draft rationale for higher biology...

Physics Higher Unit 2

4163

Note:

The Radiation and Matter component of Higher Physics will appear

on the following Science CD-ROM.

Spring 1999

Physics Higher

Support Materials

HIGHER STILL

This publication may be reproduced in whole or in part for educational purposes provided that no profit is

derived from the reproduction and that, if reproduced in part, the source is acknowledged.

First published 1999

Higher Still Development Unit

PO Box 12754

Ladywell House

Ladywell Road

Edinburgh

EH12 7YH

Physics: Mechanics and Properties of Matter (H) 1

HIGHER PHYSICS - STAFF NOTES

Higher Physics course and units

The Higher Physics course is divided into the following three units.

• Mechanics and Properties of Matter (40 hours)

• Electricity and Electronics (40 hours)

• Radiation and Matter (40 hours)

The support materials

For each of the three units the student material contains the following sections.

• Checklist

• Summary Notes

• Activities

• Problems (with numerical answers)

In addition there is a separate section dealing with uncertainties, units and prefixes.

It should be noted that the Content Statements associated with uncertainties are part of each

of the three units, see the Arrangements for Physics. Although the Higher Physics units could

be taught in any order, current practice indicates that the Mechanics and Properties of Matter

is usually taught first. Hence the section dealing with uncertainties is placed at the start of this

unit. The examples in the section on uncertainties are taken from topics in this unit. The

problem sections of the other two units contain a few additional questions on uncertainties.

The student materials are to provide assistance to the teacher or lecturer delivering a unit or

the course. They are not a self standing open learning package. They require to be

supplemented by learning and teaching strategies. This is to ensure that all the unit or course

content is covered and that the students are given the support they need to acquire the

necessary knowledge, understanding and skills demanded by the unit or the course.

Checklists

These are lists of the content statements taken directly from the Arrangements for Physics

documentation.

Summary Notes

These notes are a brief summary of all the essential content and include a few basic worked

examples. They are intended to aid students in their revision for unit and course assessment.

Explanation of the concepts and discussion of applications are for the teacher or lecturer to

include as appropriate.


Activities

The activity pages provide suggestions for experimental work. A variety of practical

activities have been included for each unit. The instruction sheet can be adapted to suit the

equipment available in the centre. Some activities are more suitable for teacher demonstration

and these have been included for use where appropriate.

For each unit there is a range of activities. Although it is desirable that students are able to

undertake practical investigations, it must be mentioned that this does not imply that all

activities must be undertaken. The teacher or lecturer should decide what to select depending

on the needs of their students and the learning and teaching approaches adopted.

For Outcome 3 of each unit one report of a practical activity is required. Some activities

suitable for the achievement of Outcome 3 have been highlighted and should be seen as an

opportunity to develop good practice.

Problems

A variety of problems have been collated to give the student opportunity for practice and to

aid the understanding of the unit or course content.

Use of the materials

The checklists may be issued at the end or at the beginning of a unit depending on the

teacher’s discretion. Hence for each unit the checklists are given with separate page numbers.

The rest of the material for each unit is numbered consecutively through the summary notes,

activities and problems.

The uncertainties section is numbered separately. Some staff may wish to cover this material

at the start of the course, others may prefer to introduce the concepts more gradually during

early experimental work. (For unit assessment, uncertainties are covered in Outcome 3. The

course assessment will contain questions which will sample uncertainties within the context

of any of the units.)

When photocopying a colour code for each section could be an advantage.

For some units it could be preferable to split the unit into subsections. For example, the

Mechanics and Properties of Matter unit might have a first subsection booklet for kinematics

which would entail selecting appropriate summary notes, activities, problems and numerical

answers.

Learning and Teaching

A variety of teaching methods can be used. Direct teaching whether it be to a whole class or

small groups is an essential part of the learning process. A good introduction to a topic; for

example, a demonstration, activity or video, is always of benefit to capture the minds of the

students and generate interest in the topic.

Applications should be mentioned and included wherever possible.


Further materials

A course booklet will be issued which will contain additional problems including:

examination type questions of a standard suitable for estimates of course performance and

evidence for appeals

revision home exercises for ongoing monitoring of progress.

Outcome 3

The Handbook: Assessing Outcome 3 – Higher Physics contains specific advice for this

outcome together with exemplar instruction sheets and sample student reports.

Specimen Course Assessment

A specimen course question paper together with marking scheme has been issued by SQA.

This pack also contains the updated ‘Details of the instrument for external assessment’ from

the Arrangements for Physics.

Checklist

Physics: Electricity and Electronics (H) 4

ELECTRICITY AND ELECTRONICS

The knowledge and understanding for this unit is given below.

Electric fields and resistors in circuits

1. State that, in an electric field, an electric charge experiences a force.

2. State that an electric field applied to a conductor causes the free electric charges in it

to move.

3. State that work W is done when a charge Q is moved in an electric field.

4. State that the potential difference (V) between two points is a measure of the work

done in moving one coulomb of charge between the two points.

5. State that if one joule of work is done moving one coulomb of charge between two

points, the potential difference between the points is one volt.

6. State the relationship V = W/Q.

7. Carry out calculations involving the above relationship.

8. State that the e.m.f. of a source is the electrical potential energy supplied to each

coulomb of charge which passes through the source.

9. State that an electrical source is equivalent to a source of e.m.f. with a resistor in

series, the internal resistance.

10. Describe the principles of a method for measuring the e.m.f. and internal resistance of

a source

11. Explain why the e.m.f. of a source is equal to the open circuit p.d. across the terminals

of a source

12. Explain how the conservation of energy leads to the sum of the e.m.f.’s round a closed

circuit being equal to the sum of the p.d.’s round the circuit.

13. Derive the expression for the total resistance of any number of resistors in series, by

consideration of the conservation of energy.

14. Derive the expression for the total resistance of any number of resistors in parallel, by

consideration of the conservation of charge.

15. State the relationship among the resistors in a balanced Wheatstone bridge.

16. Carry out calculations involving the resistance in a balanced Wheatstone bridge.

17. State that for an initially balanced Wheatstone bridge, as the value of one resistor is

changed by a small amount, the out of balance p.d. is proportional to the change in

resistance.

18. Use the following terms correctly in context: terminal p.d., load resistor, bridge

circuit, lost volts, short circuit current.

Alternating Current and Voltage

1. Describe how to measure frequency using an oscilloscope.

2. State the relationship between peak and r.m.s. values for a sinusoidally varying

voltage and current.

3. Carry out calculations involving peak and r.m.s. values of voltage and current.

4. State the relationship between current and frequency in a resistive circuit.

Checklist


Capacitance

1. State that the charge Q on two parallel conducting plates is directly proportional to the

p.d. V between the plates.

2. Describe the principles of a method to show that the p.d. across a capacitor is directly

proportional to the charge on the plates.

3. State that capacitance is the ratio of charge to p.d.

4. State that the unit of capacitance is the farad and that one farad is one coulomb per

volt.

5. Carry out calculations using C = Q/V

6. Explain why work must be done to charge a capacitor.

7. State that the work done to charge a capacitor is given by the area under the graph of

charge against p.d.

8. State that the energy stored in a capacitor is given by (charge × p.d.) and equivalent

expressions.

9. Carry out calculations using QV or equivalent expressions.

10. Draw qualitative graphs of current against time and of voltage against time for the

charge and discharge of a capacitor in a d.c. circuit containing a resistor and capacitor

in series.

11. Carry out calculations involving voltage and current in CR circuits (calculus methods

are not required).

12. State the relationship between current and frequency in a capacitive circuit.

13. Describe the principles of a method to show how the current varies with frequency in

a capacitive circuit.

14. Describe and explain the possible functions of a capacitor: storing energy, blocking

d.c. while passing a.c.

Analogue Electronics

1. State that an op-amp can be used to increase the voltage of a signal.

2. State that for the ideal op-amp:

a) input current is zero; i.e. it has infinite input resistance

b) here is no potential difference between the inverting and non-inverting inputs;

i.e. both input pins are at the same potential.

3. Identify circuits where the op-amp is being used in the inverting mode.

4. State that an op-amp connected in the inverting mode will invert the input signal.

5. State the inverting mode gain expression: V0 / V1 = -Rf / Ri.

6. Carry out calculations using the above gain expression.

7. State that an op-amp cannot produce an output voltage greater that the positive supply

voltage or less that the negative supply voltage.

