LCR RESONANCE CIRCUIT

Aim:To study the characteristics of LCR series resonance circuit and determine the resonance

frequency, bandwidth, half power frequencies and Quality factor at resonance.Apparatus:

Inductor, Capacitor, Resistor, function generator and A.C ammeter.Theory:

The circuit containing a capacitance C, inductance L and resistance R, connected in series. When an alternating e.m.f is applied to the circuit an alternate current flows in the circuit.

The impedance of the circuit is given by;

The effective reactance is inductive or capacitive depends upon XL>XC or XL<XC. The inductive reactance is proportional to the frequency and increases as the frequency increases from zero onwards. The capacitive reactance is inversely proportional to the frequency, decrease from an infinite value downwards. At certain frequency both reactance’s become equal and this frequency is called the resonant frequency. At resonance the impedance is minimum and is equal to the resistance. Under these conditions the current I = V/R and cosø=1 or ø=0. That is, the current and voltage are in phase. Such a circuit is called an acceptor circuit.

In series LCR resonance circuit the impedance of the capacitor and inductor are in opposite directions and equal in magnitude. Hence the impedance of the circuit is only the resistance; the current is maximum at the resonance frequency which is given by

The bandwidth of the LCR circuit is defined as the difference in half power frequencies. These can be determined by drawing a half power line on the characteristic curve.Band width ω = f2 – f1 Where f1 , f2 are the half power frequencies

Quality factor

Circuit diagram:

Procedure:1. Connect the circuit as shown in the circuit diagram.2. Apply input signal using signal generator.3. Vary the frequency till the ammeter records a sharp rise and fall, adjust the signal such

that the ammeter deflection is the maximum possible. This is the resonance frequency of the connected combination of the circuit.

4. Adjust the signal generator amplitude such that to get full scale deflection. In ammeter now reduce the frequency till the deflection falls considerably. Then increase the frequency in regular intervals and note down the ammeter readings.

5. Plot a graph between frequency f and current I. Observations:

Sl.No. Frequency f (Hz) Current I (mA)

Graph:

Result: 1) The resonance frequency of LCR series circuit

a) From graph_________.

b) From calculations __________.

2) Band width___________.3) Q factor ______________.

TORSIONAL PENDULUM

Aim:

To determine the rigidity modulus of the material of a given wire by dynamical

method.

Apparatus:

Solid metallic cylinders with a pointer, Experimental wire about 2m length, Stopwatch,

Screw gauge, Meter scale.

Theory & Formula

What is torsional pendulum?

A body suspended by a thread or wire which twists

first in one direction and then in the reverse direction, in the

horizontal plane is called a torsional pendulum.The first

torsional pendulum was developed by Robert Leslie in 1793

When a body is firmly attached to one end of the given

wire, whose upper end is rigidly fixed to a support and is

made to execute small torsional vibrations, the resulting

motion is rotatory simple harmonic motion with the time

period (T) given by,

Here I is the moment of inertia of the suspended body about the wire as axis and C is

the torsional couple per unit twist of the wire i.e

Substituting in (1) we get

Here = length of the wire

r = radius of the wire

= rigidity modulus of the material of the wire

Procedure:

1) The experimental wire about 80cm length is clamped in a rigid support at the upper end

through a chuck nut . The other end is clamped in another chuck nut on a solid metal

cylinder. The length of the wire between the upper and lower chuck nuts is noted with

the help of a meter scale.

2) Now twist the wire by turning the solid cylinder through a small angle in a horizontal

plane without displacing its center of gravity and release. The system starts executing

torsional oscillations about the wire as axis.

3) The torsional oscillations are counted with the pointer as reference and time for 20

oscillations is noted using a stopwatch. This enables to calculate time period (T).

4) Now increase the length of the wire by 10cm. Find the corresponding time of

oscillations and time period.

5) Measure the diameter of the wire in two mutually perpendicular directions at different

points of the wire along its length by using screw gauge. Take three observations and

tabulate them.

6) The value of /T 2 is found in each case.

7) Find the radius of the metal cylinder (R) by measuring its circumference.

8) Find the mass of the metal cylinder (M) by physical balance.

9) Using the appropriate formula for moment of inertia of the cylinder, I is calculated.

10) Knowing the mean value of /T 2, I , r and using the formula (2), is calculated.

Observations:

1) To find moment of inertia ( I ) :

The moment of inertia about its axis I = MR2/2

Mass of the disc M = 900 gm

Circumference of the disc 2R = __________cm.

Radius of the disc R = __________cm.

Moment of inertia I =__________ gm cm2

2) To find the radius ( r ) of the wire:

L.C of screw gauge =_________ cm.

Zero error =___________cm.

Sl.No PSR HSRTotal reading(cm)PSR+(HSR ‘0’

CORRECTION)*L.C123

Average diameter D = ________cm

Radius of the wire r = D / 2 = _________cm

3) To find rigidity modulus:

Sl.No

Length of wire ( )

cm

Time for 20 oscillationsTime

period T = t/20 (s)

T2

t1(S) t2(s)

1

2

3

4

5

6

Mean =

Graph:

If a graph is drawn by taking the length on X axis and T2 on Y axis, it will be a

straight line passing through the origin.

