithiumniobate crystal placed in a conoscopic beam path. The crystal isilluminated with a divergent, linearly polarized light beam, and thetransmitted light is viewed behind a perpendicular analyzer. Theoptical axis of the crystal, which is birefringent even when noelectric field is applied, is parallel to the incident and exit sur-faces; as a result, the interference pattern consists of two sets ofhyperbolas which are rotated 90h with respect to each other. Thebright lines of the interference pattern are due to light rays forwhich the difference W between the optical paths of the extraor-dinary and ordinary rays is an integral multiple of the wavelengthÖ. The Pockels effect alters the difference of the main refractiveindices, no – ne, and consequently the position of the interferen-ce lines. When the so-called half-wave voltage UÖ is applied, Wchanges by one half wavelength. The dark interference lines moveto the position of the bright lines, and vice versa. The process isrepeated each time the voltage is increased by UÖ.

The second experiment shows how the Pockels cell can be usedto transmit audio-frequency signals. The output signal of a func-tion generator with an amplitude of several volts is superposed ona DC voltage which is applied to the crystal of the Pockels cell.The intensity of the light transmitted by the Pockels cell is modu-lated by the superposed frequency. The received signal is outputto a speaker via an amplifier and thus made audible.


472 90 Pockels cell 1 1

52170 High voltage power supply 10 kV 1 1


460 01 Lens f = + 5 mm 1

460 02 Lens f = + 50 mm 1

472 401 Polarization filter 1 1

460 32 Precision optical bench, standardized cross-section, 1 m 1 1




1


522 61 AC/DC-amplifier 1

58708 Broad-band speaker 1


500 604 Safety connection leads, 10 cm, black 1

500 621 Safety connection leads, 50 cm, red 2

500 641 Safety connection leads, 100 cm, red 1 1

500 642 Safety connection leads, 100 cm, blue 1 1


P5.

4.5.

1

P5.

4.5.

2

P 5.4.5

578 62 STE photoelement

500 98 I Set 6 safety adapter sockets, black I I 1

471 830

Optics Polarization

193

Faraday effect: determining Verdet’s constant for flint glass as a function of the wavelength (P 5.4.6.1)

Faraday effect

P 5.4.6.1 Faraday effect: determiningVerdet’s constant for flint glassas a function of the wavelength

Transparent isotropic materials become optically active in a mag-netic field; in other words, the plane of polarization of linearlypolarized light rotates when passing through the material.M. Faraday discovered this effect in 1845 while seeking arelationship between magnetic and optical phenomena.

The angle of optical rotation of the plane of polarization is propor-tional to the illuminated length s and the magnetic field B.

Df = V · B · s

The proportionality constant V is known as Verdet’s constant, anddepends on the wavelength Ö of the light and the dispersion.

V =e · Ö · dn

2mc2 dÖ

For flint glass, the following equation approximately obtains:

dn=

1,8 · 10–14 m2

dÖ Ö3

In this experiment, the magnetic field is initially calibrated withreference to the current through the electromagnets using a tes-lameter, and then the Faraday effect in a flint glass square isinvestigated. To improve measuring accuracy, the magnetic fieldis reversed each time and twice the angle of optical rotation ismeasured. The proportionality between the angle of optical rota-tion and the magnetic field and the decrease of Verdet’s constantwith the wavelength Ö are verified.


560 481 Flint glass square with holder 1

460 358 Rider base with threads 1

56211 U-core with yoke 1


56213 Coil with 250 turns 2

450 63 Halogen lamp, 12 V/100 W 1

450 64 Halogen lamp housing 12 V, 50/100W 1


468 05 Monochromatic light filter, yellow 1

468 09 Monochromatic light filter, blue-green 1


46813 Monochromatic light filter, violet 1

460 02 Lens f = + 50 mm 1


460 32 Precision optical bench, standardized profile, 1 m 1




52139 Variable extralow voltage transformer 1

Ammeter, DC, I ≤ 10 A, W I = 0,2 A, e.g. 531281 Digital-analog multimeter METRAHit 24 S 1

516 60 Tangential B-probe 1

516 62 Teslameter 1

50116 Multicore cable, 6-pole, 1.5 m long 1






501461 Pair of cables, 100 cm, black 1

P5.

4.6.

1

P 5.4.6

Light Intensity Optics

194

Determining the luminous intensity as a function of the distance from the light source – Recording and evaluating with CASSY (P 5.5.1.2a)

Quantities and measuring methods of lightingengineeringP 5.5.1.1 Determining the radiant flux

density and the luminous intensity of a halogen lamp

P 5.5.1.2 Determining the luminousintensity as a function of thedistance from the light source –Recording and evaluating withCASSY

P 5.5.1.3 Verifying Lambert’s law ofradiation

There are two types of physical quantities used to characterizethe brightness of light sources: quantities which refer to the phys-ics of radiation, which describe the energy radiation in terms ofmeasurements, and quantities related to lighting engineering,which describe the subjectively perceived brightness under con-sideration of the spectral sensitivity of the human eye.

The first group includes the irradiance Ee, which is the radiatedpower per unit of area Fe. The corresponding unit of measure iswatts per square meter. The comparable quantity in lighting engi-neering is illuminance E, i. e. the emitted luminous flux per unit ofarea F, and it is measured in lumens per square meter, or lux forshort.

In the first experiment, the irradiance is measured using the Moll’sthermopile, and the luminous flux is measured using a luxmeter.The luxmeter is matched to the spectral sensitivity of the humaneye V (Ö) by means of a filter placed in front of the photoelement.A halogen lamp serves as the light source. From its spectrum,most of the visible light is screened out using a color filter; sub-sequently, a heat filter is used to absorb the infrared componentof the radiation.

The second experiment demonstrates that the luminous intensityis proportional to the square of the distance between a point-typelight source and the illuminated surface.

The aim of the third experiment is to investigate the angular distri-bution of the reflected radiation from a diffusely reflecting sur-face, e.g. matte white paper. To the observer, the surface appearsuniformly bright; however, the apparent surface area varies withthe cos of the viewing angle. The dependency of the luminousintensity is described by Lambert’s law of radiation:

Ee (F) = Ee (0) · cos F



450 63 Halogen lamp, 12 V/100 W 1 1

450 68 Halogen lamp, 12 V/50 W 1 1

52125 Transformer 2 ... 12 V 1 1 1



450 51 Lamp, 6 V/30 W 1

Transformer, 6 V AC, 12 V AC/30 VA 1



460 03 Lens f = + 100 mm 1 1


55736 Moll’s thermopile 1 1



666 243 Lux sensor 1 1 1

524 051 Lux box 1 1

524 200 CASSY Lab 1 1

666 230 Hand-held Lux-UV-IR-Meter



59013 Insulated stand rod, 25 cm long 1 1 1

590 02 Small clip plug 1 1 1

30101 Leybold multiclamp 3 2 2 4




50133 Connecting leads, dia. 2.5 mm2, 100 cm, black 2 2 2


P5.

5.1.

1

P5.

5.1.

2(a

)

P5.

5.1.

2(b

)

P5.

5.1.

3

P 5.5.1

1

521 210

Optics Light Intensity

195

Stefan-Boltzmann law: measuring the radiant intensity of a “black body” as a function of temperature (P 5.5.2.1)

Laws of radiation

P 5.5.2.1 Stefan-Boltzmann law: measuring the radiant intensityof a “black body” as a functionof temperature

P 5.5.2.2 Stefan-Boltzmann law: measuring the radiant intensityof a “black body” as a functionof temperature – Recording and evaluating withCASSY

P 5.5.2.3 Confirming the laws of radiationwith Leslie’s tube

The total radiated power MB of a black body increases in propor-tion to the fourth power of its absolute temperature T (Stefan-Boltzmann’s law).

MB = s · T 4

s = 5.67 · 10–8 W m–2 K–4: (Stefan-Boltzmann’s constant)

For all other bodies, the radiated power M is less than that of theblack body, and depends on the properties of the surface of thebody. The emittance of the body is described by the relationship

e = M MB

M: radiated power of body

In the first two experiments, a cylindrical electric oven with a bur-nished brass cylinder is used as a “black body”. The brass cylin-der is heated in the oven to the desired temperature between 300and 750 K. A thermocouple is used to measure the temperature. Awater-coolable screen is positioned in front of the oven to ensu-re that the setup essentially measures only the temperature of theburnished brass cylinder. The measurement is conducted using aMoll’s thermopile; its output voltage provides a relative measureof the radiated power M. The thermopile can be connected eitherto an amplifier or, via the amplifier box, to the CASSY computerinterface device. In the former case, the measurement must bycarried out manually, point by point; the latter configuration ena-bles computer-assisted measuring and evaluation. The aim of theevaluation is to confirm Stefan-Boltzmann’s law.

The third experiment uses a radiation cube after Leslie (“Leslie’scube”). This cube has four different face surfaces (metallic matte,metallic shiny, black finish and white finish), which can be heatedfrom the inside to almost 100 hC by filling the cube with boilingwater. The heat radiated by each of the surfaces is measured as afunction of the falling temperature. The aim of the evaluation is tocompare the emittances of the cube faces.


389 43 Black body accessory 1 1

555 81 Electric oven, 230 V 1 1

555 84 Support for electric oven 1 1 1

502 061 Safety connection box with ground 1 1

389 26 Leslie’s cube 1

389 28 Stirrer for Leslie’s cube 1

666190 Digital thermometer with one input 1 1

666193 Temperature sensor NiCr-Ni 1 1 1

55736 Moll’s thermopile 1 1 1



524 045 Temperature box (NiCrNi/NTC) 1

524 040 mV-Box 1

524 200 CASSY Lab 1



30101

666 555 Universal clamp, 0 ... 80 mm dia. 1 1

303 25 Immersion heater 1


665 009 Funnel, dia. 75 mm, plastic 1

388181 Submersible pump, 12 V 1* 1*

Low voltage power supply 1* 1*

667194 Silicone tubing, i.d. 7 x 1.5 mm, 1 m 1* 1*

50146 Pair of cables, 100 cm, red and blue 1 1 1



P5.

5.2.

1

P5.

5.2.

2

P5.

5.2.

3

P 5.5.2

4 4 3Leybold multiclamp

521 230

Velocity of light Optics

P 5.6.1Measurement according toFoucault/Michelson

P 5.6.1.1 Determining the velocity of lightby means of the rotating-mirrormethod according to Foucaultand Michelson – measuring the image shift as afunction of the rotational speedof the mirror

P 5.6.1.2 Determining the velocity of lightby means of the rotating-mirrormethod according to Foucaultand Michelson – measuring the image shift forthe maximum rotational speedof the mirror

Determining the velocity of light by means of the rotating-mirror method according to Foucault and Michelson – measuring the image shift as a function of the rotational speed of the mirror (P 5.6.1.1)

Measurement of the velocity of light by means of the rotary mir-ror method utilizes a concept first proposed by L. Foucault in1850 and perfected by A. A. Michelson in 1878. In the variationutilized here, a laser beam is deviated into a fixed end mirrorlocated next to the light source via a rotating mirror set up at adistance of a = 12.1 m. The end mirror reflects the light so that itreturns along the same path when the rotary mirror is at rest. Partof the returning light is imaged on a scale using a beam divider.A lens with f = 5 m images the light source on the end mirror andfocuses the image of the light source from the mirror on thescale. The main beam between the lens and the end mirror isparallel to the axis of the lens, as the rotary mirror is set up in thefocal point of the lens.

Once the rotary mirror is turning at a high frequency O, the shiftDO of the image on the scale is observed. In the period

Dt = 2a ,c

which the light requires to travel to the rotary mirror and back tothe end mirror, the rotary mirror turns by the angle

Da = 2 S v · Dt

Thus, the image shift is

Dx = 2Da · a

The velocity of light can then be calculated as

c = 8p · a2 · n Dx

To determine the velocity of light, it is sufficient to measure theshift in the image at the maximum speed of the mirror, which isknown. Measuring the image shift as a function of the speedsupplies more precise results.

P5.

6.1.

1

P5.

6.1.

2

196


476 40 Rotary mirror for determination of the velocity of light 1 1

He-Ne laser 0.2/1 mW max., linearly polarized 1 1

463 20 Front silvered mirror 1 1

460 12 Lens, f = approx. + 5 m 1 1

471 88 Beam splitter 1 1


311 09 Glass scale, 5 cm long 1 1

521 40 Variable low voltage transformer 0....250 V 1


559 92 Semiconductor detector 1


501 10 Straight BNC 1

300 44 Stand rod, 100 cm 1 1

300 42 Stand rod, 47 cm 1 1




300 11 Saddle base 1


301 09 Bosshead S 1

311 03 Wooden ruler, 1 m long 1 1

537 36 Rheostat 1000 V 1

537 35 Rheostat 330 V 1

502 05 Measuring junction box 1

504 48 Two-way switch 1


471 830

Determining the velocity of light in air from the path and transit time of a short light pulse (not shown: mirror T1) (P 5.6.2.1)

P 5.6.2

P 5.6.2.1 Determining the velocity of lightin air from the path and transittime of a short light pulse

P 5.6.2.2 Determining the propagationvelocity of voltage pulses incoaxial cables

Measuring with short light pulses

The light velocity measuring instrument emits pulses of light witha pulse width of about 20 ns. After traversing a known measuringdistance in both directions, the light pulses are converted intovoltage pulses for observation on the oscilloscope.

In the first experiment, the path of the light pulses is varied once,and the change in the transit time is measured with the oscillo-scope. The velocity of light can then be calculated as quotient ofthe change in the transit distance and the change in the transittime. Alternatively, the total transit time of the light pulses can bemeasured in absolute terms using a reference pulse. In this case,the velocity of light can be calculated as quotient of the transitdistance and the transit time. A quartz-controlled oscilloscopesignal can be displayed on the instrument simultaneously withthe measuring pulse in order to calibrate timing. Time measure-ment is then independent of the time base of the oscilloscope.

In the second experiment, the propagation velocity of voltagepulses in coaxial cables is determined. In this configuration, thereference pulses of the light velocity measuring instrument areoutput to an oscilloscope and additionally fed into a 10 m longcoaxial cable via a T-connector. After reflection at the cable end,the pulses return to the oscilloscope, delayed by the transit time.The propagation velocity n can be calculated from the doublecable length and the time difference between the direct andreflected voltage pulses. By inserting these values in the equation

n = c öääer

c: velocity of light in a vacuum

we obtain the relative dielectricity er of the insulator between theinner and outer conductors of the coaxial cable.

By using a variable terminating resistor R at the cable end, itbecomes possible to additionally measure the reflection behav-ior of voltage pulses, In particular, the special cases “open cableend” (no phase shift at reflection), “shorted cable end” (phaseshift due to reflection) and “termination of cable end with the50 Ö characteristic wave impedance” (no reflection) are ofspecial interest here.

P5.

6.2.

1

P5.

6.2.

2

Optics Velocity of light

197


476 50 Light velocity measuring instrument 1 1

46010 Lens, f = + 200 mm 1

460 32 Precision optical bench, standardized cross section, 1 m 1





501 091 T-adapter BNC 1

501 10 Straight BNC 1

575 35 BNC/4 mm adapter, 2-pole 1

577 79 STE regulation resistor 1 kV 1




300 44 Stand rod, 100 cm 1


30011 Saddle base 1

Schematic diagram of light velocity measurement with short light pulses

Velocity of light Optics

P 5.6.3Measuring with a periodicallight signal

P 5.6.3.1 Determining the velocity of lightusing a periodical light signaland a short measuring distance

P 5.6.3.2 Determining the velocity of lightfor different propagation media

Determining the velocity of light using a periodical light signal and a short measuring distance (P 5.6.3.1)

In determining the velocity of light with an electronically modulatedsignal, a light emitting diode which pulses at a frequency of 60 MHzis used as the light transmitter. The receiver is a photodiode whichconverts the light signal into a 60 MHz AC voltage. A connectinglead transmits a reference signal to the receiver which is synchro-nized with the transmitted signal and in phase with it at the start ofthe measurement. The receiver is then moved by the measuringdistance ∆s, so that the received signal is phase-shifted by theadditional transit time ∆ t of the light signal.