8. Identify circuits where the op-amp is being used in the differential mode.

9. State that a differential amplifier amplifies the potential difference between its two

inputs.

10. State the differential mode gain expression - Vo = (V2 - V1) Rf / Ri.

11. Carry out calculations using the above gain expression.

12. Describe how to use the differential amplifier with resistive sensors connected in a

Wheatstone bridge arrangement.

13. Describe how an op-amp can be used to control external devices via a transistor.

1

2

1

2

Checklist


Uncertainties

1. State that measurement of any physical quantity is liable to uncertainty.

2. Distinguish between random uncertainties and recognised systematic effects.

3. State that the scale-reading uncertainty is a measure of how well an instrument scale

can be read.

4. Explain why repeated measurements of a physical quantity are desirable.

5. Calculate the mean value of a number of measurements of the same physical quantity.

6. State that this mean is the best estimate of a ‘true’ value of the quantity being

measured.

7. State that where a systematic effect is present the mean value of the measurements

will be ‘offset’ from a ‘true’ value of the physical quantity being measured.

8. Calculate the approximate random uncertainty in the mean value of a set of

measurements using the relationship:

approximate uncertainty in the mean = maximum value - minimum value

number of measurements taken

9. Estimate the scale reading incurred when using an analogue display and a digital

display.

10. Express uncertainties in absolute or percentage form.

11. Identify, in an experiment where more than one physical quantity has been measured,

the quantity with the largest percentage uncertainty.

12. State that this percentage uncertainty is often a good estimate of the percentage in the

final numerical result of the experiment.

13. Express the numerical result of an experiment in the form:

final value uncertainty

Units, prefixes and scientific notation

1. Use SI units of all physical quantities in the above checklist.

2. Give answers to calculations to an appropriate number of significant figures.

3. Check answers to calculations.

4. Use prefixes (p, n, µ, m, k, M, G)

5. Use scientific notation.

Summary Notes

Physics: Electricity and Electronics (H) – Student Material 1

ELECTRIC FIELDS AND RESISTORS IN CIRCUITS

Force Fields

In Physics, a field means a region where an object experiences a force without being touched.

For example, there is a gravitational field around the Earth. This attracts masses towards the

earth’s centre. Magnets cause magnetic fields and electric charges have electric fields around

them.

Electric Fields

In an electric field, a charged particle will experience a force. We use lines of force to show

the strength and direction of the force. The closer the field lines the stronger the force. Field

lines are continuous - they start on positive and finish on negative charge. The direction is

taken as the same as the force on a positive “test” charge placed in the field.

Electric Field Patterns

Positive point charge

Negative point charge

These are called radial fields. The lines are like the radii of a circle. The strength of the field

decreases as we move away from the charge.

Electric Field Patterns

Positive and negative point charges

Parallel charged plates

The field lines are equally spaced between the parallel plates. This means the field strength is

constant. This is called a uniform field.

Electric fields have certain similarities with gravitational fields.

+ test charge

has a force

‘outwards’

+ test charge

has a force

‘inwards’

Summary Notes


Gravitational Fields

If a mass is lifted or dropped through a height then work is done i.e. energy is changed.

If the mass is dropped then the energy will change to kinetic energy.

If the mass is lifted then the energy will change to gravitational potential energy.

Change in gravitational potential energy = work done.

Electric Fields

Consider a negative charge moved through a distance in an electric field. If the charge moves

in the direction of the electric force, the energy will appear as kinetic energy. If a positive

charge is moved against the direction of the force as shown in the diagram, the energy will be

stored as electric potential energy.

If the charge moved is one coulomb, then the work done is the potential difference or voltage.

If one joule of work is done in moving one coulomb of charge between two points in an

electric field, the potential difference, (p.d.) between the two points is one volt.

1 volt = 1 joule per coulomb

In this section W will be used for the work done i.e. energy transferred.

Example:

A positive charge of 3 µC is moved, from A to B, between a potential difference of 10 V.

(a) Calculate the electric potential energy gained.

(b) If the charge is now released, state the energy change.

(c) How much kinetic energy will be gained on reaching

the negative plate?

(a) W = QV= 3 × 10-6

× 10

= 3 × 10-5

J

(b) Electric potential energy to kinetic energy

(c) By conservation of energy the energy will be the same, i.e. 3 × 10-5

J.

h

++++

----

+ Q

AB

Change in electric potential energy = work done

W = QV

Summary Notes


Moving Charges in Electric Fields

From the previous example, when the positive charge is released at plate B then the electical

potential energy is converted to kinetic energy.

QV = 1

2mv

2

Example

An electron is accelerated (from rest) through a potential difference of 200 V.

Calculate (a) the kinetic energy, Ek gained.

(b) the final speed of the electron.

(Mass of an electron = 9.1 × 10-31

kg, charge on an electron = -1.6x10-19

C)

(a) Ek = 1

2mv

2 = QV = 1.6x10

-19 × 200

= 3.2 × 10-17

J

(b) 1

2mv

2 = 3.2 × 10

-17

v2

3.2 10 2

m

3.2 10 2

9.1 10

17 17

31

v = 8.4 × 106 m s

-1

Applications of electric fields (for background interest)

A television involves the use of electron guns. The electrons gain kinetic energy by

accelerating through an electric field. Deflection of the electrons is usually done by

electromagnetic coils, although flat screen tubes are now dependent on electrostatic

deflection.

An oscilloscope also depends on electric fields acting on electrons.

Electrostatic Spraying makes use of electric fields. Paint or powder particles are blown from

a nozzle, where they acquire a charge. The object to be coated is earthed. The charged paint

or powder particles follow the field lines and so reach the object, some reaching the back of

the object as well as the front.

Other applications include photocopiers, ink jet and laser printers.

Summary Notes


Electric Current

When S is closed, the free electrons in the conductor experience an electric field which cause

them to move in one direction.

Note: The electron current will flow from the negative terminal to the positive terminal of the

battery. The energy required to drive the electron current around the circuit is provided by a

chemical reaction in the battery or by the mains power supply. The electrical energy which is

supplied by the source is converted to other forms of energy in the components which make

up the circuit.

The lamp has resistance R. In any circuit providing the resistance of a component remains

constant, if the potential difference V across the component increases the current I through

the component will increase in direct proportion. This is Ohm’s Law which is summarised

by the equation below.

A component which has a constant resistance when the current through it is increased is said

to be ohmic. Some components do not have a constant resistance, their resistance changes as

the p.d. across the component is altered, for example the transistor.

Electric Power

For a given component the power P = I V where I is the current through that component and

V is the potential difference across the component.

Resistive Heating

The expression I2 R gives the energy transferred in one second due to resistive heating.

Apart from obvious uses in electric fires, cookers, toasters, etc. consideration has to given to

heating effects in resistors, transistors and integrated circuits and care taken not to exceed the

maximum ratings for such components.

Electromotive Force (e.m.f)

The energy given to a coulomb of charge by a source of electrical energy is called the e.m.f.

of the source. This is measured in J C-1

or volts.

Note: the potential difference between two points in the external circuit is also measured in

volts, but this is concerned with electrical energy being transformed outside the source.

V = IR

P = I R = V

R

2

2

Summary Notes


Sources of e.m.f.

E.M.F’s can be generated in a great variety of ways e.g:

chemical cells, thermocouple, piezo - electric generator,

solar cell, electromagnetic generator.

Resistors in Series - Conservation of Energy

Applying the conservation of energy to resistors in series for one coulomb of charge.

Energy supplied by source = energy converted by circuit components

e.m.f. = IR1 + IR2 + IR3

IRS = IR1 + IR2 + IR3

RS = R1 + R2 + R3

Resistors in Parallel - Conservation of Charge

The total charge per second (current) passing through R1, R2 and R3 must equal the charge

per second (current) supplied from the cell i.e. passing through RP.