Result:

The rigidity modulus of the given wire =___________dyne/cm2

Viva:

1. Define Rigidity of modulus?

2. What are units of rigidity modulus?

3. Define Moment of Inertia I?

4. What are units of I in CGS and MKS units?

5. What is the meaning in calling this a pendulum?

6. Difference between simple pendulum and torsion pendulum?

7. What is Young’s modulus ?

8. Define Time Period?

9. What is the least count for scrugage?

10. What is the principle for least count?

11. Two wires made up of the same material one is thick the other one is thin.Which wire has

greater rigidity modulus, explain?

MAGNETIC FIELD ALONG THE AXIS OF A CIRCULAR COIL

Aim:

To study the variation of the magnetic field along the axis of a circular current carrying coil

using Stewart Gee’s apparatus.

Apparatus:

Stewart Gee’s apparatus, 2V DC Source, Rheostat, |Commutator and Ammeter.

Description:

Stewart and Gee’s apparatus consists of tangent galvanometer and circular coil wound over

a wooden frame. Usually two or three coils of different number of turns are provided. The wounds

of these coils are connected to terminals fixed to a panel mounted on a horizontal board provided

with leveling screws. A deflection magnetometer mounted on a wooden board can slide through the

coil and is supported on two vertical wooden planks with grooves. A meter scale with O at the

centre and graduated to 50cm either side is fixed on the board, the centre of meter scale coinciding

with the centre of the deflection magnetometer. There are indices fixed on to the vertical wooden

planks with grooves which will unable to note the distance between the centre of the circular coil

and the deflection magnetometer.

Theory & Formula:

Different theories and experiments established that the source of magnetic and electric

fields is the electric charge. A moving charge can create magnetic field and a stationary charge can

create electric field. In the case of current carrying circular coil the magnetic field will be created

and it acts along the axis of the coil. Here we find the field along the axis of the coil by making use

of tangent law, which states that

H = Hotan ………………(1)

Where Ho is the horizontal component of the earth’s magnetic field and is the deflection in

equilibrium position under the action of two forces (fields), one is the horizontal component of

earth’s magnetic field and the other is the field produced due to current carrying coil.

The magnetic field at any point on the axis or circular current carrying coil is given by

……………………………..(2)

Where n - No. of turns of the circular coil

a - radius of the coil

x – the distance of a point on the axis from the centre of the coil

i - strength of current through the coil

If the coil is placed in the magnetic meridian, the direction of magnetic field will be

perpendicular to the magnetic meridian i.e. perpendicular to the direction of horizontal component

of Earth’s magnetic field (Ho). If the direction magnetometer is placed at any point on the axis of

the coil such that the centre of the magnetic needle is acted upon by two fields of H and Ho which

are at right angle to each other. The magnetic needle shows a deflection’ ’ obeying tangent law

(eqn 1). Assuming Ho and knowing the intensity of the field H can be calculated. This can be

verified using the equation (2).

Circuit diagram:

Procedure:

The connections are made as shown in the circuit. The terminals of the circular coil are

connected to the two opposite terminals (1 & 3) of the commutator. The other two terminals of the

commutator are connected to the battery through the ammeter and rheostat. The ammeter and

rheostat are kept at large distance from the magnetometer.

The circular coil is set with its plane in the magnetic meridian. Now the scale lies in a

direction perpendicular to the magnetic meridian. The magnetometer is rotated without disturbing

the coil so that the aluminum pointer reads 0-0 on the circular scale.

The circuit is closed and the rheostat is adjusted so that magnetometer shows a deflection of

75o. Then the deflections are noted as 1 and 2 . The current is reversed using the commutator and

deflections are noted as 3 and 4. The mean deflection is noted for x=0cm.Now the

magnetometer is moved by 3cm (0.03m) away the scale towards east the readings are noted before

and after reversal of the current. The mean value is again found for x=3cm. The experiment is

repeated by moving the magnetometer in steps of 3cm and in each case the average of four

deflections e is found.

The experiment is repeated in a similar way by moving the magnetometer towards west

from the centre of the coil in steps of 3cm.

Precautions: 1) All the magnetic materials and current carrying conductors should be kept away from

the apparatus 2) The plane of the coil should be set parallel to the magnetic meridian.3) Adjust the current in such a way that large deflection of about 75o is produced at the

centre of the coil.4) The error due to parallax in reading the deflection of the needle should be avoided by

looking normally in circular scale.5) At large distances the observations are to be taken in a steps of 3cm distance.

Observations:

Current through the coil i =_______ANumber of turns in the coil n =________

The circumference of the coil 2 a = _______m

Radius of the coil a = _______mThe horizontal component of Earth’s magnetic field, Ho = 30.25 A/m. (0.38Oerstead)

Sl.No.

Distance from centre (x)m

Deflections when magnetometer is moved towards east of the coil

Avg e

He= Hotan

e

Deflections when magnetometer is moved towards west of the coil

Avg w

Hw= Hotan

w

Mean Hp= (He + Hw)/2 A/m

Hth

A/m

1 2 3 4 1 2 3 4

Graph:

A graph is drawn between distance (x) on x-axis and the corresponding values of He and Hw

On y-axis the graph is as fallows.

Result: The variation of the magnetic field along the axis of a circular current carrying coil is

observed

Viva:

1. State Ampere’s law.

2. State Biot Savart’s law.

3. What is TAN A position?

4. What is TAN B position?

5. What is the use of commutator?

6. Explain the use of Rheostat.

7. How field varies with respect to no. of turns?

8. What is the difference between a magnet and magnetic material?

9. Is current carrying conductor electrically neutral?

10. What is tangent law?

11. Define Faraday and Lenz’s law.

LIGHT EMITTING DIODE

Aim:

To study the characteristics of light emitting diode (LED)

Apparatus:

LED, 100Ω resister, Ammeter, Voltmeter and DC regulated power supply.