Df = 2S · f1 · Dt where f1 = 60 MHz

Alternatively, a medium with a greater index of refraction can beplaced in the beam path.The apparent transit time to be measured is increased by meansof an electronic “trick”. The received signal and the referencesignal are each mixed (multiplied) with a 59.9 MHz signal beforebeing fed through a frequency filter which only passes the low-frequency components with the differential frequency f1 – f2 = 0.1MHz. This mixing has no effect on the phase shift; however, thisphase shift is now for a transit time ∆ t’ increased by a factor of

f1f1 – f2

= 600

In the first experiment, the apparent transit time ∆ t’ is measuredas a function of the measuring distance ∆s, and the velocity oflight in the air is calculated according to the formula

c =Ds · f1Dt’ f1 – f2

The second experiment determines the velocity of light in variouspropagation media. In the way of accessories, this experimentrequires a tube 1 m long with two end windows, suitable for fill-ing with water, a glass cell 5 cm wide for other liquids and anacrylic glass body 5 cm wide.

To enable more precise determinations of the velocity of light, itis recommended that the frequencies f1 and f1 – f2 be measuredusing a digital counter.

198


476 30 Light transmitter and receiver 1 1 1 1

476 35 Tube with 2 end windows 1

Ethanol, completely denaturated, 1 l 1

Glycerine, 99 %, 250 ml 1


476 34 Acrylic glass block 1


460 08 Lens, f = + 150 mm 1 1 1 1

575 221 Two-channel oscilloscope 1004 1 1 1 1

575 48 Digital Counter 1* 1* 1* 1*

30011 Saddle base 2 4 3 3

31102 Vertical scale, 1 m long 1 1 1 1


Block circuit diagram

P5.

6.3.

1

P5.

6.3.

2(a

)

P5.

6.3.

2(b

)

P5.

6.3.

2(c

)

671 9720

672 1210

Measuring the line spectra of inert gases and metal vapors using a prism spectrometer (P 5.7.1.1)

P 5.7.1

P 5.7.1.1 Measuring the line spectra ofinert gases and metal vaporsusing a prism spectrometer

Prism spectrometer

To assemble the prism spectrometer, a flint glass prism is placedon the prism table of a goniometer. The light of the light sourceto be studied passes divergently through a collimator and is inci-dent on the prism as a parallel light beam. The arrangementexploits the wavelength-dependency of the refractive index of theprism glass: the light is refracted and each wavelength is devi-ated by a different angle. The deviated beams are observed usinga telescope focused on infinity which is mounted on a slewablearm; this allows the position of the telescope to be determined towithin a minute of arc. The refractive index is not linearly depen-dent on the wavelength; thus, the spectrometer must be calibrat-ed. This is done using e.g. an He spectral lamp, as its spectrallines are known and distributed over the entire visible range.

In this experiment, the spectrometer is used to observe the spec-tral lines of inert gases and metal vapors which have been excit-ed to luminance. To identify the initially “unknown” spectral lines,the angles of deviation are measured and then converted to thecorresponding wavelength using the calibration curve.

Note: as an alternative to the prism spectrometer, the goniometercan also be used to set up a grating spectrometer (see P 5.7.2.1)

P5.

7.1.

1

Optics Spectrometer

199


467 23 Spectrometer and goniometer 1

451 031 Spectral lamp He 1

451 041 Spectral lamp Cd 1

451 011 Spectral lamp Ne 1*

451 071 Spectral lamp Hg/Cd 1*

451 081 Spectral lamp TI 1*

451 111 Spectral lamp Na 1*

451 16 Housing for spectrum lamps 1

451 30 Universal choke, in housing, 230 V, 50 Hz 1

Transformer, 6 V~, 12 V~/ 30 W 1



Ray path in a prism spectrometer

521 210

Spectrometer Optics

P 5.7.2Grating spectrometer

P 5.7.2.1 Measuring the line spectra ofinert gases and metal vaporsusing a grating spectrometer

Measuring the line spectra of inert gases and metal vapors using a grating spectrometer (P 5.7.2.1)

To create a grating spectrometer, a copy of a Rowland grating ismounted on the prism table of the goniometer in place of theprism. The ray path in the grating spectrometer is essentiallyanalogous to that of the prism spectrometer (see P 5.7.1.1). How-ever, in this configuration the deviation of the rays by the gratingis proportional to the wavelength:

sinDa = n · g · Ö n: diffraction order, g: grating constant, l: wavelength,Da: angle of deviation of nth-order spectral line

Consequently, the wavelengths of the observed spectral linescan be calculated directly from the measured angles of deviation.

In this experiment, the grating spectrometer is used to observethe spectral lines of inert gases and metal vapors which havebeen excited to luminance. To identify the initially “unknown”spectral lines, the angles of deviation are measured and thenconverted to the corresponding wavelength.

The resolution of the grating spectrometer is sufficient to deter-mine the distance between the two yellow sodium D-lines Ö(D1)– Ö(D2) = 0.60 nm with an accuracy of 0.10 nm. However, thishigh resolution is achieved at the cost of a loss of intensity, as asignificant part of the radiation is lost in the undiffracted zeroorder and the rest is distributed over multiple diffraction orderson both sides of the zero order.

P5.

7.2.

1

200


467 23 Spectrometer and goniometer 1

471 23 Copy of a Rowland grating, 6000 lines/cm approx. 1

451 031 Spectral lamp He, pin contact 1

451 111 Spectral lamp Na, pin contact 1

451 011 Spectral lamp Ne, pin contact 1*

451 041 Spectral lamp Cd, pin contact 1*

451 071 Spectral lamp Hg/Cd, pin contact 1*

451 081 Spectral lamp TI, pin contact 1*

451 16 Housing for spectrum lamps w. pin socket 1

451 30 Universal choke, in housing, 230 V, 50 Hz 1

Transformer, 6 V~, 12 V~/ 30 W 1



Ray path in a grating spectrometer

521 210

Assembling a grating spectrometer for measuring transmission curves (P 5.7.2.2)

P 5.7.2

P 5.7.2.2 Assembling a grating spectrometer for measuring transmission curves

Grating spectrometer

When used in conjunction with a grating spectrometer, thesingle-line CCD camera VideoCom is ideal for relative measure-ments of spectral intensity distributions. In such measurements,each pixel of the CCD camera is assigned a wavelength

Ö = d · sin Rin the first diffraction order of the grating. The spectrometer isassembled on the optical bench using individual components.The grating in this experiment is a copy of a Rowland grating withapprox. 6000 lines/cm. The diffraction pattern behind the gratingis observed with VideoCom.

The VideoCom software makes possible comparison of twointensity distributions, and thus recording of transmission curvesof color filters or other light-permeable bodies. The spectralintensity distribution of a light source is measured both with andwithout filter, and the ratio of the two measurements is graphedas a function of the wavelength.

This experiment records the transmission curves of color filters.It is revealed that simple filters are permeable for a very broadwavelength range within the visible spectrum of light, while so-called line filters have a very narrow permeability range.

Optics Spectrometer

201

P5.

7.2.

2(b

)

P5.

7.2.

2(a

)


33747 VideoCom 1 1


460 34 Auxiliary bench with swivel joint 2 1

471 23 Copy of a Rowland grating, 6000 lines/cm approx. 1 1

46014 Adjustable slit 1 1

460 08 Lens, f = + 150 mm 1 1


460 356 Cantilever arm 100 mm 1 1



450 51 Lamp, 6 V/30 W 1 1


Transformer, 6 V AC, 12 V AC/ 30 W 1 1

467 95 Filter set red, green, blue 1 1

467 96 Filter set yellow, cyan, magenta 1 1

468 03 Monochromatic light filter, red 1* 1*

468 05 Monochromatic light filter, yellow 1* 1*

468 07 Monochromatic light filter, yellow/green 1* 1*

468 09 Monochromatic light filter, blue-green 1* 1*



Transmissions curves of various color filters

521 210

Atomic andnuclear physics

Table of contents Atomic and nuclear physics

204

P6 Atomic and nuclear physics

P 6.1 Introductory experimentsP 6.1.1 Oil-spot experiment 205

P 6.1.2 Millikan experiment 206

P 6.1.3 Specific electron charge 207

P 6.1.4 Planck's constant 208–209

P 6.1.5 Dualism of wave and particle 210

P 6.1.6 Paul trap 211

P 6.2 Atomic shellP 6.2.1 The Balmer series of hydrogen 212

P 6.2.2 Emission and absorption spectra 213

P 6.2.3 Inelastic electron collisions 214

P 6.2.4 Franck-Hertz experiment 215–216

P 6.2.5 Critical potential 217

P 6.2.6 Electron spin resonance (ESR) 218

P 6.2.7 Normal Zeeman effect 219

P 6.2.8 Optical pumping (anomalous Zeeman effect) 220

P 6.3 X-raysP 6.3.1 Demonstrating x-rays 221

P 6.3.2 Attenuation of x-rays 222

P 6.3.3 Physics of the atomic shell 223

P 6.3.4 X-ray physics with the x-ray apparatus P 224

P 6.4 RadioactivityP 6.4.1 Detection of radioactivity 225

P 6.4.2 Poisson distribution 226

P 6.4.3 Radioactive decay and half-life 227

P 6.4.4 Attenuation of R, T and H radiation 228

P 6.5 Nuclear physicsP 6.5.1 Demonstration of particle tracks 229

P 6.5.2 Rutherford scattering 230

P 6.5.3 Nuclear magnetic resonance (NMR) 231

P 6.5.4 R spectroscopy 232

P 6.5.5 H spectroscopy 233

P 6.5.6 Compton effect 234

P 6.1.1

P 6.1.1.1 Determining the size of oilmolecules

Oil-spot experiment

Atomic and nuclear physics Introductory experiments

205

Determining the size of oil molecules (P 6.1.1.1)

One important issue in atomic physics is the size of the atom. Aninvestigation of the size of molecules makes it easier to come toa usable order of magnitude by experimental means. This is esti-mated from the size of an oil spot on the surface of water usingsimple means.

In this experiment, a drop of glycerin nitrioleate as added to agrease-free water surface dusted with Lycopodium spores. As-suming that the resulting oil spot has a thickness of one mole-cule, we can calculate the size d of the molecule according to

d =V

A

from the volume V of the oil droplet and the area A of the oil spot.The volume of the oil spot is determined from the number ofdrops needed to fill a volume of 1 cm3. The area of the oil spot isdetermined using graph paper.

P6.

1.1.

1


664179 Crystallization dish, 230 mm dia., 100 mm high 1

665 844 Burette, 10 ml: 0.05, w. lateral stopcock, amber glass, Schellbach blue line 1


665 751 Graduated cylinder, 10 ml: 0.2 1

665 754 Graduated cylinder, 100 ml: 1 1




666 555 Universal clamp, 0...80 mm 1

Water, pure, 5 l 1

Glycerin trioleate, 100 ml 1

Benzine, 40–70°C 1

Determining the area A of the oil spot

675 3410

672 1240

674 2220

Introductory experiments Atomic and nuclear physics

P 6.1.2Millikan experiment

P 6.1.2.1 Determining the electricalcharge of the electron afterMillikan and demonstrating thequantum nature of the charge –measuring the suspensionvoltage and the falling speed

P 6.1.2.2 Determining the electricalcharge of the electron afterMillikan and demonstrating thequantum nature of the charge –measuring the rising speedand the falling speed

Determining the electrical charge of the electron after Millikan and demonstrating the quantum nature of the charge –measuring the suspension voltage and the falling speed (P 6.1.2.1)

With his famous oil-drop method, R. A. Millikan succeeded indemonstrating the quantum nature of minute amounts of electri-city in 1910. He caused charged oil droplets to be suspended inthe vertical electric field of a plate capacitor and, on the basis ofthe radius r and the electric field E, determined the charge q of asuspended droplet:

q =4S

· r3 · U · g

3 E

U: density of oil g: gravitational acceleration

He discovered that q only occurs as a whole multiple of an elec-tron charge e.

His experiments are produced here in two variations. In the firstvariation, the electric field

E =U

d

d: plate spacing

is calculated from the voltage U at the plate capacitor at whichthe observed oil droplet just begins to hover. The constant fallingvelocity v1 of the droplet when the electric field is switched off issubsequently measured to determine the radius. From the equi-librium between the force of gravity and Stokes friction, we derivethe equation

4S· r3 · U · g = 6S · r · J · v13

J: viscosity

In the second variant, the oil droplets are observed which are notprecisely suspended, but which rise with a low velocity v2. Thefollowing applies for these droplets:

q · U

= 4S

r3 · U · g + 6S · r · J · v2d 3

P6.

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1

P6.

1.2.

2

206


Millikan apparatus 1 1

Power supply for Millikan apparatus 1 1

313 033 Electronic stopclock P 1 2


Additionally, the falling speed v1 is measured, as in the first vari-ant. The measuring accuracy for the charge q can be increasedby causing the oil droplet under study to rise and fall over a givendistance several times in succession and measuring the total riseand fall times.

The histogram reveals the quantum nature of the change

559 411

559 421

4

Determining the specific charge of the electron (P 6.1.3.1)

P 6.1.3

P 6.1.3.1 Determining the specificcharge of the electron

Specific electron charge

The mass me of the electron is extremely difficult to determine inan experiment. It is much easier to determine the specific chargeof the electron

Z =eme

from which we can calculate the mass me for a given electroncharge e.

In this experiment, a tightly bundled electron beam is divertedinto a closed circular path using a homogeneous magnetic fieldin order to determine the specific electron charge. The magneticfield B which diverts the electrons into the path with the givenradius r is determined as a function of the acceleration voltage U.The Lorentz force caused by the magnetic field acts as a centri-petal force. It depends on the velocity of the electrons, which inturn is determined by the acceleration voltage. The specific elec-tron charge can thus be determined from the measurementquantities U, B and r according to the formula

e= 2 ·

U .me B2 · r 2

P6.

1.3.

1


207


555 571 Fine beam tube 1

555 581 Helmholtz coils with holder and measuring device 1

521 65 DC power supply 0....500 V 1

DC power supply 0....16 V, 5 A 1



516 62 Teslameter 1*

516 61 Axial B-probe 1*

501 16 Multicore cable, 6-pole, 1.5 m long 1*






Circular electron path in fine beam tube

521 545


P 6.1.4Planck’s constant

P 6.1.4.1 Determining Planck’s constant –measuring with a compactassembly

P 6.1.4.2 Determining Planck’s constant –dispersion of wavelengths witha direct-vison prism on theoptical bench

Determining Planck’s constant – measuring with a compact assembly (P 6.1.4.1)

208

When light with the frequency V falls on the cathode of a photo-cell, electrons are released. Some of the electrons reach theanode where they generate a current in the external circuit,which is compensated to zero by applying a voltage with oppo-site sign U = –U0 . The applicable relationship

e · U0 = h · V – W, W: electronic work function

was first used by R. A. Millikan to determine Planck’s constant h.

In the first experiment, a compact arrangement is used to deter-mine h, in which the light from a high-pressure mercury vaporlamp is spectrally dispersed in a direct-vision prism. The light ofprecisely one spectral line at a time falls on the cathode. A capa-citor is connected between the cathode and the anode of thephotocell which is charged by the anode current, thus generatingthe opposing voltage U. As soon as the opposing voltage reachesthe value –U0, the anode current is zero and the charging of thecapacitor is finished. U0 is measured without applying a currentby means of an electrometer amplifier.

The second experiment uses an open arrangement on the opti-cal bench. Here as well, the wavelengths of the light are dis-persed using a direct-vision prism. The opposing voltage U istapped from a DC voltage source via a voltage divider, and varieduntil the anode current is compensated precisely to zero. TheI-measuring amplifier D is used for conducting sensitive meas-urements of the anode current.

P6.

1.4.

1

P6.

1.4.

2


451 30 Universal choke 230 V, 50 Hz 1 1



532 00 I-measuring amplifier D 1




576 86 STE mono cell holder 2

577 93 STE 10-turn potentiometer 1 kE, 2 W 1


579 10 STE key switch (n.o.), single-pole 1


503 11 Set of 20 batteries 1.5 V (type MONO) 1


460 34 Auxiliary bench w. swivel joint, protractor and index bench, 0.5 m 1

460 352 Optics rider, H = 90 mm/W =50 mm 2


460 02 Lens f = + 50 mm 1

460 08 Lens f = + 150 mm 1

46014 Adjustable slit 1

46013 Projection objective, f = + 150 mm 1

466 05 Direct-vision prism 1

466 04 Holder for direct-vision prism 1

502 04 Distribution box 1


500 414 Connection lead, black, 25 cm 1

500 440 Connection lead, yellow-green, 100 cm 1

500 444 Connection lead, black, 100 cm 1


501 461 Pair of cables, 1 m, black 1

P6.