Conservation of charge gives:

I = I1 + I2 + I3 (Since I = Q

t for each resistor)

E

R =

E

R +

E

R +

E

R

1 2 3 4

Rs = equivalent

series resistance

Rp = equivalent

parallel resistance

Summary Notes


Internal Resistance

In choosing a suitable power supply for a circuit, you would have to ensure that it :

gives the correct e.m.f

is able to supply the required maximum current

When a power supply is part of a closed circuit, it must itself be a conductor. All conductors

have some resistance. A power supply has internal resistance, r.

Energy will be wasted in getting the charges through the supply (the heat from the supply will

be noticeable) and so the energy available at the output (the terminal potential difference)

will fall. There will be “lost volts”. The lost volts = I r

The greater the current, the more energy will be dissipated in the power supply until

eventually all the available energy (the e.m.f.) is wasted and none is available outside the

power supply. This maximum current is the short circuit current. This is the current which

will flow when the terminals of the supply are joined with a short piece of thick wire.

Open Circuit

When no current is taken from the power supply, no energy is wasted. The terminal

potential difference is therefore the maximum available and equals the e.m.f.

General Circuit

With S closed and using the conservation of energy

e.m.f. = lost volts + t.p.d.

e.m.f. = lost volts + output voltage

E = Ir + V

which is: E = Ir + IR

Notice that the total resistance of the circuit is R + r, giving the equation:

E = I ( R + r)

The short circuit current is the maximum which can be supplied by a source. This occurs

when there is no external component and R = 0.

Any power supply can be thought of as a source of constant

e.m.f. E, in series with a small resistance, the internal

resistance.

With S open, the voltmeter reading gives the e.m.f. (an open

circuit).

With S closed, the voltmeter reading will fall (lost volts). The

voltmeter now gives the output voltage, the terminal potential

difference, t.p.d.

VR

r

SE

Summary Notes


Example

A cell of e.m.f. 1.5 V is connected in series with a 28resistor.

A voltmeter measures the voltage across the cell as 1.4 V.

Calculate:

(a) the internal resistance of the cell

(b) the current if the cell terminals are short circuited

(c) the lost volts if the external resistance R is increased to 58 Ω.

(a) E = Ir + IR = Ir + V

Lost volts = Ir = E - V = 1.5 - 1.4 = 0.1 V

r = lost volts

I =

0.1

1

I = V

R =

1.4

28 = 0.05 A

r = 0.1

0.05 = 2

(b)

A short circuit occurs when R = 0 (no external resistance)

I

R + r =

E

r =

1.5

2 = 0.75 A

(c) Lost volts = Ir

I

R + r =

E

28 + 2 = 1.5

= 0.05 A

Lost volts = 0.05 × 2

= 0.1 V

E r

V

R = 28

Summary Notes


Wheatstone Bridge Circuit

Any method of measuring resistance using an ammeter or voltmeter necessarily involves

some error unless the resistances of the meters themselves are taken into account. The use of

digital voltmeters largely overcomes this as they tend to have very high resistances.

Further error may be introduced if the meter is not correctly calibrated. The only situation

where neither of these errors matter is if the meter reading is zero. The Wheatstone bridge

circuit is one such example of using a meter as a null deflection indicator.

Bridge Circuit

If VOA = VOB there is no p.d. between A and B hence no

current flows. The potentials at A and at B depend on the ratio

of the resistors that make up each of the two voltage dividers.

The voltmeter forms a ‘bridge’ between the two voltage

dividers to make up a bridge circuit.

Balanced Bridge

No potential difference will exist across AB when

R

R

R

R

1

2

3

4

The bridge is balanced when the voltmeter or galvanometer

(milliammeter) reads zero.

Unbalanced Bridge

If the bridge is initially balanced, and the resistor × is altered by a small amount × then the

out of balance p.d. (reading on G) is directly proportional to the change in resistance,

provided the change is small.

Hence for small ×,

reading on G ×

R4

A B

R1 R3

R2

5 V

0 V

V

O

Alternative ‘diamond’

Representation with

galvanometer

+1.5 V

G

R1 R2

R4X+X

X/

Reading on G

Summary Notes


ALTERNATING CURRENT AND VOLTAGE

Peak and r.m.s. values

The graph of a typical alternating voltage is shown below.

The maximum voltage is called the peak value.

From the graph it is obvious that the peak value would not be a very accurate measure of the

voltage available from an alternating supply.

In practice the value quoted is the root mean square (r.m.s.) voltage.

The r.m.s. value of an alternating voltage or current is defined as being equal to the value of

the direct voltage or current which gives rise to the same heating effect (same power output).

Consider the following two circuits which contain identical lamps.

The variable resistors are altered until the lamps are of equal brightness. As a result the direct

current has the same value as the effective alternating current (i.e. the lamps have the same

power output). Both voltages are measured using an oscilloscope giving the voltage equation

below. Also, since V=IR applies to the r.m.s. valves and to the peak values a similar equation

for currents can be deduced.

Note: a moving coil a.c. meter is calibrated to give r.m.s. values.

IpeakI = 1

2

VpeakV = 1

2andr.m.s. r.m.s.

Summary Notes


Graphical method to derive relationship between peak and r.m.s. values of alternating

current

The power produced by a current I in a resistor R is given by I2 R. A graph of I

2 against t for

an alternating current is shown below. A similar method can be used for voltage.

The average value of I2 is

An identical heating effect (power output) for a d.c. supply = I2

r.m.s R

[since I (d.c.) = Ir.m.s.]

Average power output for a.c. =

I2 r.m.s R = hence I

2r.m.s. = giving Ir.m.s. = I Peak

Frequency of a.c.

To describe the domestic supply voltage fully, we would have to include the frequency i.e.

230 V 50 Hz.

An oscilloscope can be used to find the frequency of an a.c. supply as shown below.

I2 Peak

2

I2

Peak

2 R

I2 Peak

2

I2 Peak

2

Time base = 0.005 s cm-1

Wavelength = 4 cm

Time to produce one wave = 4 × 0.005

= 0.02 s

Frequency = 1

time to produce one wave

= 1

0 02. = 50 Hz

R

2

Summary Notes


Mains supply

The mains supply is usually quoted as 230 V a.c. This is of course 230 V r.m.s. The peak

voltage rises to approximately 325 V. Insulation must be provided to withstand this peak

voltage.

Example

A transformer is labelled with a primary of 230 Vr.m.s. and secondary of 12 Vr.m.s. What is the

peak voltage which would occur in the secondary?

V peak = 2 × V r.m.s.

V peak = 1.41 × 12

V peak = 17.0 V

Summary Notes


CAPACITANCE

The ability of a component to store charge is known as capacitance.

A device designed to store charge is called a capacitor.

A typical capacitor consists of two conducting layers separated by an insulator.

Circuit symbol

Relationship between charge and p.d.

Charge is directly proportional to voltage.

Q

V = constant

For any capacitor the ratio Q/V is a constant and is called the capacitance.

farad (F) capacitance = charge

voltage

The farad is too large a unit for practical purposes.

In practice the micro farad (µF) = 1 × 10-6

F and the nano farad (nF) = 1 × 10-9

F are used.

Example

A capacitor stores 4 × 10-4

C of charge when the potential difference across it is 100 V.

What is the capacitance ?

C = Q

V

4 10

100

-6

= 4 µF

The capacitor is charged to a chosen voltage by

setting the switch to A. The charge stored can be

measured directly by discharging through the

coulomb meter with the switch set to B. In this

way pairs of readings of voltage and charge are

obtained.

Q

V0

coulombs (C)

volts (V)

Summary Notes


Energy Stored in a Capacitor

A charged capacitor can be used to light a bulb for a short time, therefore the capacitor must

contain a store of energy. The charging of a parallel plate capacitor is considered below.

For a given capacitor the p.d. across the plates is directly proportional to the charge stored

Consider a capacitor being charged to a p.d. of V and holding a charge Q.

Q = C × V and substituting for Q and V in our equation for energy gives:

Energy stored in a capacitor = 1

2QV =

1

2CV =

1

2 Q

C

2

2

Example

A 40F capacitor is fully charged using a 50 V supply. How much energy is stored?

Energy = 1

2CV =

1

2 40 10 25002 6

= 5 × 10-2

J

There is an initial surge ofelectrons from the negativeterminal of the cell onto oneof the plates (and electronsout of the other plate towardsthe +ve terminal of the cell).