Theory:

The device is a p-n junction diode made from p-type and n-type semiconductors, usually

GaAs, GaP or SiC. They emit light only when an external applied voltage is used to forward bias

the diode above a minimum threshold value. The gain in electrical potential energy delivered by

this voltage is sufficient to force electrons to flow out of the n-type material, across the junction

barrier, and into the p-type region. This threshold voltage for the onset of current flow across the

junction and the production of light is V0.

The emission of light occurs after electrons enter into the p-region (and holes into the n-

region). These electrons are a small minority surrounded by holes (essentially the anti-particles of

the electrons) and they will quickly find a hole to recombine with. Energetically, the electron

relaxes from the excited state (conduction band) to the ground state (valence band). The diodes are

called lightemitting because the energy given up by the electron as it relaxes is emitted as a photon.

Above the threshold value, the current and light output increases exponentially with the bias

voltage across the diode. The quanta of energy or photon has an energy E = hf. The relation

between the photon energy and the turn-on voltage V0, is

eV0 = Eg = hf =

Where Eg is the size of the energy gap, V

0

is the threshold voltage, f and λ are the frequency

and wavelength of the emitted photons, c is the velocity of light, e is the electronic charge and h is

Planck’s constant.

Circuit diagram:

LED symbol

Procedure:

1. A particular LED circuit can be connected as shown in above Fig. Be sure the power

supply is off and the voltage knob is set to zero before you modify the circuit.

2. Turn on the power supply and very slowly increases the supply voltage until the

LED just starts to glow.

3. Current and voltage across the LED are measured by ammeter and voltmeter. Be

sure the ammeter is in series and voltmeter is in parallel to the LED device as show in above fig.

4. By varying supply voltage, current flow in the LED can be measured as a function

of voltage across the LED. Do not exceed the 20 mA maximum current rating for this LED.

5. A graph cab be plotted current vs voltage across LED, as shown below.

Graph:

Observation:

Result:

1. The voltage vs current characteristics of given LED is plotted.

2. The voltage at which conduction begins is (turn-on voltage V0) __________Volts.

Viva:

1. What is meant by characteristics?

2. In which bias light can be emitted?

3. What is the process across the junction to obtain the light?

4. What is direct band gap semiconductor? Give example.

5. What is indirect band gap semiconductor? Give example.

6. What is cut off voltage?

7. Is their any change in light intensity by varying current strength? Why?

8. Can we use Ge and Si for LED manufacturing, why?

9. Give some names of materials used in LED.

10. What is the main factor to get different colors of LED’s?

ENERGY GAP OF A SEMICONDUCTOR

Aim:

To determine the energy gap of a semi conductor diode

Sl.No. Voltage V (volts) Current I (mA)

Apparatus:

Germanium diode, Thermometer, Regulated DC power supply, Micro ammeter, Heater,

Copper vessel and Bakelite lid.

Theory:

`A p-n junction diode consists of a p- type and n-type semiconductors. The band gap in these extrinsic semiconductors will be the same as that in a pure semiconductor. Holes are majority and electrons are minority carriers in a p-type material. Similarly electrons are majority and holes are minority carriers in n-type material. When these semiconductors form a junction, a space charge region called a depletion layer forms at their junction. The electric field in this space charge region prevents majority carriers from crossing the junction while it favors the moment of the minority carriers across the junction. The majority carriers arise due to the impurity introduced in each region while the minority carriers are generated only due to the temperature effect. In other words, minority carriers are generated through the breaking of the covalent bonds which require supply of energy equal to Eg therefore, by studying the temperature variation of the minority carriers it is possible to evaluate Eg. The variation of minority carriers can be carried out through a study of temperature variation reverse saturation current which is the current in the diode under reverse bias condition. It is given by,

Where k is the Boltzmann constant η =1 for Ge , η =2 for Si

Where D is constant

lnI0 = lnD - Eg/kT

Where, M is the slope i.e.

M =

Eg = 2.303 x k x 103 x M

Formula:

Eg = 2303 slope x Boltzmann’s constant

Boltzmann’s constant=1.38x10-23J/K = 8.62x10-5eV/K

Eg = 2303 x 8.62 x 10-5 x slope

Eg = 0.198 x slope (eV)

Circuit diagram:

Procedure:

Connections are made as per the circuit diagram pour some oil in the copper vessel fix the

diode to the Bakelite lid such that it is reverse biased. Bakelite lid is fixed to the copper vessel, a

hole is provided on the lid through the thermometer is inserted in to the vessel. With the help of

heater, heat the copper vessel till temperature reaches up to 75oC.The temperature on oil bath

stabilizes say at 80oC. Note the current reading at 80oC, apply suitable voltage say 1.5V (which is

kept constant) and note the corresponding current with every 5oC fall of temperature, till the

temperature reaches the room temperature.

A graph is plotted taking 1000/T on x-axis and logI0 on y-axis, a straight line is obtained

the slope of the straight line is determined and using the above equation the band gap is calculated.

Observations:

Table

Sl.No Temperature Current I0(µA) T=(t+273)oK 1000/T (K-1) logI0

t(oC)

Graph:

Result:

The width of the forbidden energy gap in given diode is __________eV.

Viva:

1. Define energy gap.

2. what are the theoretical energy gap values for the Si and Ge?