1.4.

1

P6.

1.4.

2


558 77 Photo cell for determining Planck's constant 1 1

558 79 Compact arrangement for determining Planck's constant 1

558 791 Supply unit for photo cell 1

451 15 High-pressure mercury lamp 1 1

451 19 Lamp socket E27 on rod for high-pressure mercury lamp 1

Determining Planck’s constant – selection of wavelengths with interference filters on the optical bench (P 6.1.4.3a)

P 6.1.4

P 6.1.4.3 Determining Planck’s constant –selection of wavelengths withinterference filters on the opticalbench

Planck’s constant

In determining Planck's constant using the photoelectric effect, itmust be ensured that only the light of a single spectral line of thehigh-pressure mercury vapor lamp falls on the cathode of thephotocell at any one time. As an alternative to a prism, it is alsopossible to use narrow-band interference filters to select thewavelength. This simplifies the subsequent optical arrangement,and it is no longer necessary to darken the experiment room.Also, the intensity of the light incident on the cathode can beeasily varied using an iris diaphragm.

In this experiment, the capacitor method described previously(see P 6.1.4.1) is used to generate the opposing voltage U be-tween the cathode and the anode of the photocell. The voltage atthe capacitor is measured without current using the electrometeramplifier.

Note: The opposing voltage U can alternatively be tapped from aDC voltage source. The I-measuring amplifier D is recommendedfor sensitive measurements of the anode current (see P 6.1.4.2).

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209


558 77 Photo cell for determining Planck's constant 1 1

558 791 Supply unit for photo cell 1 1

451 15 High-pressure mercury lamp 1 1

451 19 Lamp socket E27 on rod for high-pressure mercury lamp 1 1

460 03 Lens f = + 100 mm 1 1

460 26 Iris diaphragm 1 1

558 792 Filter wheel with iris diaphragm 1 1

468 401 Interference filter 578 nm 1 1






562 791 Plug-in unit 230V/12 V AC/20 W; with female plug 1 1

578 22 STE capacitor 100 pF, 630 V 1 1

579 10 STE key switch n.o. single-pole 1 1


460 34 Auxiliary bench with swivel joint 1


460 352 Optics rider, H = 90 mm/W =50 mm 2 2



501 10 Straight BNC 1 1

501 09 BNC adapter for 4 mm socket, 1-pole 1 1

340 89 Coupling plug 1 1

500 440 Connection lead, 100 cm 2 2


502 04 Distribution box 1 1


P 6.1.5Dualism of wave and particle

P 6.1.5.1 Diffraction of electrons in apolycrystalline lattice (Debye-Scherrer diffraction)

P6.1.5.2 Optical analogy to diffraction of electrons in apolycrystalline lattice

Diffraction of electrons in a polycrystalline lattice (Debye-Scherrer diffraction) (P 6.1.5.1)

In 1924, L. de Broglie first hypothesized that particles could havewave properties in addition to their familiar particle properties,and that their wavelength depends on the linear momentum p

Ö =h

ph: Planck’s constant

His conjecture was confirmed in 1927 by the experiments ofC. Davisson and L. Germer on the diffraction of electrons atcrystalline structures.

The first experiment demonstrates diffraction of electrons at poly-crystalline graphite. As in the Debye-Scherrer method with x-rays, we observe diffraction rings in the direction of radiationwhich surround a central spot on a screen. These are caused bythe diffraction of electrons at the lattice planes of microcrystalswhich fulfill the Bragg condition

2 · d · sin P = n · ÖP: angular aperture of diffraction ringd: spacing of lattice planes

As the graphite structure contains two lattice-plane spacings,two diffraction rings in the first order are observed. The electronwavelength

Ö =h

ö2 · me · e · Ume: mass of electron, e: elementary charge

is determined by the acceleration voltage U, so that for the angu-lar aperture of the diffraction rings we can say

sin P “ 1.

öUThe second experiment illustrates the Debye-Scherrer methodused in the electron diffraction tube by means of visible light.Here, parallel, monochromatic light passes through a rotatingcrossed grating. The diffraction pattern of the crossed grating atrest, consisting of spots of light arranged around the centralbeam in a network-like pattern, is deformed by rotation into ringsarranged concentrically around the central spot.

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210


Electron diffraction tube 1

Stand rod for electron tubes 1


1

450 63 Halogen lamp, 12 V/100 W 1

450 64 Halogen lamp housing, 12 V, 50/100W 1


521 25 Transformer 2....12 V 1

460 03 Lens f = + 100 mm 1



301 01 Leybold multiclamp



Optical analogon of Debye-Scherrer diffraction (P 6.1.5.2)

555 626

555 600



500 642 I Safety connection lead, 100 cm, blue I 1 I500 644 I Safety connection lead, 100 cm, black I 2 I

555 629 Cross grating, rotatable


5

Observing individual lycopod spores in a Paul trap (P 6.1.6.1)

P 6.1.6

P 6.1.6.1 Observing individual lycopodspores in a Paul trap

Paul trap

Spectroscopic measurements of atomic energy levels are nor-mally impaired by the motion of the atoms under study with res-pect to the radiation source. This motion shifts and broadens thespectral lines due to the Doppler effect, which becomes stronglyapparent in high-resolution spectroscopy. The influence of theDoppler effect is reduced when individual atoms are enclosed ina small volume for spectroscopic measurements. For chargedparticles (ions), this can be achieved using the ion trap develop-ed by W. Paul in the 1950's. This consists of two rotationally sym-metrical cover electrodes and one ring electrode. The applicationof an AC voltage generates a time-dependent, parabolic poten-tial with the form

U(r, z, t) = U0 · cos Ct · r 2 – 2z 2

2 · r 20

z: coordinate on the axis of symmetry,r: coordinate perpendicular to axis of symmetry,r0: inside radius of ring electrode

An ion with the charge q and the mass m remains trapped in thispotential when the conditions

0.4 · R <q

< 1.2 R where R =r 2

0 · C2

m U0

are fulfilled.

This experiment demonstrates how a Paul trap works using amodel which can be operated with no special requirements atstandard air pressure and with 50 Hz AC. When a suitable volt-age amplitude U0 is set, it is possible to trap lycopod spores forseveral hours and observe them under laser light. Tilting of theentire ion trap causes the trapped particles to move radially with-in the ring electrode. When a voltage is applied between thecover electrodes, it is possible to shift the potential along thez-axis.

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211


558 80 Paul trap 1 1

He-Ne laser, linearly polarized 1 1

460 01 Lens f = + 5 mm 1 1

460 34 Auxiliary bench w. swivel joint, 0.5 m 1



522 27 Power supply 450 V DC 1 1

521 35 Variable extra low voltage transformer S 1 1

562 11 U-core with yoke 1 1

562 12 Clamping device 1 1

562 18 Extra-low voltage coil, 50 turns 1 1

562 16 Coil with 10,000 turns 1 1


536 211 Measuring resistor 10 ME, 1 W 1 1





500 98 Set of 6 safety adapter sockets, black 1 1


500 440 Connection lead, 100 cm, yellow/green 1 1

502 04 Distribution box 1 1

471 830

Atomic shells Atomic and nuclear physics

P 6.2.1The Balmer series of hydrogen

P 6.2.1.1 Determining the wavelengthsHR, HT and HH from the Balmerseries of hydrogen

P 6.2.1.2 Observing the Balmer series ofhydrogen using a prismspectrometer

Determining the wavelengths HR, HT and HH from the Balmer series of hydrogen (P 6.2.1.1)

In the visible range, the emission spectrum of atomic hydrogenhas four lines, HR, HT, HH and HF; this sequence continues into theultraviolet range to form a complete series. In 1885, Balmer em-pirically worked out a formula for the frequencies of this series

V = R∞, · ( 1–

1 ), m: 3, 4, 5, ... 22 m2

R∞ = 3.2899 · 1015 s–1: Rydberg constant

which could later be explained using Bohr’s model of the atom.

In this experiment, the emission spectrum is excited using a Bal-mer lamp filled with water vapor, in which an electric dischargesplits the water molecules into an excited hydrogen atom and ahydroxyl group. The wavelengths of the lines HR, HT and HH aredetermined using a high-resolution grating. In the first diffractionorder of the grating, we can find the following relationship be-tween the wavelength Ö and the angle of observation P:

Ö = d · sin Pd: grating constant

The measured values are compared with the values calculatedaccording to the Balmer formula.

In the second experiment the Balmer series are studied bymeans of a prism spectroscope (complete device).

P6.

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212


451 13 Balmer lamp 1 1

451 14 Power supply unit for Balmer lamps 1 1

471 23 Copy of a Rowland grating, approx. 5700 lines/cm 1


460 02 Lens f = + 50 mm 1

460 03 Lens f = + 100 mm 1







467112 School spectroscope 1

Emission spectrum of atomic hydrogen Observing the Balmer series of hydrogen using a prism spectrometer (P 6.2.1.2)

Displaying the line spectra of inert gases and metal vapors (P 6.2.2.1)

P 6.2.2

P 6.2.2.1 Displaying the line spectra ofinert gases and metal vapors

P 6.2.2.2 Qualitative investigation of theabsorption spectrum of sodium

Emission and absorption spectra

When an electron in the shell of an atom or atomic ion drops froman excited state with the energy E2 to a state of lower energy E1,it can emit a photon with the frequency

O =E2 – E1

h

h: Planck’s constant

In the opposite case, a photon with the same frequency isabsorbed. As the energies E1 and E2 can only assume discretevalues, the photons are only emitted and absorbed at discretefrequencies. The totality of the frequencies which occur is re-ferred to as the spectrum of the atom. The positions of the spec-tral lines are characteristic of the corresponding element.

The first experiment disperses the emission spectra of metalvapors and inert gases (mercury, sodium, cadmium and neon)using a high-resolution grating and projects these on the screenfor comparison purposes.

In the second experiment, the flame of a Bunsen burner is alter-nately illuminated with white light and sodium light and observedon a screen. When sodium is burned in the flame, a dark shadowappears on the screen when illuminating with sodium light. Fromthis it is possible to conclude that the light emitted by a sodiumlamp is absorbed by the sodium vapor, and that the same atomiccomponents are involved in both absorption and emission.

P6.

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P6.

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Atomic and nuclear physics Atomic shells

213


451 011 Spectral lamp Ne 1

451 041 Spectral lamp Cd 1

451 062 Spectral lamp Hg 100 1

451 111 Spectral lamp Na 1 1

451 16 Housing for spectral lamps with pin contact 1 1


460 02 Lens f = + 50 mm 1

460 03 Lens f = + 100 mm 1

471 23 Copy of a Rowland grating, approx. 5700 lines/cm 1



441 53 Translucent screen 1 1





Sodium chloride, 250 g 1

666 962 Spatula, double-ended, 150 mm, 9 mm wide, stainless steel 1

666 711 Butane gas burner, gas and air regulation valve 1

666 712 Butane gas cartridges, 200 g, set of 3, for 666 711/713 1


450 51 Lamp, 6 V/30 W 1


30011 Saddle base 1


521 210 Transformer, 6 V AC, 12 V AC/30 VA 1

673 5700


P 6.2.3Inelastic electron collisions

P 6.2.3.1 Discontinuous energy emissionof electrons in a gas-filled triode

Discontinuous energy emission of electrons in a gas-filled triode (P 6.2.3.1)

In inelastic collision of an electron with an atom, the kinetic ener-gy of the electron is transformed into excitation or ionizationenergy of the atom. Such collisions are most probable when thekinetic energy is exactly equivalent to the excitation or ionizationenergy. As the excitation levels of the atoms can only assumediscrete values, the energy emission in the event of inelasticelectron collision is discontinuous.

This experiment uses tube triodes filled with helium or neon todemonstrate this discontinuous emission of energy. After accel-eration in the electric field between the cathode and the grid, theelectrons enter an opposing field which exists between the gridand the anode. Only those electrons with sufficient kinetic ener-gy reach the anode and contribute to the current I flowing be-tween the anode and ground. Once the electrons in front of thegrid have reached a certain minimum energy (which depends onthe gas), they can excite the gas atoms through inelastic colli-sion. When the acceleration voltage U is continuously increased,the inelastic collisions initially occur directly in front of the grid,as the kinetic energy of the electrons reaches its maximum valuehere. After collision, the electrons can no longer travel againstthe opposing field. The anode current I is thus greatly decreased.When the acceleration voltage U is increased further, the excita-tion zone moves toward the cathode, the electrons can againaccumulate energy on their way to the grid and the current Iagain increases. Finally, the electrons can excite gas atoms asecond time, and the anode current drops once more.

P6.

2.3.

1

214


Gas filled triode 1

Stand for electron tubes 1

521 65 DC power supply 0....500 V 1

531 100 Voltmeter, DC, U < 100 V, e. g.Multimeter METRAmax 2

531 100 Amperemeter, DC, I < 100 µA, e. g.Multimeter METRAmax 2 1




Anode current I as a function of the acceleration voltage U for He

555 614

555 600

2

1

4

6

Franck-Hertz experiment with mercury – recording with the oscilloscope (P 6.2.4.1b)

P 6.2.4

P 6.2.4.1 Franck-Hertz experiment withmercury – recording with the oscilloscope,the XY recorder or point bypoint

P 6.2.4.2 Franck-Hertz experiment withmercury – measuring and evaluating withCASSY

Franck-Hertz experiment

In 1914, J. Franck and G. Hertz reported observing discontinuousenergy emission when electrons passed through mercury vapor,and the resulting emission of the ultraviolet spectral line (Ö =254 nm) of mercury. A few months later, Niels Bohr recognizedthat their experiment supported his model of the atom.

This experiment is offered in two variations, which differ only inthe means of recording and evaluating the measurement data.The mercury atoms are enclosed in a tetrode with cathode, grid-type control electrode, acceleration grid and target electrode.The control grid ensures a virtually constant emission current ofthe cathode. An opposing voltage is applied between the accel-eration grid and the target electrode. When the acceleration volt-age U between the cathode and the acceleration grid is in-creased, the target current I corresponds closely to the tubecharacteristic once it rises above the opposing voltage. As soonas the electrons acquire sufficient kinetic energy to excite themercury atoms through inelastic collisions, the electrons can nolonger reach the target, and the target current drops. At thisacceleration voltage, the excitation zone is directly in front of theexcitation grid. When the acceleration voltage is increased fur-ther, the excitation zone moves toward the cathode, the electronscan again accumulate energy on their way to the grid and thetarget current again increases. Finally, the electrons can excitethe mercury atoms once more, the target current drops again,and so forth. The I(U) characteristic thus demonstrates periodicvariations, whereby the distance between the minima WU = 4.9 Vcorresponds to the excitation energy of the mercury atoms fromthe ground state 1S0 to the first 3P1 state.

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P6.

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)

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215


555 85 Mercury Franck-Hertz tube 1 1 1 1

555 861 Socket for Franck-Hertz-tube with multi-pin plug 1 1 1 1

555 81 Electric oven, 230 V 1 1 1 1

555 88 Franck-Hertz supply unit 1 1 1 1

666 193 Temperature sensor NiCr-Ni 1 1 1 1



XY-Yt recorder



524 200 CASSY Lab 1


Franck-Hertz curve

575 664 1


P 6.2.4Franck-Hertz experiment

P 6.2.4.3 Franck-Hertz experiment with neon – recording with the oscilloscope,the XY recorder or point bypoint

P 6.2.4.4 Franck-Hertz experiment with neon – measuring and evaluating withCASSY

Franck-Hertz experiment with neon (P 6.2.4.4)

When neon atoms are excited by means of inelastic electron col-lision at a gas pressure of approx. 10 hPa, excitation is most like-ly to occur to states which are 18.7 eV above the ground state.The de-excitation of these states can occur indirectly via inter-mediate states, with the emission of photons. In this process, thephotons have a wavelength in the visible range between red andgreen. The emitted light can thus be observed with the naked eyeand e.g. measured using the school spectroscope Kirch-hoff/Bunsen (467 112).