Once some charge is on theplate it will repel more chargeand so the current decreases.In order to further charge thecapacitor the electrons mustbe supplied with enoughenergy to overcome thepotential difference across theplates i.e. work is done incharging the capacitor.

Eventually the current ceasesto flow. This is when thep.d. across the plates of thecapacitor is equal to thesupply voltage.

The energy stored in the capacitor is given by the area underthegraph

Area under graph= 1 Q x V2

Energy stored = 1 Q x V 2

Q

Charge

p.d.V

If the voltage across thecapacitor was constant workdone = Q x V, but since V isvarying, the work done =area under graph.

Summary Notes


Capacitance in a d.c. Circuit

Charging

Consider the following circuit:-

When the switch is closed the current flowing in the circuit and the voltage across the

capacitor behave as shown in the graphs below.

Consider the circuit at three different times.

time

current

0

Supply voltage

p.d. acrosscapacitor

0time

As soon as the switch isclosed there is no charge onthe capacitor the current islimited only by theresistance in the circuit andcan be found using Ohm’slaw.

As the capacitor charges ap.d. develops across theplates which opposes thep.d. of the cell as a resultthe supply currentdecreases.

The capacitor becomesfully charged and the p.d.across the plates is equaland opposite to that acrossthe cell and the chargingcurrent becomes zero.

0 0

- -- - - -

+ ++ ++ +

0

A A A

Summary Notes


Discharging

While the capacitor is discharging the current flowing in the circuit and the voltage across

the capacitor behaves as shown in the graphs below.

Although the current/time graph has the same shape as that during charging the currents in

each case are flowing in opposite directions. The discharging current decreases because the

p.d. across the plates decreases as charge leaves them.

Factors affecting the rate of charge/discharge of a capacitor

When a capacitor is charged to a given voltage the time

taken depends on the value of the resistance in the

circuit. The larger the resistance the smaller the initial

charging current, hence the longer it takes to charge

the capacitor as Q = It

When a capacitor is charged to a given voltage the time

taken depends on the value of the capacitor. The larger

the capacitor the longer the charging time, since a larger

capacitor requires more charge to raise it to the same

p.d. as a smaller capacitor as V= Q

If the cell is taken out of the circuit and theswitch is set to A, the capacitor willdischarge

Consider this circuit when the capacitor isfully charged, switch to position B

AA

- - - -

+ + + +BA A B

p.d. acrosscapacitor

time

Current

0 0time

Supply voltage

(The area under this I/t graph = charge. Both curves will

have the same area since Q is the same for both.)

Current

Time

Current

Time

large capacitor

small capacitor

small resistor

large resistor

C

Summary Notes


Example

The switch in the following circuit is closed at time t = 0

Immediately after closing the switch what is:

(a) the charge on C

(b) the p.d. across C

(c) the p.d. across R

(d) the current through R.

When the capacitor is fully charged what is:

(e) the p.d. across the capacitor

(f) the charge stored.

(a) Initial charge on capacitor is zero.

(b) Initial p.d . is zero since charge is zero.

(c) p.d. is 10 V = Vs - Vc = 10 - 0 = 10 V

(d) I

R = V =

10

10 = 10 A 6

3

(e) Final p.d. across the capacitor equals the supply voltage = 10 V.

(f) Q = CV = 2 × 10-6

× 10 = 2 × 10-5

C.

1 M

1 µF

Vs

10 V

Summary Notes


Resistors and Capacitors in a.c. Circuits

Frequency response of resistor

The following circuit is used to investigate the relationship between current and frequency in

a resistive circuit.

The results show that the current flowing through a resistor is independent of the frequency

of the supply.

Frequency response of capacitor

The following circuit is used to investigate the relationship between current and frequency in

a capacitive circuit.

The results show that the current is directly proportional to the frequency of the supply.

To understand the relationship between the current and frequency consider the two halves of

the a.c. cycle.

The electrons move back and forth around the circuit passing through the lamp and charging

the capacitor one way and then the other (the electrons do not pass through the capacitor).

The higher the frequency the less time there is for charge to build up on the plates of the

capacitor and oppose further charges from flowing in the circuit More charge is transferred

in one second so the current is larger.

Summary Notes


Applications of Capacitors (for background interest)

Blocking capacitor

A capacitor will stop the flow of a steady d.c. current . This is made use of in the a.c./d.c.

switch in an oscilloscope. In the a.c. position a series capacitor is switched in allowing

passage of a.c. components of the signal, but blocking any steady d.c. signals.

Flashing indicators

A low value capacitor is charged through a

resistor until it acquires sufficient voltage to

fire a neon lamp. The neon lamp lights when

the p.d. reaches 100 V. The capacitor is

quickly discharged and the lamp goes out

when the p.d. falls below 80V.

120 V

1 - 2 M

Crossover networks in loudspeakers

In a typical crossover network in low cost

loudspeaker systems, the high frequencies are

routed to LS-2 by the capacitor.

LS 1 LS 2

Smoothing

The capacitor in this simple rectifier circuit is storing charge during the half cycle that the

diode conducts. This charge is given up during the half cycle that the diode does not conduct.

This helps to smooth out the waveform.

Capacitor as a transducer

A parallel plate capacitor can be used to convert mechanical movements or vibration of one

of its plates into changes in voltage. This idea forms the basis of many measuring systems,

e.g. by allowing a force to compress the plates we have a pressure transducer.

Summary Notes


ANALOGUE ELECTRONICS

Analogue and Digital Signals

An analogue system transmits information in the form of a continuously varying signal.

A digital system has the information broken up into a series of discrete values or steps.

A simple example showing these definitions would be analogue and digital watches.

an analogue watch has a set of numbers in a circle and hands that point to them. The

hands sweep round the face in a continuous way.

a digital watch has a series of numbers that are displayed, the numbers changing at the

end of each second, minute or hour.

The Op-Amp (Operational Amplifier)

As with any amplifier, the operational amplifier (op-amp) will change the size of an input

electrical signal. A diagram of the basic set-up of an op-amp is shown below.

The op-amp has two separate inputs - an inverting input (“-” terminal) and a non-inverting

input (“+” terminal). The amplifier must have an energy supply and this is provided by the

supply voltages +Vs and -Vs across the amplifier. Often the power supply voltages are not

shown on circuit diagrams of op-amps.

Activities

Physics Support Materials: Higher Resource Guide 20

The Inverting Amplifier

If an amplifier is set up in the configuration shown below, it is said to be in the inverting

mode.

The input potential, V1, is applied to the inverting input (-ve input). The non-inverting

input (+ve input) is connected straight to “ground”, 0 V.

There is also a resistor, Rf, (feedback resistor) connected between the output and the inverting

input. This feedback resistor reduces the overall gain of the amplifier and allows

the gain to be stabilised controlled.

When the input voltage signal to the op-amp, d.c or a.c, is compared to the output voltage

signal it is found that the sense or ‘sign’ of the output is opposite to that of the input - the

voltage has been inverted, hence the reason why this circuit is called the “inverting mode”.

Some examples of this are given below:

-

+

V1V0

0 V

Rf

R1

Activities

Physics Support Materials: Higher Resource Guide 21

Inverting Mode Gain Equation

The ideal op-amp fulfils two conditions:

no current flows into the op-amp. Its input resistance is infinite.

there is no potential difference between the inverting and non-inverting inputs.

The following inverting mode gain equation can be verified by experiment.

Saturation

From the inverting mode gain equation, it would seem that by inserting any pair of resistors

R1 and Rf in the inverting amplifier circuit it is possible to provide any gain required. It could

therefore be possible to produce either very low or very high output voltages from any input

voltage.

This is not possible. The output of an op-amp circuit is limited by the size of the power

supply used (conservation of energy). In theory, the maximum output voltage possible

would be equal to the supply voltage. (However, in reality it is limited to approximately

85% of the supply voltage.)

When the maximum output voltage has been reached, the amplifier is said to be saturated.

In theory : -15V V 0 +15 V

[In practice : -13V V 0 +13 V (13V 85% of 15 V)]

-

+

+15V

-15V

V 0

Summary Notes

Physics Support Material: Electricity and Electronics (H) – Student Material 22

Example

An inverting mode operational amplifier is set up as shown below.