3. What is conduction band?

4. What is valance band?

5. In which bias diode is connected in this circuit? Why?

6. What is majority carrier? How they are generated?

7. What is minority carrier? How they are generated?

8. What are the majority and minority carriers for the P-type semiconductor?

9. What are the majority and minority carriers for the N-type semiconductor?

10. What is intrinsic semi conductor?

11. What u meant by Fermi energy level?

12. What is Doping and Dopant?

13. What u meant by Extrinsic or impure semi conductor?

14. What is P-type semi conductor?

15. What is N-type semi conductor?

16. Why P-type semi conductor is called Acceptor impurity?

17. Why N-type semi conductor is called Donor impurity?

18. What is P-N junction diode?

19. What you meant by Forward Biasing?

20. What you meant by Reverse Biasing?

MELDE’S EXPERIMENT

Aim:

To determine the frequency of an electrically driven tuning fork-Melde’s apparatus

Apparatus:

An electrically maintained tuning fork, smooth pulley fixed to a stand, a light pan, thread

battery, meter scale, plug key and connecting wires.

Formula:

Longitudinal mode of vibration of the thread:

Hz

Where n = frequency of tuning fork (Hz)

= average length of a loop (cm)

T = tension applied to the thread (dynes)

ρ = mass per unit length of the thread (gm/cm)

Transverse mode vibration of the thread:

Hz

Where n = frequency of tuning fork (Hz)

= average length of a loop (cm)

T = tension applied to the thread (dynes)

ρ = mass per unit length of the thread (gm/cm)

Description:

Melde’s apparatus consists of a tuning fork. It is maintained in a state of continuous

vibration electrically. One terminal of the coil of electromagnet is connected to the make and break

arrangement. The other end is connected to the external electric circuit consisting of a cell, rheostat

and plug key connected in series. One end of the thread of length about 2 meters is joined to a

screw attached to one prong of the fork and the other end is passed over a smooth pulley and light

pan is fixed at the other end of the thread. When the fork is vibrated electrically, stationary waves

of well defined loops are formed. Melde’s apparatus can be arranged in two modes of vibration.

1) Longitudinal mode of vibration 2) Transverse mode of vibration.

Procedure:

1) When the apparatus is arranged in longitudinal mode of vibration :

This mode is arranged in a way such that the direction of motion of the prong is along the

length of the thread.

After arranging in this mode, suitable load is placed in the pan. In the normal position when

the circuit is closed, the electromagnet attracts the prong of the fork towards it. This breaks the

electrical circuit and the prong moves back closing the circuit. The electromagnet again attracts the

prongs towards it. This is repeated again and excited electrically. After adjusting the length of the

thread and weights in the pan, the string starts vibrating and forms many well defined loops. Well

defined loops are formed when the frequency of each segment of the string is exactly half of the

frequency of tuning fork.

The distance between a definite numbers of well defined loops is measured with a meter

scale. From this the average length ’ ’ of each loop is calculated.

The total load attached to the thread including the pan is noted. The tension applied to the

string T = Mg. where g is acceleration due to gravity.

The mass of the thread is determined correct to a milligram. The mass per unit length of the

string (ρ) is determined. Then the frequency of the tuning fork is calculated by the relation.

= Hz

The experiment is repeated for various tensions and readings are tabulated.

Observations:

Mass per unit length (linear density) ρ = x/y = 0.0022 gm/cm

Mass of the card board pan m =_____gm

Acceleration due to gravity g=980cm/s2

Table

Sl

No.

Load applied

into the pan

M gm

μ = M+m

gm

Tension

T = μg

dynes

No of

loops ‘p’

Length of

p loops

=L cm

Length of

each loop

= L/p cm

√T

Avg =

2) When the apparatus is arranged in transverse mode of vibration:

This mode is arranged is in such a way that the direction of motion of the prong is at right

angle to the length of the string

After arranging the fork in this mode the same experimental procedure as in longitudinal

mode of vibration and the average value of √T/ is calculated. The experiment is repeated with

different values of tension and readings are tabulated.

Now the frequency is calculated by using the given formula

= Hz

Table

Sl

No.

Load applied

into the pan

M gm

μ = M+m

gm

Tension

T = μg

dynes

No of

loops ‘p’

Length of

p loops

=L cm

Length of

each loop

= L/p cm

√T

Avg =

Result:

1) The frequency of vibrating tuning fork in longitudinal mode of vibration is ……….Hz

2) The frequency of vibrating tuning fork in transverse mode of vibration is ………. Hz

Viva:

1. What do u mean by Frequency?

2. Define Resonance?

3. What u meant by Progressive wave?

4. How many types of progressive waves are there?

5. Difference between transverse wave and longitudinal wave?

6. What u meant by standing wave?

7. In our experiment which type of wave passing along the thread?

PIN DIODE CHARACTERISTICS

Aim:

To study the characteristics of PIN Diode

Apparatus:

PIN diode board consisting of PIN photo diode optically coupled with matching LED, two

variable power supplies (0-5V), milli ammeter (0-10mA), micro ammeter (0-200µA) and volt

meter (0-5V).

Theory:

P-heavily doped P-region

I-lightly n-doped intrinsic region

N-heavily doped N-region

A PIN diode is a diode with a wide, lightly doped intrinsic region between a p-type

semiconductor and an n-type semiconductor region. The p-type and n-type regions are typically

heavily doped because they are used for ohmic contacts.