The Franck-Hertz experiment with neon is offered in two varia-tions, which differ only in the means of recording and evaluatingthe measurement data. In both variations, the neon atoms areenclosed in a glass tube with four electrodes: the cathode K, thegrid-type control electrode G1, the acceleration grid G2 and thetarget electrode A. Like the Franck-Hertz experiment with mer-cury, the acceleration voltage U is continuously increased andthe current I of the electrons which are able to overcome theopposing voltage between G2 and A and reach the target ismeasured. The target current is always lowest when the kineticenergy directly in front of grid G2 is just sufficient for collisionexcitation of the neon atoms, and increases again with theacceleration voltage. We can observe clearly separated luminousred layers between grids G1 and G2; their number increases withthe voltage. These are zones of high excitation density, in whichthe excited atoms emit light in the visible spectrum.

216

P6.

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)

P6.

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3(a)

P6.

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4


555 870 Neon Franck-Hertz tube 1 1 1 1

555 871 Holder with socket and screen for neon FH tube 1 1 1 1

555 872 Connecting cable for Ne-FH 1 1 1 1

555 88 Franck-Hertz supply unit 1 1 1 1



XY-Yt recorder 1


524 200 CASSY Lab 1

50146 Pair of cables, 1 m, red and blue 2 2


Luminous layers between control electrode and acceleration grid

575 664


P 6.2.6Electron spin resonance(ESR)

P 6.2.6.2 Electron spin resonance inDPPH – determining the magnetic fieldas a function of the resonancefrequency

P 6.2.6.3 Resonance absorption of apassive RF oscillator circuit

Electron spin resonance in DPPH – determining the magnetic field as a function of the resonance frequency (P 6.2.6.2)

The magnetic moment of the unpaired electron with the totalangular momentum j in a magnetic field assumes the discreteenergy states

Em = – gj · BB · m · B where m = –j, –j + 1, ... , j

BB = 9,274 · 10–24 J: Bohr’s magneton

T

gj: g factor

When a high-frequency magnetic field with the frequency V isapplied perpendicularly to the first magnetic field, it excites tran-sitions between the adjacent energy states when these fulfill theresonance condition

h · V = Em+1 – Em

h: Planck’s constant.

This fact is the basis for electron spin resonance, in which theresonance signal is detected using radio-frequency technology.The electrons can often be regarded as free electrons. The g-fac-tor then deviates only slightly from that of the free electron (g =2.0023), and the resonance frequency V in a magnetic field of1 mT is about 78.0 MHz. The actual aim of electron spin reso-nance is to investigate the internal magnetic fields of the samplesubstance, which are generated by the magnetic moments of theadjacent electrons and nuclei.

The first two experiments verify electron spin resonance indiphenyl-picryl-hydrazyl (DPPH). DPPH is a radical, in which afree electron is present in a nitrogen atom. In the simple configu-ration of the first experiment, the magnetic field B which fulfillsthe resonance condition is determined for three different reso-nance frequencies V. In the second experiment, the resonancefrequencies can be set in a continuous range from 13 to 130MHz. The aim of the evaluation in both cases is to determine theg factor.

The object of the final experiment is to verify resonance absorp-tion using a passive oscillator circuit.

218

P6.

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2

P6.

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3


514 55 ESR basic unit 1 1

514 57 ESR control unit 1 1



575 24 Screened cable BNC/4 mm

Ammeter, DC, I ≤ 3 A, e.g.531 100 Multimeter METRAmax 2 1

Voltmeter, AC, U ≤ 1 V, e.g.531 100 Multimeter METRAmax 2 1

Ammeter, DC, I ≤ 1 mA, e.g.531 100 Multimeter METRAmax 2

30011 Stand base 3 2




Diagram of resonance condition of free electrons

1

555 604

2

The Zeeman effect is the name for the splitting of atomic energylevels in an external magnetic field and, as a consequence, thesplitting of the transitions between the levels. The effect waspredicted by H. A. Lorentz in 1895 and experimentally confirmedby P. Zeeman one year later. In the red spectral line of cadmium(Ö = 643.8 nm), Zeeman observed a line triplet perpendicular tothe magnetic field and a line doublet parallel to the magneticfield, instead of just a single line. Later, even more complicatedsplits were discovered for other elements, and were collectivelydesignated the anomalous Zeeman effect. It eventually becameapparent that the normal Zeeman effect is the exception, as itonly occurs at transitions between atomic levels with the totalspin S = 0.

In the first and third experiment, the Zeeman effect is observed atthe red cadmium line perpendicular and parallel to the magneticfield, and the polarization state of the individual Zeeman compo-nents is determined. The observations are explained on the basisof the radiating characteristic of dipole radiation. The so-called Scomponent corresponds to a Hertzian dipole oscillating parallelto the magnetic field, i. e. it cannot be observed parallel to themagnetic field and radiates linearly polarized light perpendicularto the magnetic field. Each of the two D components correspondsto two dipoles oscillating perpendicular to each other with aphase differential of 90°. They radiate circularly polarized light inthe direction of the magnetic field and linearly polarized light par-allel to it.

In the second and fourth experiment, the Zeeman splitting of thered cadmium line is measured as a function of the magnetic fieldB. The energy interval of the triplet components

WE = h

· e

· B4S me

me: mass of electron, e: electron charge, h: Planck’s constantB: magnetic induction

is used to calculate the specific electron charge.

Measuring the Zeeman split of the red cadmium line as a function of the magnetic field (P 6.2.7.4)

P 6.2.7

P 6.2.7.1 Observing the normal Zeemaneffect in transverse andlongitudinal configuration –spectroscopy using a Lummer-Gehrcke plate

P 6.2.7.2 Measuring the Zeeman split ofthe red cadmium line as afunction of the magnetic field –spectroscopy using a Lummer-Gehrcke plate

P 6.2.7.3 Observing the normal Zeemaneffect in transverse andlongitudinal configuration –spectroscopy using a Fabry-Perot etalon

P 6.2.7.4 Measuring the Zeeman split ofthe red cadmium line as afunction of the magnetic field –spectroscopy using a Fabry-Perot etalon

Normal Zeeman effect

P6.

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3(b

)

P6.

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P6.

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219


451 12 Cadmium lamp for Zeeman-Effekt 1 1 1 1 1

451 30 Universal choke, in housing, 230 V, 50 Hz 1 1 1 1 1

521 55 High current power supply 1 1 1 1 1

514 50 Electromagnet for Zeeman-Effect 1 1

471 20 Optical system for observing the Zeeman-Effect 1 1

471 21 Lummer-Gehrcke plate 1 1

562 11 U-core with yoke 1 1 1

562 131 Coil, 10 A, 480 turns 2 2 2

560 315 Pair of pole pieces with great bore 1 1 1

471 221 Fabry-Perot etalon 1 1 1

460 32 Precision optical bench, stand. cross section, 1 m 1 1 1

460 358 Rider base, Width: 148 mm 1 1 1


460 08 Lens, f = + 150 mm 2 2 2

472 601 Quarter-wavelength plate 1 1



467 95 Filter set red, green, blue 1

468 41 Holder for interference filters 1 1

468 400 Interference filter, 644 nm 1 1

460 135 Ocular with scale 1 1

337 47 VideoCom 1

516 62 Teslameter 1 1

516 60 Tangential B-probe 1 1



300 42 Stand rod, 47 cm 1 1



501 20 Connecting lead, Ø 2.5 mm2, 25 cm, red 1 1

501 21 Connecting lead, Ø 2.5 mm2, 25 cm, blue 1 1

501 30 Connecting lead, Ø 2.5 mm2, 100 cm, red 1 1

501 31 Connecting lead, Ø 2.5 mm2, 100 cm, blue 1 1

add. required: PC with Windows 95/NT or higher 1


P 6.2.8Optical pumping(anomalous Zeeman effect)

P 6.2.8.1 Optical pumping: observing the pumping signal

P 6.2.8.2 Optical pumping: measuring and observing theZeeman transitions in theground state of Rb-87 with D+

and D- pumped light

P 6.2.8.3 Optical pumping: measuring and observing theZeeman transitions in theground state of Rb-85 with D+

and D- pumped light

P 6.2.8.4 Optical pumping: measuring and observing theZeeman transitions in theground state of Rb-87 as afunction of the magnetic fluxdensity B

P 6.2.8.5 Optical pumping: measuring and observing theZeeman transitions in theground state of Rb-85 as afunction of the magnetic fluxdensity B

P 6.2.8.6 Optical pumping: measuring and observing two-quantum transitions Measuring and observing the Zeeman transitions in the ground state of Rb-87 with D+- pumped light (P 6.2.8.2)

The two hyperfine structures of the ground state of an alkali atomwith the total angular momentums

F+ = l + 1

, F– = l – 1

2 2

split in a magnetic field B into 2F± + 1 Zeeman levels having anenergy which can be described using the Breit-Rabi formula

E =–∆E

+ BKglmF ±∆E ö1 +

4mF K + K2

2 (2 l + 1) 2 2 l + 1

where K = gJBB – glBK · B

∆E

∆E: hyperfine structure interval,I: nuclear spin, mF: magnetic quantum number,BB: Bohr’s magneton, BK: nucelar magneton,gJ: shell g factor, gI: nuclear g factor

Transitions between the Zeeman levels can be observed using amethod developed by A. Kastler. When right-handed or left-hand-ed circularly polarized light is directed parallel to the magneticfield, the population of the Zeeman level differs from the thermalequilibrium population, i. e. optical pumping occurs, and RFradiation forces transitions between the Zeeman levels.

The change in the equilibrium population when switching fromright-handed to left-handed circular pumped light is verified inthe first experiment. The second and third experiments measurethe Zeeman transitions in the ground state of the isotopes Rb-87and Rb-85 and determine the nuclear spin I from the number oftransitions observed. The observed transitions are classifiedthrough comparison with the Breit-Rabi formula. In the next twoexperiments, the measured transition frequencies are used forprecise determination of the magnetic field B as a function of themagnet current I. The nuclear g factors gI are derived using themeasurement data. In the final experiment, two-quantum transi-tions are induced and observed for a high field strength of theirradiating RF field.

P6.

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1

P6.

2.8.

2-6

220


558 820 Rubidium high frequency lamp 1 1

558 825 Helmholtz coils on stand rider 1 1

558 830 Absorption chamber with rubidium absorption cell 1 1

558 835 Silicon photodetector 1 1

558 836 I/U-converter for silicon photodetector 1 1

530 88 Plug-in power unit, 9.2 V DC, regulated 1 1

558 811 Operational device for optical pumping 1 1

521 45 DC power supply 0....+/- 15 V 1 1

522 551 Function generator, 12 MHz, internal sweep 1



Two channel/ XY storage oscilloscope, e.g.1 1

531 582 Multimeter METRAport 32 S 1 1

504 48 Two-way switch 1 1

468 000 Line filter 795 nm 1 1


472 611 Quarter-wavelength plate (200 nm) 1 1

460 021 Lens f = + 50 mm, brass handle 2 2

460 031 Lens f = + 100 mm, brass handle 1 1



460 352 Optics rider, H = 90 mm/W =50 mm 1 1

666 768 Circulation thermostat 30 ... 100 °C 1 1

200 66843



Silicone tube, 1.0 m long, 6.0 x 2.0 4 4

575 294 Analog/digital oscilloscope HM 507

Determining the ion dose rate of the x-ray tube with molydenum anode (P 6.3.1.4)

P 6.3.1

P 6.3.1.1 Fluorescence of a luminescentscreen due to x-rays

P 6.3.1.2 X-ray photography: exposure of film stock due tox-rays

P 6.3.1.3 Detecting x-rays using anionization chamber

P 6.3.1.4 Determining the ion dose rateof the x-ray tube withmolydenum anode

Detection of x-rays

Soon after the discovery of x-rays by W. C. Röntgen, physiciansbegan to exploit the ability of this radiation to pass through mat-ter which is opaque to ordinary light for medical purposes. Thetechnique of causing a luminescent screen to fluoresce with x-ray radiation is still used today for screen examinations, althoughimage amplifiers are used additionally. The exposure of a film dueto x-ray radiation is used both for medical diagnosis and materialstesting, and is the basis for dosimetry with films. As x-rays ionizegases, they can also be measured via the ionization current of anionization chamber.

The first experiment demonstrates the transillumination with x-rays using simple objects made of materials with differentabsorption characteristics. A luminescent screen of zinc-cadmi-um sulfate is used to detect x-rays; the atoms in this compoundare excited by the absorption of x-rays and emit light quanta inthe visible light range. This experiment investigates the effect ofthe emission current I of the x-ray tube on the brightness and theeffect of the high voltage U on the contrast of the luminescentscreen.

The second experiment records the transillumination of objectsusing x-ray film. Measuring the exposure time required to pro-duce a certain degree of exposure permits quantitative conclu-sions regarding the intensity of the x-rays.

The aim of the last two experiments is to detect x-rays using anionization chamber. First, the ionization current is recorded as afunction of the voltage at the capacitor plates of the chamber andthe saturation range of the characteristic curves is identified.Next, the mean ion dose rate

J =Iion

m

is calculated from the ionization current Iion which the x-radiationgenerates in the irradiated volume of air V, and the mass m of theirradiated air. The measurements are conducted for variousemission currents I and high voltages U of the x-ray tube.

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Atomic and nuclear physics X-rays

221


554 811 X-ray apparatus 1 1 1

554 838 X-ray film holder 1

554 840 Plate capacitor x-ray 1



577 02 STE resistor 1 GV, 0.5 W 1







Fluorescence of a luminescent screen due to x-rays (P 6.3.1.1)

1

1

554 896 X-ray film Agfa Dentus M2 1

554 897 I Developer for X-ray film I I 1 I554 898 I Fixative for X-ray film I I 1 I

X-rays Atomic and nuclear physics

P 6.3.2Attenuation of x-rays

P 6.3.2.1 Investigating the attenuation ofx-rays as a function of theabsorber material and absorberthickness

P 6.3.2.2 Investigating the wavelengthdependency of the attenuationcoefficient

P 6.3.2.3 Investigating the relationshipbetween the attenuation coefficient and the atomicnumber Z

Investigating the attenuation of x-rays as a function of the absorber material and absorber thickness (P 6.3.2.1)

The attenuation of x-rays on passing through an absorber withthe thickness d is described by Lambert's law for attenuation:

I = I0 · e–Bd

I0: intensity of primary beamI: transmitted intensity

Here, the attenuation is due to both absorption and scattering ofthe x-rays in the absorber. The linear attenuation coefficient Bdepends on the material of the absorber and the wavelength Ö ofthe x-rays. An absorption edge, i.e. an abrupt transition from anarea of low absorption to one of high absorption, may be ob-served when the energy h · V of the x-ray quantum just exceedsthe energy required to move an electron out of one of the innerelectron shells of the absorber atoms.

The object of the first experiment is to confirm Lambert's lawusing aluminum and to determine the attenuation coefficients Bfor six different absorber materials averaged over the entirespectrum of the x-ray apparatus.

The second experiment records the transmission curves

T(Ö) = l (Ö)

l0(Ö)

for various absorber materials. The aim of the evaluation is toconfirm the Ö3 relationship of the attenuation coefficients forwavelengths outside of the absorption edges.

In the final experiment, the attenuation coefficient B(Ö) of differentabsorber materials is determined for a wavelength Ö which liesoutside of the absorption edge. This experiment reveals that theattenuation coefficient is closely proportional to the fourth powerof the atomic number Z of the absorbers.

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222


554 811 X-ray apparatus 1 1 1

559 01 End-window counter for R, T, H- and x-rays 1 1 1

554 834 Absorption accessory x-ray 1

554 832 Set of absorber foils 1 1


Bragg reflection: diffraction of x-rays at a monocrystal (P 6.3.3.1)

P 6.3.3

P 6.3.3.1 Bragg reflection: diffraction of x-rays at a monocrystal

P 6.3.3.2 Investigating the energy spectrum of an x-ray tube as afunction of the high voltage andthe emission current

P 6.3.3.3 Duane-Hunt relation and determination of Planck's constant

P 6.3.3.4 Fine structure of the characteristic x-ray radiation ofa molydenum anode

P 6.3.3.5 Edge absorption: filtering x-rays

P 6.3.3.6 Moseley's law and determination of the Rydberg constant

P 6.3.3.7 Compton effect: verifying the energy loss of thescattered x-ray quantum

P 6.3.3.8 Fine structure of the charac-teristic x-ray radiation of acopper anode

Physics of the atomic shell

The fourth experiment reveals the fine structure of the character-istic lines KR and KT and explains these on the basis of the finestructure of the atomic levels involved.