(a) If V1 is set at +0.8 V, calculate the output voltage V0.

(b) If an a.c signal of peak voltage 1.5 V is applied to V1, sketch the input voltage, V1,

and the output voltage, V0.

Activities


The Differential Amplifier

If the amplifier is set up in the configuration shown below, it is said to be in the differential

mode.

There are two input potentials,V1 and V2, one applied to each of the input terminals of the op-

amp.

There is a feedback resistor, Rf, connected between the output and the inverting input. This

allows control over the gain of the amplifier as it did for the inverting mode.

When the op-amp is used in this mode, it amplifies the difference between the inputs V1 and

V2, with a gain set by the ratio

Summary Notes


Example

A differential amplifier is set up as shown below.

For the following values shown, calculate the output voltage, V0.

(a) V1 = +5.0 V, V2 = +4.8 V

(b) V1 = -2.0 V, V2 = +4.5 V

(a) V1 = +5.0 V, V2 = +4.8 V, R1 =R2 = 10 kΩ, Rf = R3 = 100 kΩ, V0 = ?

(b) V1 = -2.0 V, V2 = +4.5 V, R1 =R2 = 10 kΩ, Rf = R3 = 100 kΩ, V0 = ?

But supply voltage = + 15 V hence output voltage, V0, will saturate at + 15 V

V0 = (V2 - V1)RfR1

V0 = (4.8 - 5.0)100

10

V0 = - 2.0 V

V0 = (V2 - V1)R f

R1V0 = (4.5 - (-2.0))

100

10V0 = + 65 V in theory.

Summary Notes


The differential amplifier as part of a monitoring system

The setting of the variable resistor can be adjusted so as to achieve an output voltage of zero

for a particular temperature setting. The bridge circuit would then be balanced, that is the

potential difference V2 - V1 = 0 V.

The potential, V2, will remain constant as long as the resistance of the variable resistor is not

changed. Any change in temperature will change the potential, V1, and will therefore

produce a potential difference between V2 and V1.

The amplifier will then amplify the difference between V2 and V1, giving an output potential,

V0. The output voltage will increase as the change in thermistor resistance, ∆Rt, increases.

The amplifier is, effectively, amplifying the out-of-balance potential difference from the

Wheatstone Bridge.

Practical Application

The output voltage could be calibrated by placing the thermistor in melting ice (0 oC), then in

boiling water (100 oC), noting the output potential, V0, for each case. The range could then be

divided into 100 equal divisions to give an electronic thermometer over the range 0 - 100 oC.

-

+

V0

0 V

Rf

R1

R2

R3t

+Vs

0 V

V1

V2

10 k

0-10 k

WheatstoneBridge input

DifferentialAmplifier

10 k

10 k

100 k

100 k

10k

Summary Notes


Control Circuits

A transistor, such as those shown below, can act as an electrical switch.

If the input voltage to these transistors, Vi, is positive, then it switches on allowing a current

to flow between the collector and emitter or source and drain, otherwise it is off.

There are two types of transistor switches:

These transistors can be used with a Wheatstone Bridge/differential amplifier circuit to

switch a device on or off.

Low light-level indicator

bipolar n-p-n transistor n-channel enhancement MOSFET

+V S

0V

base

emitter

collector

V i

-V S

0V

gatesource

drain

V i

(i) A positive (+ve) potential (>+0.7 V)is needed for the input, Vi, to switch

transistor on .(ii) The collector arm is connected to a

positive (+ve) supply rail.(iii) If the input potential is negative

(<0.7 V), the transistor is off.

(i) A positive (+ve) potential >1.8 V isneeded for the input, Vi, to switch

transistor on .(ii) The drain is connected to a positive

(+ve) supply rail.(iii) if the input potential is negative or

<1.8 V the transistor is off.

Activities


The variable resistor in the Wheatstone Bridge is adjusted so that, at a particular light level,

the output of the op-amp is zero or less so that the transistor is off. In practice, the variable

resistor would be adjusted until the warning lamp is just off. In this situation, V1 ≈ V2.

If the light level falls, the resistance of the LDR will increase causing the voltage V1 to fall.

If V1 falls, then V1 < V2, therefore (V2 - V1) will be positive (+ve).

This will cause the output voltage, V0, to be positive also, switching on the transistor and

the Warning Lamp lights.

If the light level to the LDR increases, then the opposite will be true.

The resistance of the LDR will decrease causing the voltage V1 to increase.

If V1 increases, then V1>V2, (V2 - V1) will be negative causing the output to be negative and

the transistor will not switch on.

The gain of the circuit (about 1000) is deliberately chosen to be large so that a small variation

from the balance point of the Wheatstone Bridge produces a large enough output voltage to

switch the transistor on.

Modifications

This circuit does have its limitations however. If the output device to be used has a high

power rating requiring a current larger than the transistor can safely supply, then a relay

switch must be used with the transistor to switch on an external circuit.

An example of this type of switch is shown below. In this case, a relay can be energised by

the current through the transistor (the collector current) and its contacts can then be used to

switch on a high-power device such as a heater.

Notice that as the temperature falls the resistance of the thermistor increases, causing V1 to

fall. this means V1 < V2 giving a positive output voltage V0. The transistor will be switched

on, which will energise the relay switch. The heater will be turned on.

+Vs230 Vmains

-

+

Rf

R1

R2

R3

0V

V1

V2

1K

1K

100K0-10K

WheatstoneBridge input

DifferentialAmplifier

+Vs

V0

Transistor Switchand Output

Vi

relay

heater

t

10

K

10

K

10

0K

Activities


Control Circuit Diagrams

The Wheatstone Bridge arrangement can be shown as two straight potential dividers or as a

diamond arrangement. They are the same circuit, just drawn a different way.

Straight potential dividers

Diamond arrangement bridge circuit

All the above circuits are identical examples of the sensor bridge circuit that can be used with

a differential amplifier. It is important to recognise each circuit for what it is and how it

behaves.

+Vs

0V

V1

t

V2

to differentialamplifier

10

K

10

K

+Vs

t

t

0V

+Vs

to op-amp

V1

V2

0V

V1

V2

10 k 10 k

10 k

10 k

to op-amp

Activities


ACTIVITY 1

Title: Electric Field Patterns

Apparatus: Van de Graaff generator, petri dish with oil and seeds, set of shaped electrodes

overhead projector, some sawdust

Instructions

2-D Patterns

Connect up the apparatus as shown and use the Van de Graaff generator to produce a high

voltage between two point electrodes in the oil.

Draw the electric field pattern present between the two point electrodes as shown by the

seeds.

Repeat the above but using two plane electrodes, producing a uniform electric field

between them.

3-D Patterns

While the Van de Graaff is switched on and charging, throw a small amount of sawdust at

the dome.

Sketch the path taken by the pieces of sawdust after they came into contact with the dome.

The sawdust is affected by the radial field around the dome.

Explain the behaviour of the pieces of sawdust after they came into contact with the

charging dome.

Activities


ACTIVITY 2

Title: The Cathode Ray Tube

Apparatus: Cathode Ray Deflection Tube and stand, EHT supply (for electron gun and

heater), HT supply (for deflection plates)

Instructions

Work Done by Electric Field

Note the value of the EHT voltage used in the electron gun.

Calculate the work done on each electron by the electric field in the electron gun.

Hence calculate the speed of the electrons as they leave the electron gun and enter the

evacuated tube.

Deflection Plates

Sketch the path followed by the electron beam as it passes between the deflection plates

when:

(a) bottom plate is positive, top plate is negative

(b) top plate is positive, bottom plate is negative.

Explain the effect the following changes have on the path followed by the electron beam:

(a) decrease EHT voltage on electron gun

(b) decrease HT voltage on deflection plates

Sketch the paths followed by the electron beam after the above changes.

Activities


L3

L2

L1

V

A

No. ofbulbs lit

Current I t.p.d. V(A) (V)

Internalresistance ()

0

1

2

3

“lost volts”(V)

ACTIVITY 3

Title: E.m.f. and Internal Resistance with parallel circuits

Apparatus: 6 V battery, parallel circuit board, ammeter, voltmeter to measure the terminal

potential difference (t.p.d.).

Instruction

Connect up the circuit above, with all lamps unscrewed so that they are off.

Copy the table below.