In normal operation of a PIN diode, a sufficiently large reverse bias voltage is applied across

the device so that the intrinsic region is fully depleted of charge carriers. That is the intrinsic n and

p carrier’s concentrations are negligibly small in comparison with the impurity concentration in this

region.

When an incident photon has an energy greater than or equal to the band gap energy of the

semiconductor material, the photon can give up it’s energy and excite an electron from valence

band to conduction band. This process generates free electron hole pairs which are known as photo

carriers since they are photon generated charge carriers. Due to the reverse bias of PIN diode the

high electric field present in the depletion region causes the carriers to separate and be collected

across the reverse biased junction this gives rises to a current flow in the external circuit this

current flow is known as the photo current.

The wide intrinsic region also means the diode will have a low capacitance when reverse

biased.

In PIN diode the depletion region exists almost completely with in the intrinsic region. This

depletion region is much larger than in a PN diode and almost constant size, independent of the

reverse bias applied to the diode. This increases the volume where electron hole pairs can be

generated by an incident photon. Some photo detector devices such as PIN photo diodes and photo

transistors, uses a PIN junction in their construction.

The diode design has some design tradeoffs. Increasing the dimensions of the intrinsic

region allows the diode to look like a resister at lower frequencies. It adversely affects the time

needed to turn off the diode and its shunt capacitance.

EXPERIMENTAL PROCEDURE:1) Photo current Vs irradiance characteristics of a PIN photo diode:-

Procedure:

1. Connect the circuit as shown below

2. Set PIN diode Reverse Voltage (VR) constant at 4V using variable power supply VPS1

3. Slowly increase LED current IL to 5mA by using variable power supply VPS2

4. Measure and note down photo current (IR) at increasing values of L1 2.5mA,5mA, 7.5mA,

10mA, 12.5mA, 15mA, 17.5mA, 20mA, 22.5mA, 27.5mA and 30mA.

5. Plot graph of LED Current V/s Photo current.

At VR=4V

2) Photo current V/s Bias Voltage characteristics of a PIN Photodiode:-

Procedure:

It is same as above procedure.

Plot graph of Photo current V/s Bias voltage for varies LED currents

At IL=20mA.

Sl.No. VR(V) IR(µA)

1 0.52 13 1.54 25 2.56 37 3.58 49 4.510 5

S.NO. LED current (IL) mA Photo current(IR) µA

1 2.52 53 7.54 105 12.56 157 17.58 209 22.510 2511 27.512 30

Result: The characteristics of PIN diode are studied.

Viva:

1. In PIN diode I stand for?

2. Define PIN diode.

3. What is meant by characteristics?

4. In which bias photo diode is connected? Why?

5. Is normal PN junction diode act as photo diode by exposing of radiation?

6. What is the difference between PN junction diode and PIN diode?

7. What is the use to add intrinsic layer in-between P-type and n-type layers?

8. If exposed radiation energy is less than the energy gap of the semiconductor, than photo

current will be?

9. If the carriers generated due to exposed radiation in P-type and N-type layers, are they give

the photo current? How?

10. Which source you’re using to expose the radiation on to the photo diode?

NEWTON’S RINGS

Aim:

To determine the radius of curvature of Plano -convex lens by forming Newton's rings

Apparatus:

Sodium vapour lamp, Newton's rings setup (includes -traveling microscope, a thin Plano-

convex lens, a stand, an optical flat and a magnifying glass).

Principle: Circular interference fringes can be observed if a thin film of air or some other

transparent medium of varying thickness is enclosed between a plane glass plate and a Plano-

convex lens of large focal length. Such fringes were first observed by Newton and so are called

Newton's rings

Let us suppose that a monochromatic light is incident normally on air film at ‘x’ at a

distance 'a' from ‘0'. This light is partially reflected at the top surface (y) of the air film and part

from lowest surface of air film (x). The two reflected beams will have certain path difference

depending upon the thickness of the film ‘xy’. Interference of these two reflected beams takes

place, which can be observed through a microscope placed vertically above the lens. A set of

fringes which are alternative bright and dark will be observed with the dark spot at the center of

the rings. If dm and dn are the diameters of the mth and nth dark rings and λ is the wavelength of the

given source of light then the radius of curvature of the lens is given by

cm

Where λ=5893Ao

Newton's rings

Procedure:

1) Light from the sodium vapour lamp is rendered parallel with the help of the condensing

lens Ll and this parallel beam is allowed to fall on the optical flat placed beneath the glass plate

(G). Focusing the microscope on the optical flat, the glass plate G is adjusted so that it makes an

angle of 450 to the incident beam. At this position, one should see uniform illumination in the

field of view while looking through the microscope.

2) An ink-dot is marked on piece of white paper, which is placed on the optical flat lying

on the microscope plate form. The microscope is adjusted so that the ink- dot is sharply focused,

and the paper is removed without disturbing the arrangement.

3) Place the Plano-convex lens L2 carefully on the optical flat such that the curved surface

of the lens in contact with it. When, once this done and viewed through the microscope the ring

system is seen.

4) To increase the contrast of the ring system even after adjusting the microscope for sharp

focus, the angle of the glass plate G or the position of the condensing lens is slightly adjusted or

both. Now the center of the ring system should be dark. If it is bright, the lens L 2 is cleaned with

lens cleaning paper. If necessary, the point of contact between the lens L2 and the optical flat is

varied until a dark central spot is observed.