The object of the fifth experiment is to filter x-rays using theabsorption edge of an absorber, i. e. the abrupt transition from anarea of low absorption to one of high absorption.

The sixth experiment determines the wavelengths ÖK of theabsorption edges as as function of the atomic number Z. Whenwe apply Moseley's law

1= R · (Z – D)2

ÖK

to the measurement data we obtain the Rydberg constant R andthe mean screening D.

The final experiment verifies the Compton shift of the wavelengthÖ in backscattering. This is apparent as a change in the attenu-ation coefficient of an absorber, which is placed in front of andthen behind the scattering body.

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1-5

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Atomic and nuclear physics X-rays

223


554 811 X-ray apparatus 1 1 1 1

554 85 Copper anode 1

559 01 End-window counter for R-, T-, H- and x-rays 1 1 1 1

554 832 Set of absorber foils 1

554 836 Compton accessory x-ray 1

additionally required:PC with Windows 95/NT or higher 1 1 1

The radiation of an x-ray tube consists of two components: con-tinuous bremsstrahlung radiation is generated when fast elec-trons are decelerated in the anode. Characteristic radiation con-sisting of discrete lines is formed by electrons dropping to theinner shells of the atoms of the anode material from which elec-trons were liberated by collision.

To confirm the wave nature of x-rays, the first experiment investi-gates the diffraction of the chracteristic KR and KT lines of themolybdenum anode at an NaCl monocrystal and explains theseusing Bragg's law of reflection.

The second experiment records the energy spectrum of the x-rayapparatus as a function of the high voltage and the emission cur-rent using a goniometer in the Bragg configuration. The aim is toinvestigate the spectral distribution of the continuum of brems-strahlung radiation and the intensity of the characteristic lines.

The third experiment measures how the limit wavelength Ömin ofthe continuum of bremsstrahlung radiation depends on the highvoltage U of the x-ray tube. When we apply the Duane-Hunt rela-tionship

e · U = h ·c

Ömin

to the measurement data, we can derive Planck's constant h.

e: electron charge, c: velocity of light

Splitting of the KR and KT-lines in the 3rd to 5th diffraction orders

Ionization of air due to radioactivity (P 6.4.1.1)

P 6.4.1

P 6.4.1.1 Ionization of air due to radioactivity

P 6.4.1.2 Recording the current-voltagecharacteristic of an ionizationchamber

P 6.4.1.3 Detecting radioactivity using aGeiger counter

P 6.4.1.4 Recording the characteristic ofa Geiger-Müller counter tube

Detection of radioactivity

In 1895, H. Becquerel discovered radioactivity while investigatinguranium salts. He found that these emitted a radiation which wascapable of fogging light-sensitive photographic plates eventhrough black paper. He also discovered that this radiation ion-izes air and that it can be identified by this ionizing effect.

In the first experiment, a voltage is applied between two elec-trodes, and the air between the two electrodes is ionized byradioactivity. The ions created in this way cause a charge trans-port which can be detected using an electrometer as a highlysensitive ammeter.

The aim of the second experiment is to record the current-volt-age characteristic of air ionized by radioactivity in an ionizationchamber. This experiment shows that, at low voltages, the currentrises in proportion to the voltage. At higher voltages, the currentreaches a saturation value, which depends on the intensity of thepreparation.

The third experiment uses a Geiger counter to detect radioactivi-ty. A potential is applied between a cover with hole which servesas the cathode and a fine needle as the anode; this potential isjust below the threshold of the disruptive field strength of the air.As a result, each ionizing particle which travels within this fieldinitiates a discharge collision.

The final experiment records the current-voltage characteristic ofa Geiger-Müller counter tube. Here too, the current increasesproportionally to the voltage for low voltage values, before reach-ing a saturation value which depends on the intensity or distanceof the preparation.

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Atomic and nuclear physics Radioactivity

225


559 82 Am 241 preparation 1 1

546 31 Zinc plate for photoelectric effect 1

546 33 Grid electrode 1




577 03 STE resistor 10 GE, 0.5 W 1


546 25 Ionization chamber 1






300 41 Stand rod, 25 cm 1 1


666 555 Universal clamp, 0...80 mm dia. 1 1

559 430 Ra 226 preparation 1 1

546 281 Geiger counter 1

546 38 Adapter for geiger counter 1

575 211 Two channel oscilloscope 303 1


559 01 End-window counter for R, T, H and x-rays 1


59013 Insulated stand rod, 25 cm long 1

591 21 Large clip plug 1


500 421 Connection lead, 50 cm, red 1

500 610 Safety connecting lead, 25 cm, yellow/green 1 1

501 40 Connecting lead, Ø 2.5 mm2, 25 cm, yellow/green 1



Radioactivity Atomic and nuclear physics

P 6.4.2Poisson distribution

P 6.4.2.1 Statistical variations in determinating counting rates

Statistical variations in determinating counting rates (P 6.4.2.1)

For each individual particle in a radioactive preparation, it is amatter of coincidence whether it will decay over a given timeperiod Wt. The probability that any particular particle will decay inthis time period is extremely low. The number of particles n whichwill decay over time Wt thus shows a Poisson distribution aroundthe mean value B. In other words, the probability that n decayswill occur over a given time period Wt is

wB(n) = Bn

e–Bn!

B is proportional to the size of the preparation and the time Wt,and inversely proportional to the half-life T1/2 of the radioactivedecay.

Using a computer-assisted measuring system, this experimentdetermines multiple pulse counts n triggered in a Geiger-Müllercounter tube by radioactive radiation over a selectable gate timeWt. After a total of N counting runs, the frequencies h(n) are deter-mined at which precisely n pulses were counted, and displayedas histograms. For comparision, the evaluation program calcu-lates the mean value B and the standard deviation

D = öäBof the measured intensity distribution h(n) as well as the Poissondistribution wB(N).

P6.

4.2.

1

226


559 83 Set of 5 radioactive preparations 1

559 01 End-window counter for R, T, H and x-rays 1

524 033 GM-box 1


524 200 CASSY Lab 1

591 21 Large clip plug 1

590 02 Small clip plug 1


30011 Saddle base 2


Measured and calculated Poisson distributionHistogram: h(n), curve: N · wB (n)

Determining the half-life of Ba-137m – recording and evaluating the decay curve using CASSY (P 6.4.3.4)

P 6.4.3

P 6.4.3.3 Determining the half-life of Ba-137m – recording the decay curveusing the digital counter

P 6.4.3.4 Determining the half-life of Ba-137m – recording and evaluating thedecay curve using CASSY

Radioactive decay and half-life

For the activity of a radioactive sample, we can say:

A(t) = dNdt

Here, N is the number of radioactive nuclei at time t. It is not pos-sible to predict when an individual atomic nucleus will decay.However, from the fact that all nuclei decay with the same prob-ability, it follows that over the time interval dt, the number ofradioactive nuclei will decrease by

dN = – Ö · N · dtÖ: decay constant

Thus, for the number N, the law of radioactive decay applies:

N(t) = N0 · e–Ö · t

N0: number of radioactive nuclei at time t = 0

Among other things, this law states that after the half-life

t1/2 =ln2

Ö

the number of radioactive nuclei will be reduced by half.

To determine the half-life of Ba-137m, a plastic bottle with Cs-137stored at salt is used. The metastable isotop Ba-137m arisingfrom the b-decay is released by an eluation solution. The half-time amounts to 2.6 minutes approx.

P6.

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3

P6.

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4

Atomic and nuclear physics Radioactivity

227


559 815 Cs/Ba-137m isotope generator 1 1

559 01 End-window counter 1 1



524 200 CASSY Lab 1

524 033 GM box 1

664 043 Test tubes, 160 x 16 diam. 1 1

664 103 Beaker, 250 ml, ss, hard glass 1 1


300 42 Stand rod, 47 cm 1 1


666 555 Universal clamp, 0 ... 80 mm dia. 2 2


Radioactivity Atomic and nuclear physics

P 6.4.4Attenuation of R, T and H radiation

P 6.4.4.1 Measuring the range of Rradiation in air

P 6.4.4.2 Attenuation of T radiation whenpassing through matter

P 6.4.4.3 Confirming the law of distancefor T radiation

P 6.4.4.4 Absorption of H radiation whenpassing through matter

Absorption of H radiation when passing through matter (P 6.4.4.4)

High-energy R and T particles release only a part of their energywhen they collide with an absorber atom. For this reason, manycollisions are required to brake a particle completely. Its range R

R “ E 20

n · Z

depends on the initial energy E0, the number density n and theatomic number Z of the absorber atoms.

Low-energy R and T particles or H radiation are braked to a cer-tain fraction when passing through a specific absorber densitydx, or are absorbed or scattered and thus disappear from thebeam. As a result, the radiation intensity I decreases exponen-tially with the absorption distance x.

I = I0 · e–B · x

B: attenuation coefficient

The first experiment determines the range R of monoenergetic Rparticles in air. Here, the ionization current I is measured in anionization chamber of variable height as a function of thedistance d between the cover and the Am-241 preparation. Theionization current initially increases with the distance d beforeremaining constant at distances which are greater than therange.

The second experiment examines the attenuation of T radiationfrom Sr-90 in aluminum as a function of the absorber thicknessd. This experiment shows an exponential decrease in the inten-sity. As a comparison, the absorber is removed in the third exper-iment and the distance between the T preparation and thecounter tube is varied. As one might expect for a point-shapedradiation source, the following is a good approximation for theintensity:

I (d) “ 1

d 2

The fourth experiment examines the attenuation of H radiation inmatter. Here too, the decrease in intensity is a close approxima-tion of an exponential function. The attenuation coefficient Bdepends on the absorber material and the H energy.

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3

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2

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1

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4

228


559 82 Am 241 preparation 1

546 25 Ionization chamber 1

546 27 Telescopic cylinder 1

546 35 Adapter for ionization chamber 1



575 24 Screened BNC/4 mm 1

531 100 Multimeter METRAmax 2 1

311 52 Vernier calipers, plastic 1




666 555 Universal clamp, 0...80 mm dia. 1

500 610 Safety connecting lead, 25 cm, yellow/green 1

501 40 Connecting lead, Ø 2.5 mm2, 25 cm, yellow/green 1


559 83 Set of 5 radioactive preparations 1 1 1

559 18 Holder with absorber foils 1

559 01 End-window counter for R, T, H and x-rays 1 1

Counter S 1 1

590 02 Small clip plug 1 1

591 21 Large clip plug 1 1



460 97 Scaled metal rail, 0.5 m 1

Geiger counter 1

559 94 Set of absorbers and targets 1

300 51 Stand rod, right angled 1


667 9182

575 471

Demonstrating the tracks of R-particles in the Wilson cloud chamber (P 6.5.1.1)

P 6.5.1

P 6.5.1.1 Demonstrating the tracks of R-particles in the Wilson cloudchamber

Demonstration of particle tracks

In a Wilson cloud chamber, a saturated mixture of air, water andalcohol vapor is briefly caused to assume a supersaturated statedue to adiabatic expansion. The supersaturated vapor condens-es rapidly around condensation seeds to form tiny mist droplets.Ions, which are formed e.g. through collisions of R particles andgas molecules in the cloud chamber, make particularly efficientcondensations seeds.

In this experiment, the tracks of R particles are observed in a Wil-son cloud chamber. Each time the pump is vigorously pressed,these tracks are visible as traces of droplets in oblique light forone to two seconds. An electric field in the chamber clears thespace of residual ions.

P6.

5.1.

1

Atomic and nuclear physics Nuclear physics

229


559 57 Wilson cloud chamber 1

559 59 Radium source for Wilson cloud chamber 1



450 51 Lamp, 6 V/30 W 1



301 06 Bench clamp 1

30011 Saddle base 1

Ethanol, fully denaturated, 1l 1


Droplet traces in the Wilson cloud chamber

521 210

671 9720

Nuclear physics Atomic and nuclear physics

P 6.5.2Rutherford scattering

P 6.5.2.1 Rutherford scattering: measuring the scattering rateas a function of the scatteringangle and the atomic number

Rutherford scattering: measuring the scattering rate as a function of the scattering angle and the atomic number(P 6.5.2.1)

The fact that an atom is “mostly empty space” was confirmed byRutherford, Geiger and Marsden in one of the most significantexperiments in the history of physics. They caused a parallelbeam of R particles to fall on an extremely thin sheet of gold leaf.They discovered that most of the R particles passed through thegold leaf virtually without deflection, and that only a few weredeflected to a greater degree. From this, they concluded thatatoms consist of a virtually massless extended shell, and a prac-tically point-shaped massive nucleus.

This experiment reproduces these observations using an Am-241preparation in a vacuum chamber. The scattering rate N(P) ismeasured as a function of the scattering angle P using a Geiger-Müller counter tube. As scattering materials, a sheet of gold leaf(Z = 80) and aluminum foil (Z = 13) are provided. The scatteringrate confirms the relationship

N(P) “ 1and N(P) “ Z 2.

sin4 P2

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5.2.

1(a

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)

230


559 82 Am 241 preparation 1 1

559 56 Rutherford scattering chamber 1 1

559 52 Aluminum foil in holder 1 1

559 93 Discriminator preamplifier 1 1

562791 Plug-in power unit 1

501 16 Multicore cable, 6-pole, 1.5 m 1


378 752 Rotary-vane vacuum pump D 2.5 E 1 1

378 764 Exhaust filter 1* 1*

378 031 Small flange DN 16 KF with hose nozzle 1 1

307 68 Vacuum tubing, 8/18 mm dia. 1 1



Scattering rate N as a function of the scattering angle P

Nuclear magnetic resonance in polystyrene, glycerine and Teflon (P 6.5.3.1)

P 6.5.3

P 6.5.3.1 Nuclear magnetic resonancein polystyrene, glycerine andTeflon

Nuclear magnetic resonance (NMR)

The magnetic moment of the nucleus entailed by the nuclear spinI assumes the energy states

Em = – gl · BK · m · B with m = –I, –I + 1, . . . , I

BK = 5,051 · 10–27 J: nuclear magneton

T

gI: g factor of nucleus

in a magnetic field B. When a high-frequency magnetic field withthe frequency V is applied perpendicularly to the first magneticfield, it excites transitions between the adjacent energy stateswhen these fulfill the resonance condition

h · V = Em+1 – Em

h: Planck’s constant

This fact is the basis for nuclear magnetic resonance, in whichthe resonance signal is detected using radio-frequency technol-ogy. For example, in a hydrogen nucleus the resonance frequen-cy in a magnetic field of 1 T is about 42.5 MHz. The precise valuedepends on the chemical environment of the hydrogen atom, asin addition to the external magnetic field B the local internal fieldgenerated by atoms and nuclei in the near vicinity also acts onthe hydrogen nucleus. The width of the resonance signal alsodepends on the structure of the substance under study.

This experiment verifies nuclear magnetic resonance in poly-styrene, glycerine and Teflon. The evaluation focuses on theposition, width and intensity of the resonance lines.


231

P6.

5.3.

1


NMR supply unit

1

516 60 Tangential B-probe 1*

516 62 Teslameter 1*

501 16 Multicore cable, 6-pole, 1.5 m long 1*


Diagram of resonance condition of hydrogen

514 602

514 606 NMR probe unit 1


562 131 Coil, 10 A, 480 turns 2



500 621 I Safety connection lead, 50 cm, red I 1500 641 I Safety connection lead, 100 cm, red I 1500 642 I Safety connection lead, 100 cm, blue I 1

575 294 Analog/digital oscilloscope HM 507

1


P 6.5.4R spectroscopy

P 6.5.4.1 R spectroscopy of radioactivesamples

P 6.5.4.2 Determining the energy loss ofR radiation in air

P 6.5.4.3 Determining the energy loss ofR radiation in aluminum and ingold

P 6.5.4.4 Determining the age of an Ra-226 sample

R spectroscopy of radioactive samples (P 6.5.4.1)

Up until about 1930, the energy of R rays was characterized interms of their range in air. For example, a particle of 5.3 MeV(Po-210) has a range of 3.84 cm. Today, R energy spectra can bestudied more precisely using semiconductor detectors. Thesedetect discrete lines which correspond to the discrete excitationlevels of the emitting nuclei.