Note down the current (I) and corresponding t.p.d. (V) values when no lamps are screwed

in, and enter them into the table.

Repeat the above for each case as one, then two, then three lamps are screwed in and light

up.

Using Ohm’s Law, complete the final column of the table by calculating the value of the

internal resistance of the battery.

Activities


ACTIVITY 4

Title: Internal resistance of a cell (Outcome 3)

Apparatus: 1.5 V cell, variable resistor (1-10), voltmeter and ammeter

Instructions

Use the voltmeter to measure the e.m.f. of the cell.

Connect the apparatus as shown in the circuit diagram.

Set the variable resistor to its maximum setting.

Record the readings on the ammeter and voltmeter.

Adjust the variable resistor and take a range of readings.

For each pair of readings determine the lost volts.

Use an appropriate format to determine the internal resistance of the cell.

Activities


ACTIVITY 5

Title: The Balanced Wheatstone Bridge

Apparatus: Wheatstone Bridge board, 1.5 V cell, 20-0-100 µA ammeter, 1 k/10 k

resistance boxes, set of unknown resistances A, B and C, decade resistance

board.

Schematic diagram showing position of resistances Circuit diagram

Instructions

Part A

Connect the 1 k resistances, decade resistance board and unknown resistance A as shown

in the diagram above.

By finding the value of resistance of the decade resistance board which exactly balances

the Wheatstone Bridge, find the value of resistance A.

Repeat to find the value of resistances B and C.

Part B

Replace R2 with a 10 k resistor.

Predict the value of the decade resistance board that will balance the Wheatstone Bridge

for each of the resistors A, B and C with this value of R2.

Confirm your predictions by experiment.

Activities


ACTIVITY 6

Title: The Out-of-Balance Wheatstone Bridge

Apparatus: Wheatstone Bridge board, 1.5 V cell, 20-0-100 µA ammeter, 1 k/10 k

resistance boxes, set of resistances A, B and C, decade resistance board.

Instructions

Connect the circuit as shown in the diagram.

Adjust the resistance of the decade resistance board so that the Wheatstone Bridge is

balanced.

Increase the resistance of the decade resistance board in 10 steps, noting the value of the

out-of- balance current each time.

Record your results and complete the table.

Plot a graph of change in resistance, R (), on the ×-axis and out-of-balance current, I,

(µA) on the y-axis.

ResistanceBoard

Resistor B

µA

R1 R2

1 k 1 k

Activities


ACTIVITY 7

Title: The Out-of-Balance Wheatstone Bridge - Applications

Apparatus: Wheatstone Bridge board, 6 V battery, 20-0-100 µA ammeter, 1 k/10 k

resistance boxes, decade resistance board, LDR, thermistor probe, strain gauge

(already set up).

Instructions

Part A - Light Meter

Connect the circuit up as shown.

Balance the Wheatstone Bridge circuit with

the LDR on your bench. There is no need to

“remove” the protective resistor as the

circuit is quite sensitive. Take care not to

cast shadows over the LDR when finding

balance.

Find the out-of-balance current when the

LDR is in a light place then in a dark place.

Explain why the measured current is greater

than zero for one condition and less than

zero for the other.

Part B -Thermometer

Place the probe in an ice/water mixture in a

beaker. (0 °C)

Balance the Wheatstone Bridge with the

probe in the ice/water mixture.

Place the probe in a beaker of boiling water.

(100 °C)

Measure and record the out-of-balance

current obtained with the probe in the

boiling water.

Predict the current obtained when the probe

is removed and is measuring room

temperature.

Calculate the value of room temperature

from your results.

What assumptions are you making about the

temperature of the probe, its resistance, and

the out-of-balance current?

Continued...

Activities


ACTIVITY 7 (continued)

Instructions (continued)

Part C - Strain Gauge

The hacksaw blade has been fitted with two strain gauges, one on each side of the blade.

The resistance of a strain gauge changes when its shape is deformed - either stretched or

compressed. When the hacksaw blade is bent, one of the strain gauges will “stretch” while

the other one will “compress”. The two strain gauges are connected to one arm of a

Wheatstone Bridge circuit.

The strain gauge circuit should already be

set up for you.

Balance the Wheatstone Bridge circuit

when the hacksaw blade is straight.

Bend the hacksaw blade in one direction.

Note the out-of-balance current.

Bend the hacksaw blade in the other

direction.

Note the out-of-balance current.

Explain how the out-of-balance current is

used to show -

(a) the amount of bending/strain put on

the hacksaw blade

(b) the direction of the bending/strain

put on the hacksaw blade.

µA

680 ResistanceBoard

4.5 V

Straingauge (back)

Straingauge (front)

Activities


ACTIVITY 8

Title: Alternating Current – Peak and r.m.s. values

Aim: To establish a relationship between peak and equivalent direct (r.m.s.) values of

voltage.

Apparatus: Lab pack, 6 V battery, oscilloscope, variable resistor (0-22 Ω), 2 × 2.5 V

lamps, connecting leads.

Instructions

Set up Circuit 1.

Switch the time-base on the oscilloscope OFF.

Adjust the supply and the oscilloscope to give a measured peak alternating voltage of 1 V

on the oscilloscope

Leave Circuit 1 switched on.

Set up Circuit 2.

Adjust the variable resistor until the lamp is the same brightness as the lamp in Circuit 1.

Use the oscilloscope to measure the direct voltage across this lamp.

Repeat the measurements for peak voltages of 2 V, 3 V, 4 V and 5 V.

Plot a graph of direct voltage against peak voltage.

Determine the gradient of the graph.

State the relationship between Vd.c. and Vpeak using the value obtained from the gradient of

the graph.

tooscilloscope

variablea.c. supply

Circuit 1 Circuit 2

tooscilloscope

Activities


ACTIVITY 9

Title: Calibration of Signal Generator

Aim: To calibrate the frequency scale on a signal generator.

Apparatus: Oscilloscope, signal generator, connecting leads

Instructions

Connect the output of the signal generator to the Y-inputs of the oscilloscope as shown.

Switch the time-base ON.

Set the signal generator to 10 Hz and switch on.

Adjust the oscilloscope controls to obtain a recognisable waveform.

Calculate the frequency from the trace on the screen. It is useful to record : the timebase

setting, divisions for one cycle, and time for one cycle with the frequency in your table of

readings.

Repeat for other frequency values of 100 Hz, 10000 Hz and 10,000 Hz.

Compare the measured and stated values of frequency.

Include a column for percentage uncertainty in your table and complete this column

assuming the oscilloscope is 100% accurate.

State which scale on the signal generator is most prone to uncertainty.

Activities


ACTIVITY 10

Title: Charge and potential difference for a capacitor (Outcome 3)

Apparatus: Electrolytic capacitor (about 5000 µF), coulomb meter, voltmeter, 6 × 1.5 V

battery, changeover switch

Instructions

Discharge the capacitor by shorting with connecting lead.

Connect the circuit and set the switch to charge the capacitor as shown in the diagram.

Allow enough time for the capacitor to charge fully.

Set the switch to B to fully discharge the capacitor through the coulomb meter.

Repeat for other charging voltages.

Use an appropriate format to show the relationship between charge and voltage.

V

A B

Coulomb meter

Activities


ACTIVITY 11

Title: Charging and Discharging Characteristics for a Capacitor

Aim: To observe the variation of the current through, and the p.d. across, a capacitor during

the charge and discharge cycles.

Apparatus 2200 µF capacitor, 10 kΩ resistor, ammeter and voltmeter, 6 V battery

stopclock

Instructions

Part 1 Charging

Set up the circuit as shown with the switch open.

Close the switch and start the stopclock.

Record values of current I and p.d. V every 10 seconds until the measured p.d. becomes

constant.

Plot graphs of current I and p.d. V against time for the charging cycle.

Describe the change in the current and p.d. during the charging cycle.

Part 2: Discharging

Fully charge the capacitor as in Part 1.

Disconnect the leads from the battery and join them together, as shown above.

Close the switch and note values for current I and p.d. V for the capacitor every 10

seconds from time t = 0.

Plot graphs of current I and p.d. V against time for the discharge cycle.

Explain the change in current and p.d. during the discharging cycle.