5) Place the cross wires on the central dark ring and then move microscope to the left

horizontally, by counting the rings, till the 20th dark ring is reached. Note down the reading. The

microscope is now moved to the right side and reading of the microscope screw is recorded for

18th, 16th, 14th, etc., up to 4th dark ring.

6) On reaching the center of the Newton's rings, the microscope is moved further to the

right side and the readings of the screw are recorded till we reach again the 20th dark ring. The

readings are tabulated as shown below.

7) The diameters of the successive rings are evaluated from the above observation and

graph is plotted between d2 and the ring number.

Table

Sl.No. Ring No.Microscope Readings Diameter

d=(y-x)cmd2 (cm2)

Right side (x) cm Left side (y) cm

1 20

2 18

3 16

4 14

5 12

6 10

7 08

8 06

9 04

Graph:

Precautions:

1) The lens surfaces must be well cleaned.

2) The center of the ring system should be dark.

3) Readings for dark rings only should be taken. '

4) The fine screw may suffer from the backlash error. This error may be avoided by moving the

screw only in one direction.

Result:

Radius of curvature of Plano -convex lens is ____________cm.

RC CIRCUIT

Aim:

To determine the capacitance and the time constant of RC- circuit

Apparatus:

Resistor, capacitor, function generator and Cathode Ray Oscilloscope.

Principle:

When the constant potential V is applied to an RC-circuit the voltage across the capacitor

increases exponentially as per the relation

Vc = V(1-e-t/RC) + Vie-t/RC……………(1)

Where Vi is the initial voltage

When t=0, Vc= 0 then Vi = 0

Vc = V(1-e-t/RC)…………….(2)

Where RC is the time constant ( ) of the circuit. If the capacitor is allowed to change to a

known time T seconds the potential difference across the capacitor is given by

Vc = Vf = V (1-e-T/RC) + Vie-T/RC

Vf = V – Ve-T/RC + Vie-T/RC

Vf = V – (V- Vi)e-T/RC

(V – Vi) e-T/RC= V – Vf

(V – Vi)/ (V – Vf) = e-T/RC

T/RC = In[(V – Vi)/ (V – Vf)]

T = 2.303RClog [(V – Vi)/ (V – Vf)]

= RC =

Thus by applying a constant potential V to an RC circuit for a known time T and measuring

the value of one potential difference Vf across the capacitor, the time constant ( ) can be

determined . Knowing the value R of the resistance the value of the capacitor C can be found out.

Circuit Diagram:

Procedure:

1) Connect the circuit as show in circuit diagram.

2) Apply a signal of constant amplitude to the capacitor for a known time, using function

generator.

3) Connect the CRO probe across the capacitor. The shape of the waveform appears as

follows:

The amplitude of the waveform gives the voltage across the capacitor, which can be

calculated by noting down the distance between the minima V i and the maxima Vf on the y-axis of

the CRO screen and multiplying it with the attenuator value of the y amplifier of the CRO.

The applied time T can be calculated by noting down the distance between the starting and

terminating points of the sweep voltage on the x-axis of the CRO screen and multiplying it with the

value of the time base.

The constant applied potential V is noting but the amplitude of the input square wave,

which can be obtained by connecting the CRO directly to the function generator. Using the values

of V,Vi and Vf the time constant can be calculated. Now noting the value of resistance in the

circuit, the capacitance C can be determined.

The experiment is repeated for different values of time period (T), keeping resistance (R)

constant and for different values of resistance (R), keeping time period (T) constant. The observed

values are tabulated.

TABLE-1

To find time constant

R =_______

V = 5v.

Sl.No. Time Period(ms) Initial voltage(vi) Final voltage(vf)Time constant(τ)

ms

1

2

3

4

5

TABLE-2

To find the unknown capacitance

T =_______ms

Sl.No. Resistance Initial voltage(vi) Final voltage(vf) Capacitance(μf)

1

2

3

4

5

V =5v.

Result:

1) Time constant of the RC circuit = _______ ms.

2) Capacitance of the unknown capacitance =_________ μf.

Viva:

1. Define time constant of RC circuit?2. What is tine period?3. What is difference between time period and time constant?4. Can time constant vary with respect to time period?5. What is resistor?6. What happens if we connect the circuit with out resister?7. What is capacitor?8. What is capacitance?9. What are the units for the capacitor?10. Explain initial and final voltages across capacitor?11. Abbreviate CRO12. Explain applications of RC circuit.

LASER

Aim:

To determine the single slit width by forming diffraction pattern.

Apparatus:

He-Ne laser, single slit, scale, screen and traveling microscope.

Formula:

The width of the slit is given by d = /

Where λ is the wave length of light (6328A0) and θ is the diffraction angle

Theory:

The single slit may be treated as large number of equally spaced point sources and each

point on the slit is a source of Huygen’s secondary wavelets which interfere with the wavelets

emanating from other points. The secondary wavelet traveling in the direction parallel to the slit

comes to focus on the screen at a point. Since all the rays are in same phase, diffraction pattern is

point of maximum intensity. The secondary waves traveling in the direction making an angle θ

converges to some point on the screen. The intensity of this point will be maximum or minimum

depending upon the path difference between the secondary waves originating from the

corresponding points on the wave front.

If the path difference d = nλ Where λ is the wave length of light and n =1, 2,3…. , then

the point will be dark. Thus this point represents the minima of the diffraction pattern.

If the path difference is odd multiple of half wave length i.e d = (2n+1) λ/2.Then the

point will be bright. Thus this point represents the maxima of the diffraction pattern. Thus,

approximately, between two minima there will be maxima. Thus the diffraction pattern due to a

single slit consists of central maxima followed by alternate dark and bright bands on either side of

it.