The aim of the first experiment is to record and compare the Renergy spectra of the two standard preparations Am-241 and Ra-226. To improve the measuring accuracy, the measurement isconducted in a vacuum chamber.

In the second experiment, the energy E of R particles is measur-ed as a function of the air pressure p in the vacuum chamber. Themeasurement data is used to determine the energy per unit ofdistance dE /dx which the R particles lose in the air. Here,

x =p

· x0p0

x0: actual distance, p0: standard pressure

is the apparent distance between the preparation and the detec-tor.

The third experiment determines the amount of energy of R par-ticles lost per unit of distance in gold and aluminum as the quo-tient of the change in the energy WE and the thickness Wx of themetal foils.

In the final experiment, the individual values of the decay chainof Ra-226 leading to the R energy spectrum are analyzed todetermine the age of the Ra-226 preparation used here. Theactivities A1 and A2 of the decay chain “preceding” and “follow-ing” the longer-life isotope Pb-210 are used to determine the ageof the sample from the relationship

A2 = A1 ·(1 – e– T )I

I = 22.3 a: lifetime of Pb-210

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3

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2

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232


559 82 Am 241 preparation 1 1 1

559 430 Ra 226 preparation 1 1 1

559 56 Rutherford scattering chamber 1 1 1 1

559 52 Aluminium foil in holder 1

559 93 Discriminator preamplifier 1 1 1 1

524 010 Sensor-CASSY 1 1 1 1

524 058 MCA Box 1 1 1 1

524 200 CASSY Lab 1 1 1 1

501 16 Multicore cable, 6-pole, 1.5 m 1 1 1 1

501 02 BNC cable, 1 m 1 1 1 1

501 01 BNC cable, 0.25 m 1 1 1 1


378 752 Rotary-vane vacuum pump D 2.5 E 1 1 1 1

378 764 Exhaust filter 1* 1* 1* 1*

307 68 Vacuum tubing 8/18 mm 1 1 1 1

378 031 Small flange DN 16 KF with hose nozzle 1 1 1 1



378 015 Cross DN 16 KF 1

378 776 Metering valve DN 16 KF 1

additionally required:1 PC with Windows 95/NT or higher 1 1 1 1


378 510 Pointer manometer 1

Absorption of H radiation (P 6.5.5.3)

P 6.5.5H spectroscopy

Compton scattering, it often occurs that only a part of the H ener-gy is transferred to the crystal, as there is a certain probabilitythat the scattered H quantum will exit the crystal. The H quanta areregistered in a continuous distribution in which the upper andlower limits are determined by the maximum and minimum ener-gy which can be transferred to the electron in Compton scatter-ing. A third possible interaction, pair formation, is only significantat H energies above 2 MeV.

In the first experiment, the output pulses of the scintillationcounter are investigated using the oscilloscope and the multi-channel analyzer MCA-CASSY. The total absorption peak andthe Compton distribution are identified in the pulse-amplitudedistribution generated with monoenergetic H radiation.

The aim of the second experiment is to record and compare theH energy spectra of standard preparations. The total absorptionpeaks are used to calibrate the energy of the scintillation count-er and to identify the preparations.

The third experiment examines the attenuation of H radiation invarious absorbers. The aim here is to show how the attenuationcoefficient B depends on the absorber material and the H energy.

A Marinelli beaker is used in the fourth experiment for quantita-tive measurements of weakly radioactive samples. This appara-tus encloses the scintillator crystal virtually completely, ensuringa defined measurement geometry. Lead shielding considerablyreduces the interfering background from the laboratory environ-ment.

The final experiment records the continuous spectrum of a pureT radiator (Sr-90/Y-90) using the scintillation counter. To deter-mine the energy loss dE/dx of the T particles in aluminum, alumi-num absorbers of various thicknesses x are placed in the beampath between the preparation and the detector.

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233


559 84 Mixed preparation R, T, H 1

559 83 Set of 5 radioactive preparations 1 1 1

559 885 Calibrating preparation 137 Cs, 5 kBq 1

559 901 Scintillation counter 1 1 1 1 1

559 912 Detector-output stage 1 1 1 1 1

559 94 Set of absorbers and targets 1 1

559 89 Scintillator screening 1 1

559 891 Socket for scintillator 1 1 1 1 1

559 88 Marinelli beaker 2

521 68 High voltage power supply 1.5 kV 1 1 1 1 1

524 010 Sensor-CASSY 1 1 1 1 1

524 058 MCA Box 1 1 1 1 1

524 200 CASSY Lab 1 1 1 1 1


501 02 BNC cable, 1 m 1*

300 42 Stand rod, 47 cm 1 1 1 1


666 555 Universal clamp, 0...80 mm dia. 1 1 1 1

Potassium chloride, 250 g 4

additionally required:PC with Windows 95/NT or higher 1 1 1 1 1


When interpreting H energy spectra recorded with a scintillationcounter, it is necessary to take several interactive processes ofthe H radiation with the scintillator crystal into consideration. Inthe photoeffect, the H quanta transfer their entire energy to thecrystal and are registered in the total absorption peak. Due to

P 6.5.5.1 Detecting H radiation with ascintillation counter

P 6.5.5.2 Recording and calibrating a Hspectrum

P 6.5.5.3 Absorption of H radiation

P 6.5.5.4 Identifying and determining theactivity of weakly radioactivesamples

P 6.5.5.5 Recording a T spectrum usinga scintillation counter

672 5210


P 6.5.6Compton effect

P 6.5.6.1 Quantitative observation of theCompton effect

Quantitative observation of the Compton effect (P 6.5.6.1)

In the Compton effect, a photon transfers a part of its energy E0and its linear momentum

p0 =E0

c

c: speed of light in a vacuum

to a free electron by means of elastic collision. Here, the laws ofconservation of energy and momentum apply just as for the col-lision of two bodies in mechanics. The energy

E(P) = E0

1 + E0 · (1 – cos P)

m · c2

m: mass of electron at rest

and the linear momentum

p = E

c

of the scattered photon depend on the scattering angle P. Theeffective cross-section depends on the scattering angle and isdescribed by the Klein-Nishina formula:

dD=

1· r 2

0 · p2

· (p0 + p

– sin2P)dE 2 p20 p p0

r0 = 2,5 · 10–15 m: classic electron radius

In this experiment, the Compton scattering of H quanta with theenergy E0 = 667 keV at the quasi-free electrons of an aluminumscattering body is investigated. For each scattering angle P, acalibrated scintillation counter records one H spectrum with andone without aluminum scatterer as a function of the respectivescattering angle. The further evaluation utilizes the total absorp-tion peak of the differential spectrum. The position of this peakgives us the energy E(P). Its integral counting rate N(P) is com-pared with the calculated effective cross-section.

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234


559 800 Apparatus set Compton 1

559 809 Cs-137 preparation, 3.7 MBq 1

559 84 Mixed preparation alpha, beta, gamma 1

559 901 Scintillation counter 1

559 912 Detector output stage 1

521 68 High voltage power supply 1.5 kV 1


524 058 MCA Box 1

524 200 CASSY Lab 1


Measuring arrangement

Solid-statephysics

236

Table of contents Solid-state physics

P7 Solid-state physics

P 7.1 Properties of crystalsP 7.1.1 Structure of crystals 237

P 7.1.2 X-ray structural analysis 238

P 7.1.3 X-ray structural analysiswith the x-ray apparatus P 239

P 7.1.4 Elastic and plastic deformation 240

P 7.2 Conduction phenomenaP 7.2.1 Hall effect 241

P 7.2.2 Electrical conduction in solid bodies 242

P 7.2.3 Photoconductivity 243

P 7.2.4 Luminescence 244

P 7.2.5 Thermoelectricity 245

P 7.2.6 Superconductivity 246

P 7.3 MagnetismP 7.3.1 Dia-, para- und ferromagnetism 247

P 7.3.2 Ferromagnetic hysteresis 248

P 7.4 Scanning probe microscopyP 7.4.1 Scanning tunneling microscope 249

Investigating the crystal structures of tungsten using a field emission microscope (P 7.1.1.1)

P 7.1.1

P 7.1.1.1 Investigating the crystal structures of tungsten using afield emission microscope

Structure of crystals

In the field emission microscope, the extremely fine tip of atungsten monocrystal is arranged in the center of a sphericalluminescent screen. In the vicinity of the tip, the electric field be-tween the crystal and the luminescent screen reaches such ahigh field strength that the conducting electrons can “tunnel” outof the crystal and travel radially to the luminescent screen. Here,an image of the emission distribution of the crystal tip is created,magnified by a factor of

V =Rr

R = 5 cm: radius of luminescent screenr = 0,1-0,2 Bm: radius of tip

In the first part of this experiment, the tungsten tip is purified byheating it to a white glow. The structure which appears on theluminescent screen after the electric field is applied correspondsto the body-centered cubic lattice of tungsten, which is observedin the (110) direction, i.e. the direction of one of the diagonals ofa cube face. Finally, a minute quantity of barium is vaporized inthe tube, so that individual barium atoms can precipitate on thetungsten tip to produce bright spots on the luminescent screen.When the tungsten tip is heated carefully, it is even possible toobserve the thermal motion of the barium atoms.

P7.

1.1.

1

Solid-state physics Properties of crystals

237


554 60 Field emission microscope 1

554 605 Connection plate FEM 1

301 339 Pair of stand feet 1


521 39 Variable extra low voltage transformer 1







Properties of crystals Solid-state physics

P 7.1.2X-ray structural analysis

P 7.1.2.1 Bragg reflection: determining the lattice constantsof monocrystals

P 7.1.2.2 Laue diagrams: investigating the lattice structureof monocrystals

P 7.1.2.3 Debye-Scherrer photography:determining the lattice-planespacings of polycrystallinepowder samples

P 7.1.2.4 Debye-Scherrer Scan: determining the lattice-planespacings of polycrystallinepowder samples

Laue diagrams: investigating the lattice structure of monocrystals (P 7.1.2.2)

238

When x-rays of the wavelength Ö are diffracted at a crystal, maxi-ma occur at the reflection angles R, T, H which, when measuredwith respect to the crystal axes a, b, c, fulfill the Laue conditions

h · Ö = a · (cosR0 – cosR), h = 0, ±1, ±2, ... k · Ö = b · (cosT0 – cosT), k = 0, ±1, ±2, ... l · Ö = c · (cosH0 – cosH), l = 0, ±1, ±2, ...R0, T0, H0: angle of incidence

W. H. and W. L. Bragg described the behavior of x-rays incrystals in simplified terms as reflection at a set of parallel latticeplanes. Reflection can only occur for the glancing angles P whichfulfill the Bragg condition

2 · d · sinP = n · Ö with n = 1, 2, 3, . . .d: lattice plane spacing, n: diffraction order

For a cubic lattice with the lattice constant a, the spacing of thelattice planes can be expressed using the Laue indices h, k, l:

d =a

öh 2 + k 2 + l 2

In the first experiment, the Bragg reflection of Mo-KR radiation(Ö = 71.080 pm) at NaCl and LiF monocrystals is used to deter-mine the lattice constant. The KT component of the x-ray radia-tion can be suppressed using a zirconium filter.

To make Laue diagrams at NaCl and LiF monocrystals, thebremsstrahlung radiation of the x-ray apparatus is used in thesecond experiment as “white” x-radiation. The positions of the“colored” reflections on an x-ray film behind the crystal and theirintensities can be used to determine the crystal structure and thelengths of the crystal axes through application of the Laue con-dition.

In the last two experiments, Debye-Scherrer photographs areproduced by irradiating samples of a fine crystal powder withMo-KR radiation. Among many unordered crytallites of the sam-ple, the x-rays diffract at those which have an orientation con-forming to the Bragg condition. The diffracted rays describeconical sections for which the aperture angles P can be derived

P7.

1.2.

4

P7.

1.2.

3

P7.

1.2.

2

P7.

1.2.

1


554 811 X-ray apparatus 1 1 1 1

559 01 End-window counter for a, b, g and x-rays 1 1

554 77 LiF monocrystal for Bragg reflecion 1

554 842 Set of 2 crystal powder-holder 1

554 838 Film holder x-ray 1 1

554 87 LiF crystal for Laue diagrams 1

554 88 NaCl crystal for Laue diagrams 1

667 091 Pestle, porcelain, 100 mm, for 667 092 1

667 092 Mortar, porcelain, 63 mm dia. 1

311 54 Precision vernier calipers 1


from a photograph. This experiment determines the lattice spa-cing corresponding to P as well as its Laue indices h, k, l, andthus the lattice structure of the crystallite.

Laue diagram of NaCl Debye-Scherrer photograph of NaCl

1

1

554 896 X-ray film Agfa Dentus M2 1 1

554 897 I Developer for X-ray film I I 1 I 1 I554 898 I Fixativer for X-ray film I I 1 I 1 I

Properties of crystals Solid-state physics

P 7.1.4Elastic and plastic deformation

P 7.1.4.1 Investigating the elastic andplastic extension of metal wires

Investigating the elastic and plastic extension of copper wires (P 7.1.4.1)

The shape of a crystalline solid is altered when a force is applied.We speak of elastic behavior when the solid resumes its originalform once the force ceases to act on it. When the force exceedsthe elastic limit, the body is permanently deformed. This plasticbehavior is caused by the migration of discontinuities in thecrystal structure.

In this experiment, the extension of iron and copper wires is in-vestigated by hanging weights from them. A precision pointerindicator measures the change in length Ws, i. e. the extension

Z =Wss

s: length of wire

After each new tensile load

D =F

A

F: weight of load pieces, A: wire cross-section

the students observe whether the pointer returns to the zeroposition when the strain is relieved, i.e. whether the strain isbelow the elasticity limit DE. Graphing the measured values in atension-extension diagram confirms the validity of Hooke's law

D = E · ZE: modulus of elasticity

up to a proportionality limit DP.

P7.

1.4.

1

240


550 35 Copper wire, 100 m, 0.20 mm dia. 1

550 51 Iron wire, 100 m, 0.20 mm dia. 1


340 911 Pulley, plug-in, 50 mm diameter 1

381 331 Pointer for linear expansion 1

340 82 Double scale 1

314 04 Support clip, for plugging in 2






300 44 Stand rod, 100 cm 1

Load-extension diagram for a typical metal wire

Investigating the Hall effect in silver (P 7.2.1.1)

P 7.2.1

P 7.2.1.1 Investigating the Hall effect insilver

P 7.2.1.2 Investigating the anomalousHall effect in tungsten

P 7.2.1.3 Determining the density andmobility of charge carriers in n-germanium

P 7.2.1.4 Determining the density andmobility of charge carriers in p-germanium

P 7.2.1.5 Determining the band gap ofgermanium

Hall effect

In the case of electrical conductors or semiconductors within amagnetic field B, through which a current I is flowing perpendic-ular to the magnetic field, the Hall effect results in an electricpotential difference

UH = RH · B · l ·1

d

d: thickness of sample

The Hall coefficient

RH =1

· p · B2

p – n · B2n

e (p · Bp + n · Bn)2

e: elementary charge

depends on the concentrations n and p of the electrons andholes as well as their mobilities Bn and Bp, and is thus a quantitywhich depends on the material and the temperature.

The first two experiments determine the Hall coefficient RH of twoelectrical conductors by measuring the Hall voltage UH forvarious currents I as a function of the magnetic field B. A nega-tive value is obtained for the Hall coefficient of silver, which indi-cates that the charge is being transported by electrons. A posi-tive value is found as the Hall coefficient of tungsten. Conse-quently, the holes are mainly responsible for conduction in thismetal.

The third and fourth experiments explore the temperature-depen-dency of the Hall voltage and the electrical conductivity

D = e · (p · Bp + n · Bn)

using doped germanium samples. The concentrations of thecharge carriers and their mobilities are determined under theassuption that, depending on the doping, one of the concentra-tions n or p can be ignored. In the final experiment, the electricalconductivity of undoped germanium is measured as a function ofthe temperature to provide a comparison. The measurement datapermits determination of the band gap between the valence bandand the conduction band in germanium.

Solid-state physics Conduction phenomena

241

P7.

2.1.

4

P7.

2.1.

3

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2

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2.1.

1

P7.