Compare the direction of current during the charging and discharging cycles and explain

any differences.

Activities


ACTIVITY 12

Title: Response of resistance in a variable frequency a.c. circuit

Aim: To establish a relationship between the current through a resistor and the frequency of

the a.c. supply.

Apparatus: resistor (20 - 50 ), signal generator, a.c. ammeter, a.c. voltmeter

Instructions

Set up the circuit as shown with the supply switched off.

Set the frequency of the supply to 300 Hz.

Switch on and note the ammeter reading.

Repeat in steps of 50 Hz up to 800 Hz, ensuring the p.d. of the supply is kept constant.

Comment on the current through the resistor as the frequency is increased

State if the resistance of a resistor is affected by the frequency of the a.c. supply.

State why the p.d. of the supply must remain constant.

V A

Activities


ACTIVITY 13

Title: Current and frequency in a capacitive circuit (Outcome 3)

Apparatus: Signal generator, a.c. voltmeter or oscilloscope, a.c. ammeter, 4.7 µF

capacitor.

Instructions

Connect the circuit as shown in the circuit diagram.

An oscilloscope may be used in place of the voltmeter.

Set the output of the signal generator to about 3 V.

Vary the source frequency and record readings of current and frequency using

a range of 100 Hz to 1 kHz.

Ensure that the supply voltage remains constant.

Use an appropriate format to show the relationship between current

and frequency.

~

Activities


ACTIVITY 14

Title: Uses of Capacitors - the photographic flash

Aim: To show the principle behind the operation of a photographic flash.

In photography, where light has to be supplied by the flash unit, the light has to be supplied in

the short period of time that the shutter is open. In this time a large amount of light energy

must be emitted. This is stored as electrical energy in a capacitor until it is needed.

Apparatus: 1.5 µF capacitor, neon lamp, 100 k resistor, 120 d.c. supply, 1 SPST switch

1 push switch

Instructions

Set up the circuit as shown.

To switch on the “flash unit”, close switch F.

To simulate the shutter opening for a very short time, close switch S and release quickly.

Note what happens.

Explain what happens to the p.d. across the capacitor when switch F is closed?

If switch F remains closed state what will happen to the capacitor after switch S has been

released and the lamp has flashed.

The neon lamp requires a p.d. of 100 V across it to make it light. Explain why the lamp is

able to light in this circuit.

neon lamp

F

S

100 k

120 V dc

Activities


ACTIVITY 15

Title: Uses of Capacitors - d.c. power supply

Aim: To show the effect of capacitors in the production of a smooth d.c. supply from an a.c.

supply.

In the following circuits, the 120 resistor represents the load resistor or device being driven

by the supply e.g. a radio. The oscilloscope indicates the form of the output p.d. across the

load resistor.

Instructions

Set up circuit 1 as shown.

Draw the circuit and sketch the waveform displayed on the oscilloscope screen.

Set up each of the other circuits, in turn.

Draw the circuits and sketch the waveforms produced.

Explain whether the waveform produced in circuit 2 is a.c. or d.c.

Describe the effect of the capacitor on the waveforms produced in circuit 3.

State what effect the size of the capacitance has on the smoothing of the supply.

CIRCUIT 1

12 V a.c. 12 V a.c. 120

CIRCUIT 2

diode

(a) 5 µF(b) 10 µF(c) 20 µF

12 V a.c. 120

CIRCUIT 3 C =

C+

CIRCUIT 4

2200 µF+

120

120

12 V a.c.

Activities


INFORMATION SHEET FOR ACTIVITIES 16, 17, 18, 19, 20, 21 AND 22

The Amplifier Circuit Board

A diagram of the Nuffield Operational Amplifier circuit board is shown below.

It is important to become familiar with the input potentiometers in order to work successfully

with the op-amp circuit board.

Activities


ACTIVITY 16

Title: Familiarisation - Using The Input Potentiometers

Apparatus: Op-Amp Board, Dual Rail -15 - 0 - 15 V Power Supply, Multimeter and leads.

Instructions

Part A: Positive (+ve) input potential.

Connect up the top input potentiometer and voltmeter using the connections shown.

Adjust the top input potentiometer to confirm that you can obtain a range of voltages on

the voltmeter from 0 to +15 V.

Repeat the above but this time connecting up the bottom input control to obtain a range of

voltages from 0 to +15 V also.

continued....

Activities


ACTIVITY 16 (continued)


Part B: Negative (-ve) input potential.

Connect up the top input potentiometer and voltmeter using the connections shown below.

Adjust the top input potentiometer to confirm that you can obtain a range of voltages on

the voltmeter from 0 to -15 V.

Repeat the above but this time connecting up the bottom input control to obtain a range of

voltages from 0 to -15 V also.

V

-V s

0V

Negative supply rail

Zero volt rail

Activities


ACTIVITY 17

Title: The Inverting Amplifier


The circuit diagram for the circuit and results table are shown below.

Instructions

Connect up the top input potentiometer and two voltmeters using the connections shown .

The circuit board connections shown above are for positive (+ve) input potentials and a

gain of 10, since R1 = 10 k and Rf is set to 100 k.

Connect R1 at 10 k and Rf at 100 k. Set V1 to 1.2 V.

Measure the output voltage and record in your own table. Repeat this measurement for the

other values of V1 and Rf shown in the sample table

Complete the last two columns of your table.

Write a conclusion to your experiment including a comment on the polarity of V0

compared to V1.

100K

Rf() R1()V1

(V)

V0

(V)

R f

R1

V 0

V 1

100K

100K

100K

10K

10K

10K

10K

10K

10K

10K

10K

10K

10K

10K

10K

0.5

-0.3

-1.0

8.0

4.5

-6.0

-0.8

1.2

Activities


ACTIVITY 18

Title: Saturation


Instructions

Connect up the following circuit using the top input potentiometer and two voltmeters

from the circuit diagram below. This circuit is identical to the circuit used in Activity 17.

Set the value of the input voltage, V1, to the values shown in the tables and record the

corresponding value of the output voltage, V0 in your own table.

Graph the results of both tables from your experiment on axes similar to those below.

State the gain setting of the inverting amplifier used?

Describe what happens to the value of the output voltage, V0, as the input voltage, V1, is

increased.

State the maximum output voltages available from the amplifier.

-

+

V1V0

0V

Rf

R1

VV

10K

100K

Activities


ACTIVITY 19

Title: Square Wave Generator


Instructions

Connect the op-amp board as an inverting amplifier, using the resistor values shown.

Connect the signal generator to the input of the inverting amplifier.

Connect the oscilloscope across the inputs of the op-amp, AB.

Set the signal generator to approximately 3 V at a frequency of 200 Hz.

Adjust the Y-gain and time-base controls of the oscilloscope until you obtain a steady

wave pattern.

Accurately sketch the wave pattern produced.

Now connect the oscilloscope across the outputs of the op-amp, CD.

Without adjusting any of the controls on the oscilloscope or signal generator, sketch the

wave pattern produced at the output.

Accurately sketch the wave pattern produced this time.

State how the phase of the output potential, V0, compares to that of the input potential, V1.

Compare the frequency of the output potential, V0, to V1.

State the gain of the amplifier in this circuit.

Hence state the minimum value of V1 that will produce a saturated output potential, V0.

As the input potential from the signal generator, V1, is increased, explain what happens to

the output potential, V0.

Activities


-

+

V 1V 0

0V

R f

R1

V

R2

V 2

R3

In this circuit, Rf and R3 will

always be taken as 100 k due

to the limitations of the board.

ACTIVITY 20

Title: The Differential Amplifier

Apparatus: Op-Amp Board, Dual Rail -15 - 0 - 15 V Power Supply, Multimeter and leads.,

100 kΩ and 10 kΩ resistor panels.

The circuit diagram for the circuit is shown below and the results table is given on the

following page.

Instructions

Connect up the two input potentiometers using the connections shown. The circuit board

is shown for positive (+ve) input potentials with a gain of 1, but negative (-ve) input

potentials are also used as are different settings for the gain.

(Continued...)

Activities


ACTIVITY 20 (Continued)


Set Rf and R3 at 100 kΩ.

For each of the values of R1 and R2, V2 and V1 given on the sample table record the output

voltage V0 in your own table.

Complete the other columns in your table.