Procedure:

1. The He-Ne laser is mounted on its saddle on the optical bench.

2. A single slit is mounted next to the laser on an upright as shown in fig.

3. The laser is switched on and the position of the slit is adjusted such that the laser beam

passes through the slit and falls on a screen opposite to it. Due to diffraction a bright central

maximum with a large number of maxima of diminishing intensity on its either side are observed

on the screen.

4. The position of the first minima on the either sides of the center maxima are marked on

the screen. The distance ‘2x’ between the marks is measured.

5. The distance ‘ ‘of the screen from the slit is measured.

6. The slit width ‘d’ can be calculated from the formula.

7. The distance between the screen and slit is changed to other value and step 4 is repeated,

the observations are entered in the table.

Observations:

S.NO (cm) x (cm) = x / d (cm)

Precautions:

1. Don’t stare in to the LASER light.

2. Experimental setup should be adjusted so that the correct diffraction pattern is obtained

on the screen.

3. The distance between the slit and the screen should be large.

4. The background should be dark.

5. Switch of the laser after completion of the experiment.

6. Handle the laser carefully as it is very sensitive and precious.

Result:

The width of the slit =

Viva:

1. LASER stands for?

2.

DIFFRACTION GRATING -NORMAL INCIDENCE METHOD

Aim:

To determine the wavelength of light by normal incidence method.

Apparatus:

Spectrometers, Diffraction grating, Mercury vapour lamp, spirit level and magnifying lens.

Description:

Diffraction grating consists of a large number of parallel slits of equal width and separated from

one another by equal opaque spaces.

A plane transmission grating consists of a glass plate over which fine equidistant parallel lines

are drawn very closely by means of a diamond point. Gratings usually have about 15000 lines per

inch. The ruled portions of the plate behave as opaque and the un-ruled portions as slits, which

transmit light. For laboratory work replicas or copies of the real gratings cast on celluloid d film

fixed to a glass plate are supplied.

Principle:

Diffraction is the phenomenon of the bending of the light rays which occurs when light is

passed close to sharp edges or through narrow apertures or openings.

Consider a plane transmission grating with alternative opaque and transparent portions. Let a plane

wave front reach the grating surface. Thus a parallel beam of light rays is incident normally on the

grating. Most of these rays are transmitted in the direction of the incident light through the

transparent portions BC, DE etc., of the grating and if a converging lens is placed in their path, they

are brought to focus at '0' this will be very bright image. Some of the incident light is diffracted at

the edges such as B,D and F etc. at different angles. If we consider those rays bent at B and D at an

angle ө from the direction of the incident light, all such rays form a parallel beam and after passing

through the lens, they are brought to focus at’ I’. The intensity at I will be maximum or minimum

depending upon the path difference between the diffracted rays from B and D. If 'd' is the grating

element (distance between two consecutive lines on the grating) this path difference is equal to d

sin i.e. DK as shown in figure.

Thus if d sin = nλ (an integral number of wavelength) the images are formed in the focal

plane of the lens. These are called first order, second order etc. images. Thus one set of images will

be formed one side of the central bright image O. Also the diffraction or bending of light rays takes

place to the other side of the incident direction and corresponding images of different orders are

formed on the other side of the central image O. Thus in the field of view of a telescope of which

the lens L forms images of different orders (n=I,2,3, etc.) are observed. If the incident light if

monochromatic, each order of diffracted image will be of the same color, but if white light is

incident on the grating each diffracted image consists of a whole spectrum. Thus spectra of

different orders are formed on either side of the central white image.

Formula:

The wavelength of any spectral line λ is given by

λ = sin /n Ao

where d = grating element (distance between two consecutive lines on the grating) = angle of diffraction

n = order of the spectrumProcedure:

I. All the preliminary adjustments of the of the spectrometer are made

2. The least count of the Vernier is determined.

3. The number of lines per inch as marked on the grating is noted and then N, the number of

lines per centimeter is calculated.

4. The grating is set with tits plane vertical and parallel to the axis of the spectrometer. The

grating is fixed on the prism table with its plane perpendicular to the line joining two of the leveling

screws X and Y as shown in the figure, so that the grating side faces the collimator. Then the

Telescope and the prism table are turned so that the reflected image is seen through the telescope.

Either of the screw X and Y is adjusted until the image is symmetrical w.r.t the horizontal cross

wires now the plane of the grating is vertical and parallel to the axis of the spectrometer

5. The grating is set so that the lines on it are parallel to the slits. For this the prism table is

rotated until the light from the collimator falls approximately normally on the grating. The

telescope is turned to one side to catch the diffracted image of the first order. The screw Z is

adjusted until the image is symmetrical with respect to the horizontal cross wires. With this

adjustment other images also will be symmetrical w.r.t the cross wires and the lines will be parallel

to the slit.

6. Now the telescope is brought into the line with the collimator and the vertical cross wire

is made to coincide with the image. The position of the Telescope is noted on the vernier. The

telescope is rotated through 90o and clamped. Now the telescope is perpendicular to the collimator,

the prism table is then rotated until the image formed by reflection at the ruled side of the grating

coincides with the cross wire. The plane of the grating in this position is inclined 45 o to the

incident light. The reading corresponding to this position of the prism table is rotated back through

45o exactly by working on the tangent screw. To this position the grating is normal to the axis of

the collimator with its ruled side facing the collimator. This light is made to be incident normal on

the grating.