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5


586 81 Hall effect apparatus, silver 1

586 84 Hall effect apparatus, tungsten 1

586 850 Base unit for Hall effect (Ge) 1 1 1

586 853 n-Ge on plug-in board 1

586 852 p-Ge on plug-in board 1

586 851 Ge undoped on plug-in board 1

532 13 Microvoltmeter 1 1

516 62 Teslameter 1 1

516 60 Tangential B-probe 1 1 1 1



524 200 CASSY Lab 1 1 1

524 038 B-box 1 1


521 39 Variable extra low voltage transformer 1 1

521 50 AC/DC power supply 0....15 V 2 2 1

DC power supply 0....16 V, 5 A 1 1 1

562 11 U-core with yoke 1 1 1 1

560 31 Pair of bored pole pieces 1 1 1 1

562 13 Coil with 250 turns 2 2 2 2


300 41 Stand rod, 25 cm 1 1 1 1


300 02 Stand base, V-shape, 20 cm 1 1 1 1 1

501 46 Pair of cables, 1 m, red and blue 4 4 7 7 4


additionally required:PC with Windows 95/NT or higher 1 1 1

521 545

Conduction phenomena Solid-state physics

P 7.2.2Electrical conduction in solid bodies

P 7.2.2.1 Measuring the temperature-dependency of a noble metalresistor

P 7.2.2.2 Measuring the temperature-dependency of a semiconductorresistor

Measuring the temperature-dependency of a noble metal resistor and a semiconductor resistor (P 7.2.2.1/2)

The temperature-dependency of the specific resistance U is asimple test for models of electric conductivity of conductors andsemiconductors. In electrical conductors, U increases with thetemperature, as the collisions of the quasi-free electrons from theconduction band with the atoms of the conductor play anincreasingly important role. In semiconductors, on the otherhand, the specific resistance decreases as the temperatureincreases, as more and more electrons move from the valenceband to the conduction band, thus contributing to the conduc-tivity.

These experiments measure the resistance values as a functionof temperature using a Wheatstone bridge. The computer-as-sisted CASSY measured-value recording system is ideal forrecording and evaluating the measurements. For the noble metalresistor, the relationship

R = RU · T

U

U = 240 K: Debye temperature of platinum

is verified with sufficient accuracy in the temperature rangeunder study. For the semiconductor resistor, the evaluation re-veals a dependency with the form

R “ e–

WE2kT

k = 1.38 · 10–23 J: Boltzmann constant

K

with the band spacing E = 0.48 eV.

P7.

2.2.

2

P7.

2.2.

1

242


586 80 Noble metal resistor 1

586 82 Semiconductor resistor 1

555 81 Electric oven for 230 V 1 1

524 031 Current supply box 1 1


524 045 Temperature box (NiCrNi/NTC) 1 1


524 200 CASSY Lab 1 1

502 061 Safety connection box with ground 1 1



Recording the current-voltage characteristic of a CdS photoresistor (P 7.2.3.1)

P 7.2.3

P 7.2.3.1 Recording the current-voltagecharacteristic of a CdS photoresistor

Photoconductivity

Photoconductivity is the phenomenon in which the electrical con-ductivity D of a solid is increased through the absorption of light.In CdS, for example, the absorbed energy enables the transitionof activator electrons to the conduction band and the reversal ofthe charges of traps, with the formation of electron holes in thevalence band. When a voltage U is applied, a photocurrent Iphflows.

The object of the experiment is to determine the relationshipbetween the photocurrent Iph and the voltage U at a constantradiant flux Fe as well as between the photocurrent Iph and theradiant flux Fe at a constant voltage U in the CdS photoresistor.

P7.

2.3.

1


243





450 51 Lamp, 6 V/30 W 1




460 08 Lens f = + 150 mm 1

460 32 Precision optical bench, standardized cross section 1 m 1



DC power supply 0....16 V, 5 A 1

531 281 Digital-analog multimeter METRAHit 24 S 1

531 301 Digital-analog multimeter METRAHit 26 S 1

500 422 Connecting lead, 50 cm, blue 1


521 210

521 545

Seebeck effect: Determining the thermoelectric voltage as a function of the temperature differential (P 7.2.5.1)

P 7.2.5

P 7.2.5.1 Seebeck effect: Determining the thermoelectricvoltage as a function of thetemperature differential

Thermoelectricity

When two metal wires with different Fermi energies EF touch,electrons move from one to the other. The metal with the lowerelectronic work function WA emits electrons and becomes posi-tive. The transfer does not stop until the contact voltage

U =WA, 1 – WA, 2

e

e: elementary charge

is reached. If the wires are brought together in such a way thatthey touch at both ends, and if the two contact points have a tem-perature differential T = T1 – T2, an electrical potential, the ther-moelectric voltage

UT = U(T1) – U(T2),

is generated. Here, the differential thermoelectric voltage

R =dUT

dT

depends on the combination of the two metals.

In this experiment, the thermoelectric voltage UT is measured asa function of the temperature differential T between the twocontact points for thermocouples with the combinationsiron/constantan, copper/constantan and chrome-nickel/con-stantan. One contact point is continuously maintained at roomtemperature, while the other is heated in a water bath. The differ-ential thermoelectric voltage is determined by applying a best-fitstraight line

UT = R · T

to the measured values.

P7.

2.5.

1


245


557 01 Set of 3 simple thermocouples 1


532 13 Microvoltmeter 1

382 34 Thermometer, -10° to + 110 °C 1

666 767 Hot plate, 150 mm dia., 1500 W 1


Thermoelectric voltage as a function of the temperatureTop: chrome-nickel/constantan, Middle: iron/constantan, Bottom: cupper/constantan

Conduction phenomena Solid-state physics

P 7.2.6Superconductivity

P 7.2.6.1 Determining the transition temperature of a high-temperature superconductor

P 7.2.6.2 Meißner-Ochsenfeld effect in ahigh-temperature superconductor

Determining the transition temperature of a high-temperature superconductor (P 7.2.6.1)

In 1986, K. A. Müller and J. G. Bednorz succeeded in demonstrat-ing that the compound YBa2Cu3O7 becomes superconducting attemperatures far greater than any known up to that time. Sincethen, many high-temperature superconductors have been foundwhich can be cooled to their transition temperature using liquidnitrogen. Like all superconductors, high-temperature supercon-ductors have no electrical resistance and demonstrate the phe-nomenon known as the Meissner-Ochsenfeld effect, in whichmagnetic fields are displaced out of the superconducting body.

The first experiment determines the transition temperature of thehigh-temperature superconductor YBa2Cu3O7-x. For this pur-pose, the substance is cooled to below its critical temperature ofTc = 92 K using liquid nitrogen. In a four-point measurementsetup, the voltage drop across the sample is measured as afunction of the sample temperature using the computer-assistedmeasured value recording system CASSY.

In the second experiment, the superconductivity of theYBa2Cu3O7-x body is verified with the aid of the Meissner-Ochsenfeld effect. A low-weight, high field-strength magnetplaced on top of the sample begins to hover when the sample iscooled to below its critical temperature so that it becomes super-conducting and displaces the magnetic field of the permanentmagnet.

P7.

2.6.

1

P7.

2.6.

2

246


667 552 Experiment kit for determining transition temperature and electrical resistance 1


524 200 CASSY Lab 1


667 551 Experiment kit for Meissner-Ochsenfeld effect 1


Meißner-Ochsenfeld effect in a high-temperature superconductor

Dia-, para- and ferromagnetic materials in an inhomogeneous magnetic field (P 7.3.1.1)

P 7.3.1

P 7.3.1.1 Dia-, para- and ferromagneticmaterials in an inhomogeneousmagnetic field

Dia-, para- and ferromagnetism

Diamagnetism is the phenomenon in which an external magneticfield causes magnetization in a substance which is opposed tothe applied magnetic field in accordance with Lenz's law. Thus,in an inhomogeneous magnetic field, a force acts on diamagnet-ic substances in the direction of decreasing magnetic fieldstrength. Paramagnetic materials have permanent magneticmoments which are aligned by an external magnetic field.Magnetization occurs in the direction of the external field, so thatthese substances are attracted in the direction of increasingmagnetic field strength. Ferromagnetic substances in magneticfields assume a very high magnetization which is orders ofmagnitude greater than that of paramagnetic substances.

In this experiment, three 9 mm long rods with different magneticbehaviors are suspended in a strongly inhomogeneous magneticfield so that they can easily rotate, allowing them to be attractedor repelled by the magnetic field depending on their respectivemagnetic property.

P7.

3.1.

1

Solid-state physics Magnetism

247


560 41 Apparatus for experiments on dia- and paramagnetism 1




521 39 Variable extra low voltage transformer 1





500 422 Connecting lead, 50 cm, blue 1

Placement of a sample in the magnetic field

Magnetism Solid-state physics

P 7.3.2Ferromagnetic hysteresis

P 7.3.2.1 Recording the magnetizationand hysteresis curves of aferromagnet

Recording the magnetization and hysteresis curves of a ferromagnet (P 7.3.2.1a)

In a ferromagnet, the magnetic induction

B = Br · B0 · H

B0 = 4S · 10–7 Vs: magnetic field constant

Am

reaches a saturation value Bs as the magnetic field H increases.The relative permiability Br of the ferromagnet depends on themagnetic field strength H, and also on the previous magnetictreatment of the ferromagnet. Thus, it is common to represent themagnetic induction B in the form of a hysteresis curve as a func-tion of the rising and falling field strength H. The hysteresis curvediffers from the magnetization curve, which begins at the origin ofthe coordinate system and can only be measured for completelydemagnetized material.

In this experiment, a current I1 in the primary coil of a transform-er which increases (or decreases) linearly over time generatesthe magnetic field strength

H =N1 · I1L

L: effective length of iron core,N1: number of windings of primary coil.

The corresponding magnetic induction value B is obtainedthrough integration of the voltage U2 induced in the secondarycoil of a transformer:

B =1

· ∫ U2 · dtN2 · A

A: cross-section of iron coreN2: Number of windings of secondary coil

The computer-assisted measurement system CASSY is used tocontrol the current and to record and evaluate the measuredvalues. The aim of the experiment is to determine the relative per-meability Br in the magnetization curve and the hysteresis curveas a function of the magnetic field strength H.

P7.

3.2.

1 (b

)

P7.

3.2.

1 (a

)

248


562 11 U-core with yoke 1 1

562 12 Clamping device 1 1

2 2



524 200 CASSY Lab 1 1


576 71 Rastered socket panel section 1



500 424 Connecting lead, 50 cm, black 1


Recording the magnetization and

hysteresis curves of a ferromagnet

(P 7.3.2.1 b)

522 621

562 14 Coil with 500 turns

Investigating a graphite surface using a scanning tunneling microscope (P 7.4.1.1)

P 7.4.1

P 7.4.1.1 Investigating a graphite surfaceusing a scanning tunnelingmicroscope

P 7.4.1.2 Investigating a gold surfaceusing a scanning tunnelingmicroscope

P 7.4.1.3 Investigating a MoS2 probeusing a scanning tunnelingmicroscope

Scanning tunneling microscope

The scanning tunneling microscope was developed in the 1980'sby G. Binnig and H. Rohrer. It uses a fine metal tip as a localprobe; the probe is brought so close to an electrically conductivesample that the electrons “tunnel” from the tip to the sample dueto quantum-mechanical effects. When an electric field is appliedbetween the tip and the sample, an electric current, the tunnelcurrent, can flow. As the tunnel current varies exponentially withthe distance, even an extremely minute change in distance of0.01 nm results in a measurable change in the tunnel current. Thetip is mounted on a platform which can be moved in all three spa-tial dimensions by means of piezoelectric control elements. Thetip is scanned across the sample to measure its topography. Acontrol circuit maintains the distance between tip and sampleextremely precisely at a constant distance by maintaining a con-stant tunnel current value. The controlled motions performedduring the scanning process are recorded and imaged using acomputer. The image generated in this manner is a composite inwhich the sample topography and the electrical conductivity ofthe sample surface are superimposed.

These experiments use a scanning tunneling microscope spe-cially developed for practical experiments, which operates atstandard air pressure. At the beginning of the experiment, ameasuring tip is made from platinum wire. The graphite sample isprepared by tearing off a strip of tape. When the gold sample ishandled carefully, it requires no cleaning; the same is valid forthe MoS2 probe. The investigation of the samples begins with anoverview scan. In the subsequent procedure, the step width ofthe measuring tip is reduced until the positions of the individualatoms of the sample with respect to each other are clearly visi-ble in the image.

249

P7.

4.1.

3

P7.

4.1.

1-2


554 58 Scanning tunneling microscope 1 1

554 584 MoS2 probe 1

additionally required:PC with Windows

Solid-state physics Scanning probe microscopy

3.1 or Windows 95 1 1

Register

AR radiation 228

R spectrum 232

aberration–, chromatic 173–, lens 173–, spherical 173

absorption edge 222–224

absorption spectrum 213

absorption– of H radiation 228, 233– of light 178– of microwaves 137– of x-rays 222–224

AC power meter 118

acceleration 23–24

accumulator 165

AC-DC generator 123

action = reaction 27, 32

active power 132

activity determination 233

AD converter 166

adder 160, 164

additive color mixing 177

address bus 167-168

addressing 167

adiabatic exponent 83

aerodynamics 64–66

air resistance 65–66

airfoil 65, 66

ALU 167

Amontons' law 82

ampere, definition of 113

amplifier 157

amplitude hologram 186-187

amplitude modulation (AM) 135

AND 163–164

angle of inclination 121

angled projection 30

angular acceleration 33–34

angular velocity 33-34

anharmonic oscillation 43

annihilation radiation 233

anomalous Hall effect 241

anomalous Zeeman effect 220

anomaly of water 71

antenna 139

apparent power 132

Archimedes' principle 61

arithmetic and logic unit 165

arithmetic operation 168

arithmetic unit 165

astigmatism 173

astronomical telescope 174

asynchronous motor 125

atom, size of 205, 239

attenuation– of R, T and H radiation 228– of x-rays 222, 224

autocollimation 172

BT radiation 228

T spectrum 233

Babinet's theorem 179

Balmer series 212

band gap 241

barrel aberration 173

beats 51, 57

bell 133

bending 13

bending radius 9

Bernoulli equation 66

Bessel method 172

Biot-Savart's law 114

bipolar transistors 156

biprism 182

birefringence 189, 191-192

black body 195

block and tackle 16

Bohr's magneton 219

Bohr's model of the atom 214–217

Boyle-Mariotte's law 82

Bragg reflection 223, 238–239

branches 168

Braun tube 143

break-away method 63

Breit-Rabi formula 220

bremsstrahlung 223–224

Brewster angle 188

bridge rectifier 156

brightness control 162

Brownian motion of molecules 81

buffer 165

building materials 69

buoyancy 61, 66

Ccalcite 189

caliper gauge 9

canal rays 147

capacitance– of a plate capacitor 102–103– of a sphere 101

capacitive impedance 126, 128–129

capacitor 102–103, 126

cathode rays 147

Cavendish hemispheres 100

center of gravity 31

central force 31

central processing unit 167

centrifugal and centripetal force 36–37

chaotic oscillation 43

characteristic radiation 223–224

characteristic(s)– of a diode 155– of a field-effect transistor 156– of a glow lamp 153– of a light-emitting diode 155– of a photoresistor 243– of a phototransistor 158– of a solar battery 152– of a transistor 156– of a tube diode 140– of a tube triode 141– of a varistor 153– of a Z-diode 155

charge, electric 91-95, 140–144

charge carrier concentration 241

charge distribution 100

charge transport 104

chromatic aberration 173

circular motion 31, 33–34

circular polarization 48, 189

circular waves 49

code converter 164

coder 164

coercive force 248

coil 127

collision 26–27, 32

color mixing 177

coma 173

combinatorial circuit 164

comparator 160

complementary colors 176

composition of forces 14

Compton effect 223, 234

computer-assisted experiments– in atomic and nuclear physics

224, 226-227– in electricity 95, 113, 115, 117,

119 –121, 134, 139– in electronics 153, 162– in heat 76, 79, 87– in mechanics 12, 24–27, 29, 35, 41, 43–44,

51–52, 54–55, 57, 59, 64–66– in optics 180–181, 194-195, 201– in solid-state physics 239, 241, 242,

246, 248

condensation heat 78

conductivity 241–242

conductor, electric 100, 105 –107, 242–243

conoscopic ray path 192

conservation of angular momentum 35

conservation of energy 26–27, 32, 35

conservation of linear momentum 26–27, 32

constant-current source 151

constant-voltage source 151

control bus 168

control, closed-loop 162

control, open-loop 161

cork-powder method 53

Coulomb's law 93-95

counter 164

counter tube 225

counting rates, determination of 226

coupled pendulums 44

coupling of oscillations 44–45

Cp, CV 83

CPU timer 167

crest factor 132

critical point 80

critical potentials 217

cross grating 179

crystal lattice 237-239

current source 151–152

current transformation of a transformer 119

curve form factor 130

cushion aberration 173

cW value 65

Register

252

Register

253

DDA converter 166

damped oscillation 42–43

Daniell element 110

data bus 167–168

data transfer 168

de Broglie wavelength 210

de Morgan's laws 163

Debye temperature 242

Debye-Scherrer diffraction of electrons 210

Debye-Scherrer photograph 238

decimeter waves 135–136

decoder 164

decomposition of forces 14

decomposition of white light 176

deflection of electrons– in an electric field 143–144– in a magnetic field 142–144

demultiplexer 164

density balance 10

density maximum of water 71

density–, measuring 10– of liquids 10– of solids 10– of air 10

detection– of radioactivity 225– of x-rays 221, 224

diamagnetism 247

dielectric constant 102–103– of water 135

differentiator 160

diffraction– at a crossed grating 179– at a double slit 50, 57, 137, 179–181– at a grating 50, 57, 179– at a half-plane 181– at a multiple grating 50, 57, 179–181– at a pinhole diaphragm 179– at a post 179– at a single slit 50, 57, 137, 179–181

diffraction– of electrons 210– of light 179–181– of microwaves 137– of ultrasonic waves 57– of water waves 50– of x-rays 223

digital control systems 66

diode 140, 155–156

diode characteristic 140, 155

directional characteristic 135– of antennas 139

dispersion– of liquids 175– of gases 175

distortion 173

doping 241

doppler effect 49, 58

dosimetry 221, 224

double mirror 182

double pendulum 44

double slit, diffraction at 50, 57, 137, 179–181

dualism of wave and particle 210

Duane and Hunt's law 223

dynamic pressure 64

Ee, determination of 206

e/m, determination of 144, 207

Earth inductor 121

Earth's magnetic field 121

echo sounder 56

eddy currents 118

edge absorption 223

edge, diffraction at 181

Edison effect 140

efficiency – of a heat pump 88– of a hot air engine 86– of a solar collector 73– of a transformer 120

elastic collision 26–27, 32

elastic deformation 240

elastic strain constant 13

elastic torsion collision 35

electric charge 91–95, 100, 140–144

electric conductor 100, 105–107, 242–243

electric current as charge transport 104

electric energy 77, 131–132

electric field 96–97

electric generator 123, 125

electric motor 124-125

electric oscillator circuit 59, 128

electric power 131–132

electric work 131–132

electrical machines 122–125

electrochemistry 110

electrolysis 109

electromagnet 111, 122

electromagnetic oscillations 59, 134

electromechanical devices 133

electrometer 91–92

electron charge 206

electron diffraction 210

electron holes 241, 243

electron spin 218-220

electron spin resonance 218

electrostatic induction 91–92, 100

electrostatics 91–92

elliptical polarization 189

emission spectrum 213

energy loss of a radiation 232

energy spectrum of x-rays 223–224

energy–, electrical 77, 131–132–, heat 76–77–, mechanical 16–17, 24–27, 32, 35, 76

energy-band interval 241

equilibrium 15

equilibrium of angular momentum 15

ESR see electron spin resonance

evaporation heat 78

excitation energies 217

excitation of atoms 214–217

expansion 69

FFalling-ball viscosimeter 62

Faraday constant 109

Faraday cylinder 100

Faraday effect 193

feedback 134

ferromagnetism 247–248

field effect transistor 156, 157

field emission microscope 237

fine beam tube 207

fine crystal structure 223

fixed pulley 16

flip-flop 164

fluorescence 244

fluorescent screen 221

focal point, focal length 172

force 13–18, 21 –, measuring on current-carrying

conductors 113– along the plane 17– in an electric field 98–99– normal to the plane 17

forced oscillation 42–43

Foucault-Michelson method 196

Fourier transformation 59

Franck-Hertz experiment 215–216

free fall 28–30

frequency 40–53, 56-59, 134–135, 137

frequency modulation (FM) 135

frequency response 130

Fresnel biprism 182

Fresnel's laws 188

Fresnel's mirror 182

friction 18

friction coefficient 18

full-wave rectifier 156

GH radiation 228

H spectrum 233

Galilean telescope 174

galvanic element 110

gas discharge 145-146

gas elastic resonance apparatus 83

gas laws 82

gas thermometer 82

Gay-Lussac's law 82

Geiger counter 225

Geiger-Müller counter tube 225

generator circuits 157

generator, electric 123, 125

geometrical optics 171–174

glowing layer 146

golden rule of mechanics 16–17

Graetz circuit 155

grating spectrometer 200, 201

grating, diffraction at 50, 57, 179

gravitation torsion balance after Cavendish 11–12

Gravitational acceleration 28-29, 40

Gravitational constant 11–12

Gyroscope 38

Hh, determination of 208–209, 233

half-life 126–127, 227

Register

254

half-plane, diffraction at 181

half-shadow polarimeter 190

half-wave rectifier 156

Ha-line 212

Hall effect 241

hammer interrupter 133

harmonic oscillation 41–43

heat capacity 75

heat conduction 72

heat energy 76–77

heat engine 84, 86–87

heat equivalent–, electric 77–, mechanical 76

heat insulation 72

heat pump 85–86, 88

helical spring 13, 41

helical spring after Wilberforce 45

helical spring waves 46

Helmholtz coils 114

high voltage 120

high-temperature superconductor 246

hologram 186–187

homogeneous electric field 98

Hooke's law 13, 240

hot-air engine 84–87

Huygens' principle 49

hydrostatic pressure 60

hyperfine structure 220

hysteresis 248

II/O elements 167

ideal gas 82

illuminance 194

image charge 99, 101

imaging aberrations 173

impedance 126–128

inclined plane 17, 31

independence principle 30–31

induction 115–117, 122

inductive impedance 127–129

inelastic collision 26–27, 32

inelastic electron collision 214–217

inelastic rotational collision 35

integrator 160

interference– of light 182– of ultrasonic waves 57– of water waves 50

interferometer 184–185

internal resistance 108, 151–152

interrupt 168

intrinsic conduction 241

inverting operational amplifier 160

ion dose rate 221

ion trap 211

ionization chamber 221, 225

ionization energy 217

ionizing radiation 225

IR position detector 12

irradiance 194

isoelectric lines 97

Jjump instructions 167

jumps 168

KKR-line 223–224

K-edge 222–224

Keplerian telescope 174

Kerr effect 191

kinetic energy 24–25

kinetic theory of gases 81–83

Kirchhoff's laws 106–107

Kirchhoff's law of radiation 195

Kirchhoff's voltage balance 99

Klein-Nishina formula 234

Kundt's tube 53

LLambert's law of radiation 194

latch 165

latent heat 78

Laue diagram 238

law of distance 224, 228

laws of images 172

laws of radiation 195

leaf spring 13

Lecher line 136, 138

LED 154–155

length measurement 9

Leslie's cube 195

lever 15

lever with unequal sides 15

light emitting diode 154–155

light waveguide 158

light, velocity of 196–198

line spectrum 199–200, 212–213

linear motion 19–25

lines of force 96, 111

lines of magnetic force 111

Lloyd's experiment 50, 182

logical operations 163–165

longitudinal waves 46

loose pulley 16

luminescence 244

luminous zone 146

Lummer-Gehrcke plate 219

Mmachine(s)–, simple 16–17–, electrical 122–125

Mach-Zehnder-Interferometer 185

magnetic field of a coil 114

magnetic field of Helmholtz coils 114

magnetic field the Earth 121

magnetic focusing 142

magnetic moment 112

magnetization curve 248

magnets 111,122

magnifier 174

Maltese-cross tube 142

Malus' law 188

mathematical pendulum 40

Maxwell measuring bridge 129

measuring bridge–, Maxwell 129–, Wheatstone 106-107–, Wien 129

measuring range, expanding 108

mechanical energy 16–17, 24–27, 32, 35, 76

Meissner-Ochsenfeld effect 246

Melde's law 48

melting heat 78

metallic conductor 242

Michelson interferometer 184

micrometer screw 9

microprocessor 168

microscope 174

microwaves 137–138

Millikan experiment 206

mixing temperature 74

mobility of charge carriers 241

modulation of light 192

modulus of elasticity 13

Mohr density balance 10

molecular motion 81

molecule, size of 205

Mollier diagram 88

moment of inertia 38–39

Moseley's law 223-224

motions–, one-dimensional 19–25–, two-dimensional 31–32–, uniform 19–25, 33–34–, uniformly accelerated 19–25, 33–34– with reversal of direction 23–25

motor, electric 124–125

multimeter 130

multiple slit, diffraction at 50, 57, 179–181

multiplexer 164

NNAND 163–164

n-doped germanium 241

Newton rings 183

Newton, definition of 21

Newton's experiments with white light 176

Newton's law 32

NMR see nuclear magnetic resonance

non-inverting operational amplifier 160

non-self-maintained gas discharge 145

NOR 163–164

normal Hall effect 241

normal Zeeman effect 219

NOT 163

NTC resistor 153

nuclear magnetic resonance 231

nuclear magneton 220

nuclear spin 220, 231

nutation 38

Oohmic resistance 105–108

Ohm's law 105

oil spot experiment 205

Register

255

one-sided lever 15

operational amplifier 159–160

opposing force 32

optical activity 190

optical analogon 210

optical pumping 220

optical transmission line 158

optoelectronics 158

OR 163–164

orbital spin 219–220

oscillation of a string 52

oscillation period 40–45, 83, 134

oscillations 40–45, 52, 59, 134

oscillator 157

oscillator circuit 59, 128

Pparallel connection– of capacitors 102– of resistors 106

parallelogram of forces 14

paramagnetism 247

particle tracks 229

path-time diagram 19–25, 33–34

Paul trap 211

S-doped germanium 241

peak voltage 132

pendulums–, coupled 44–, mathematical and physical 40

performance number 88

permanent magnets 111, 122

Perrin tube 143

phase hologram 186–187

phase transition 78–80

phase velocity 46–49

phosphorescence 244

photoconductivity 243

photodiode 158

photoelectric effect 208–209

photoresistor 153, 243

phototransistor 158

physical pendulum 40

PID controller 162

pinhole diaphragm, diffraction at 179

Planck's constant 208–209, 223

plastic deformation 240

plate capacitor 102–103

Pockels effect 192

Poisson distribution 226

polarimeter 190

polarity of electrons 143

polarization– of decimeter waves 135– of light 188-193– of microwaves 137

post, diffraction at 179

potentiometer 106

power plant generator 123

power transformation of a transformer 120

precession 38

pressure 60

primary colors 177

prism spectrometer 199

program counter 168

program memory 167

projection parabola 30

propagation velocity– of voltage pulses 197– of waves 47–49

propagation– of electrons 142– of water waves 49

PTC resistor 153

pV diagram 84–85, 87

pyknometer 10

Qquantum nature 186, 188–189, 195–197

quantum nature of charges 206

quartz, right-handed and left-handed polarization 190

Rradioactive dating 232

radioactive decay 227

radioactivity 225–226

RAM 167

range of a radiation 228

reactance 126–128

reactive power 132

real gas 80

recoil 26

rectification 140, 155

redox pairs 110

reflection –, law of 49, 56, 171– of light 171– of microwaves 137– of ultrasonic waves 56– of water waves 49

refraction–, law of 49, 171– of light 171– of microwaves 137– of water waves 49

refractive index 49, 175, 185, 188, 198

refrigerating machine 85

register 164–165

relay 133

remanence 48

resistors, special 153

resonance 2, 128

resonance absorption 218, 220

reversing pendulum 40

revolving-armature generator 123, 125

revolving-field generator 123, 125

rigid body 31-32

RMS voltage 132

rocket principle 26

rolling friction 18

rotating the plane of polarization 190, 193

rotating-crystal method 239

rotating-mirror method 196

rotation instructions 168

rotational motion 31–34

rotational oscillation 42–43

rotor 122–125

Rutherford scattering 230

Rydberg constant 223

Ssaccharimeter 190

scanning tunneling microscope 249

scattering of H quanta 234

scintillation counter 233

Seebeck effect 245

self-excited generator 123

self-maintained gas discharge 145–146

semiconductor detector 232

semiconductors 242

sequential circuit 164

series connection – of capacitors 102– of resistors 106

servo control 162

shift instructions 168

shift register 164

simple machines 16–17

single slit, diffraction at 50, 57, 137, 179–181

slide gauge 9

sliding friction 18

slit, diffraction at 50, 57, 137, 179–181

Snellius' law 49, 171

sodium D-lines 200

solar battery 152

solar collector 73

sound 59

sound waves 51, 53–55

sound, velocity of – in air 54– in gases 54– in solids 55

special resistors 153

specific conductivity 242

specific electron charge 144, 207, 219

specific heat 75

specific resistance 105, 242

spectrometer 199

spectrum 199, 212

speech analysis 59

spherical aberration 173

spherometer 9

spin 218–220, 231

spring 13

spring pendulum 41

standard potentials 110

standing wave 46, 50, 53, 136–138

standing waves 138

static friction 17–18

static pressure 64

stator 122–125

Stefan-Boltzmann's law 195

Steiner's law 39

Stirling process 84-87

storage addresses 168

straight waves 49

subprogram call 168

subtractive color mixing 177

subtractor 160

Register

256

subtractor unit 165

sugar solution, concentration of 190

superconductivity 246

superpositioning principle 30–31

surface tension 63

synchronous motor 124–125

Ttachymeter 21

telescope 174

temperature 74

temperature variations 72

terrestrial telescope 174

thermal emission in a vacuum 143

thermal expansion– of liquids 70– of solid bodies 69– of water 71

thermodynamic cycle 84–88

thermoelectric voltage 245

thermoelectricity 45

Thomson tube 144

thread waves 46, 48

three-phase generator 125

three-phase machine 125

three-pole rotor 124

time constant– L/R 127– RC 126

torsion balance 93

torsion collision 35

total pressure 64

total reflection of microwaves 137

traffic-light control system 161

transformer 119–120

transformer under load 119

transistor 156–157

transit time measurement 197

transition temperature 246

translational motion 31-32

transmission hologram 187

transmission of filters 201

transmitter 135, 137

transversal waves 46

triode 141

tube diode 140

tube triode 141

tuning fork 51

two-beam interference 50, 57

two-dimensional motion 31–32

two-pole rotor 124

two-pronged lightning rod 120

two-quantum transitions 220

two-sided lever 15

Tyndall effect 188

Uultrasonic waves 56–58

uniform acceleration 19–25, 31, 33–34

uniform motion 19–25, 31, 33–34

universal motor 124

Vvapor pressure 79

velocity 19–25

velocity filter for electrons 144

Venturi tube 64

Verdet's constant 193

vernier 9

VideoCom 25, 27, 29, 44, 181, 201

viscosity 62

voltage amplification with a tube triode 141

voltage balance 99

voltage control 162

voltage divider 106

voltage optics 189

voltage pulse 115

voltage series 110

voltage source 151–152

voltage transformation in a transformer 119

volume flow 64

volume measurement 10

volumetric expansion 70

volumetric expansion coefficient 69–70

vowel analysis 59

WWaltenhofen's pendulum 118

water 71, 135

water waves 49-50

wave machine 47

waveguide 138

wavelength 46-49, 52-53, 184

waves 46–59, 135–139, 179–187

Wheatstone measuring bridge 106–107

wheel and axle 15

white light 176

white light reflection hologram 186

Wien measuring bridge 129

Wilson cloud chamber 229

wind speed 64

wind tunnel 66

work–, electrical 77, 84–87, 131–132–, mechanical 16–17, 24–25, 76, 84–87

XXOR 163

X-ray photography 221, 224

X-ray structural analysis 238–239

X-rays 221–224, 238–239

YYoung's experiment 50, 57, 137, 179–181

ZZ-diode 154–155

Zeeman effect 219–220

Zero page 168

catalogue of physics experiments

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