7. The telescope is brought into line with the collimator and its position is adjusted so that

the white image of the slit coincides with the vertical cross wires. The position of the telescope is

read on its scale. It is now rotated to one side so as to catch the first order image and the cross wire

is set on the image and the position is noted. The difference between this reading and the direct

image gives the diffraction angle ( ) of the first order image. All the observations are noted in the

tabular form given below.

Least count of the spectrometer = M.S.D /NO.OF Divisions on vernier scale

= = (1/60)o

Grating element d = 2.54/15000 = ----------cm/line

Diffraction order(n)

Line (color)

Direct reading

Diffracted ray reading

Diffraction angle Mean =( 1 + 2)/2

λ (Ao)R1 R2 R3 R4 1 = R1-R3 2= R2- R4

Precautions:

1) Grating should be set normal to the incident light.

2) Grating should not be touched by fingers.

3) The reading of both vernier should be taken.

4) For reading magnifier should be used.

Result: The wavelength of the given mercury spectral lines are

DISPERSIVE POWER OF A

PRISM

Aim:

To determine the dispersive power of the material of a prism.

Apparatus:

Spectrometer, Prism, Mercury vapour lamp, Spirit level, Magnifier and reading lamp.

Principle:

When a beam of white light is passed through a prism, it disperses in to a spectrum. The

violet rays being deviated most and the red rays least, this is because the refractive index decreases

with the increase of wavelength. The angular separation of any two different wavelengths depends

on the characteristic of the material, known as dispersive power.

For prism

Sl.No Color Wave length(Ao)

1

2

D = (μ-1) A

For two rays D1 = (μ1-1) A

D2 = (μ2-1) A

w =

This quantity is called the dispersive power of the material of the prism, where μ=(μ1 + μ2)/2

so for determining the dispersive power of the material of the prism for the two colors, the

refractive indices for those colors are to be determined. The refractive index is given by

Where A is the angle of the prism, Dm is the angle of minimum deviation.

Procedure:

Before doing the experiment with the spectrometer the fallowing adjustments are to be

made.

Setting of the telescope

a) The telescope is first turned towards some white wall, the eye piece is shifted with

respect to the cross wires till a sharp image of the cross wires is obtained. The eye piece

is now fixed with respect to the cross wires.

b) The telescope is focused on a distant object and the parallax between the image and

cross wires is removed. Thus, the telescope is set for parallel rays.

Setting of the collimator:

The telescope is turned so that it is in line with the collimator. The distance between the

collimating lens and slit is adjusted such that a sharp image is seen. That means the collimator is

adjusted to give a parallel beam of light. The width of the slit is made as narrow as possible.

Setting of the prism table:

The prism table is first made perfectly horizontal with the help of spirit level and the

leveling space. The height of the prism table must be on the axis of collimator and telescope. The

least count of spectrometer is determined.

Least count of the spectrometer = M.S.D /NO.OF Divisions on vernier scale

= = (1/60)o

Determination of the angle of prism (A):

1. The prism is mounted on the prism table with edge A is faced towards the collimator

and the base of the prism is perpendicular to the axis of the collimator.

2. The rays from the collimator fall on the faces AB and AC of the prism from which these

rays get reflected in the direction R1 and R2.

3. The telescope is turned to receive the reflected rays R1. The image of the slit is made to

coincide exactly with the vertical cross wire.

4. The main scale and vernier scale readings are taken.

5. The total reading R1=MSR + (VSR*LC).

6. Now the telescope is turned towards the right to receive the ray R2 and again image of

the slit is made to coincide exactly with the vertical cross wire.

7. The main scale and vernier scale readings are again noted and R2 is found.

8. From these readings we get 2A, half of the 2A is gives the angle of the prism.

Table:

Sl.No.

Telescope position2A Mean

2AALeft Right

R1 R11 R2 R2

1 R1- R2 R11- R2

1

Determination of the angle of minimum deviation (Dm):

1. Telescope is placed in front of the collimator and obtains the direct image of the slit in

the telescope without placing the prism.

2. Coincide the image of the slit with the vertical cross wire making use of the clamping

screw and tangent screw.

3. Note the readings R1 and R2.

4. Now place the prism centrally on the prism table so that light incident from the

collimator falls on the face AB.

5. Turn the telescope to receive the emergent rays, which get dispersed from the face AC

of the prism.

6. Bring the ray of that particular color in the field of view for which μ has to be found

and coincide it with the vertical cross wire.

7. Now gradually rotate the prism table in the clockwise direction, the ray of particular

color will appear to turn in the anticlockwise direction. A stage will come when it will

again start moving in the clockwise direction.

8. Coincide that particular position for which the just returns back with the cross wire. This

is the position of minimum deviation.

9. Note the readings R3 and R4. Find the minimum deviation from these readings

Table:

Sl.

No.Color

Direct reading

Position of

minimum

deviation

Angle of minimum deviation Refractive

index

R1 R2 R3 R4 D1 = R1-R3 D2 =R2-R4 Dm = (D1 + D2)/2

Precautions:

1. The spectrometer must be set for parallel rays before starting the experiment.

2. The reading of both the vernier should be taken.

3. The image of the slit must be made to coincide with the point of intersection of cross

wires.

4. The collimator should be aligned with the source.

5. The slit must be as narrow as possible so that a sharp image is seen.

6. The prism must be placed in the correct position.

Result:

The dispersive power of the given prism is __________________.