Write a conclusion, including a comment on the polarity of V0 compared to (V2-V1).

Comment on the maximum gain you could obtain if V1 = 1 V and V2 = 1.5 V.

100K

Rf & R3 V2Rf

R1

100K

100K

100K

10K

10K

10K

10K

6.0

5.0

-1.5

3.5

1.5

-4.5

-1.2

1.0

R1 & R2 V1

100K

100K

100K

100K

100K

100K

100K

100K

V2-V1 V0Rf

R1(V2-V1)

2.0

-2.5

-3.0

3.0

2.5

-5.0

-0.8

4.0

() () (V) (V) (V) (V) (V)

Activities


ACTIVITY 21

Title: The Inverting Amplifier used to Control Heavier Loads

Aim: To investigate the use of a transistor and relay in a control circuit

The circuit below uses a transistor, relay and op-amp to control high current devices. Some

devices, such as motors or heaters, require a current which is too large for small transistors to

supply. The transistor can, however, be used to energise the coil of a relay which can then

switch on a separate supply to the high current device.

Apparatus: op-amp board, 2 × 5 V d.c supplies, n-p-n transistor board, relay, 6 V motor,

ammeter.

Instructions

Connect up the circuit.

Gradually increase the input voltage, V1. At some point, the relay contacts should close

and the motor will work.

Redraw the circuit, marking in the positions of ammeters required to measure

(a) the output current from the op-amp

(b) the current in the relay coils

(c) the current in the motor.

Ensure your circuit diagram is correct, then connect up an ammeter in the correct positions

and note the three current values above.

State the value of the gain of this circuit.

If the n-p-n transistor requires 0.7 V to switch on, state the value of V1 required to operate

the reed relay and also the motor.

Explain the operation of this circuit.

-

+

Rv

0-10k

0 V 0V

+5 V+Vs

1 M

100 k

M

5 Vsupply

ReedRelay

V1

Activities


ACTIVITY 22

Title: The Differential Amplifier used to Monitor Light Level

Aim: To investigate the use of a differential amplifier with a Wheatstone Bridge to monitor

light level.

The circuit below uses a LDR as a resistive sensor in a Wheatstone Bridge circuit. With the

op-amp, it can be used to monitor light level changes. The two potential dividers, R1, R2 and

R3, R4 are connected as a Wheatstone Bridge circuit. Any out of balance potential difference

from the Wheatstone Bridge is applied across the inputs of the op-amp. The resistance of R4

can be adjusted to balance the bridge at any desired light level. The output of the op-amp is

therefore proportional to the change in resistance of the LDR caused by the change in light

level.

Apparatus: op-amp board, LDR panel, 2 × 10 kΩ resistor panels.

Instructions

Ideally, this experiment should be carried out in a darkened room.

Connect up the circuit shown.

Place a 60 W lamp facing the LDR at a distance of 50 cm, and adjust R4 until the

voltmeter reads zero.

Move the lamp closer, 5 cm at a time, and record the output voltage readings.

Plot a graph of output voltage against distance.

-

+

0 V

+Vs

10 k

100 k

10 k

0 V

100 k

10 k 10 k

0-10 k

R1

R2

R3

R4V

Activities


A10 V

70

10

20

(a)

(b) A12 V

15

9

V

A

3

5

V

6 V

(c)

R = ?

A40 V

5

10

I = 2 AA

40 V

4

10

R = ?

20 V

PROBLEMS

Revision of Circuits

1. If a current of 40 mA passes through a lamp for 16 s, how much charge has passed any

point in the circuit?

2. A lightening flash lasted for 1 ms. If 5 C of charge was transferred during this time,

what was the current?

3. The current in a circuit is 2.5 × 10-2

A. How long does it take for 500 C of charge to

pass any given point in the circuit?

4. What is the p.d. across a 2 k resistor if there is a current of 3 mA flowing through it?

5. Find the readings on the meters in the following circuits.

6. Find the unknown values of the following resistors.

(a) (b)

Answers


5

25

8

10 10

20

10 10

10

10

10 10

1

20

4

5

10

20

10

10

25

5 10

12

3

6

5

A

3 k

5 k

V

7. Find the total resistance of the following combinations.

(a) (b)

(c) (d)

(e) (f)

8. If the ammeter reads 2 mA,

find the voltmeter reading.

Answers


A6 V

6 6 V6

6 V

A

5 20 2

9. Calculate the power in each of the following cases.

(a) A 12 V accumulator delivering 5 A.

(b) A 60 Ω heater with a 140 V supply.

(c) A 5 A current in a 20 heater coil.

10. An electric kettle has a resistance of 30 .

(a) What current will flow when it is connected to a 230 V supply?

(b) Find the power rating of the kettle.

11. A 15 V supply produces a current of 2 A for 6 minutes. How much energy is supplied

in this time?

12. Find the readings on the

ammeters and the voltmeter.

13. Assuming each of the four cells

cell to be identical, find:

(a) the reading on the ammeter

(b) the current through

the 20 resistor

(c) the voltage across

the 2 resistor.

14. A coil has a current of 50 mA flowing through it when the applied voltage is 12 V.

Find the resistance of the coil.

15. Write down the rules which connect the (a) potential differences and (b) the currents in

series and parallel circuits.

16. Draw the symbol for a fuse, diode, capacitor, variable resistor, battery and a d.c. power

supply.

17. What is the name given to the circuit

opposite.

Write down the relationship between

V1, V2, R1 and R2.

18. Find the values of V1 and V2 of the circuit in question 17 if:

(a) R1 = 1 kΩ R2 = 49 kΩ

(b) R1 = 5 kΩ R2 = 15 kΩ.

10 V

R2

R1 V1

V2

Answers


19. Explain what would happen to the

readings on V1 and V2 if light was

shone onto the L.D.R.

Suppose the L.D.R. was replaced with

a thermistor which was then heated.

Explain the effect on the readings.

20. (a) What would be the polarity of A and B when connected to a 5 V supply, so

that the LED would light?

(b) What is the purpose of R in the circuit shown above?

(c) If the L.E.D. rating is 200 mA at 1.5 V, find the value of R.

V1

V2

10 V

R1

A

B

R

Answers


+ test charge

+ -

+ test charge

++++

----

- Q

----

+ Q

++++

ELECTRICY AND ELECTRONICS PROBLEMS

Electric fields and resistors in circuits

1. Draw the electric field pattern for the following charges:

(a) (b) (c)

2. Describe the motion of the small test charges in each of the following fields.

(a) (b)

(c) (d)

3. An electron volt is a unit of energy. It represents the change in potential energy of an

electron which moves through a potential difference of 1 volt. If the charge on an

electron is 1.6x10-19

C, what is the equivalent energy in joules?

4. Mass of an electron = 9.1 10-31

kg Charge on an electron = 1.6 10-19

C

The electron shown opposite is accelerated

across a p.d. of 500 V.

(a) How much electrical work is done?

(b) How much kinetic energy has it gained?

(c) What is its final speed?

5. Electrons are ‘fired’ from an electron gun at a screen. The p.d. across the gun is

2000 V. After leaving the positive plate the electrons travel at a constant speed to the

screen. Assuming the apparatus is in a vacuum, at what speed will the electrons hit

the screen?

----

- e

+500 V++++

Answers


A1 A23

12 4

X

Y

12 V

12

8 24

S

230 V

6. What would be the increase in speed of an electron accelerated from rest by a p.d. of

400 V?

7. An ×-ray tube is operated at 25 kV and draws a current of 3 mA.

(a) Calculate

(i) the kinetic energy of each electron as it hits the target

(ii) the velocity of impact of the electron as it hits the target

(iii) the number of electrons hitting the target each second.

(mass of electron = 9.1 × 10-31

kg charge on electron = 1.6 × 10-19

C)

(b) What happens to the kinetic energy of the electrons?

8. Sketch the paths which (a) an a-particle,

(b) a b-particle,

and (c) a neutron,

would follow if each particle entered the given electric fields with the same velocity.

(Students only studying this unit should ask for information on these particles).

9. State what is meant by (a) the e.m.f. of a cell

(b) the p.d. between 2 points in the circuit.

10. Prove the expressions for the total resistance of resistors in (a) a series and (b) a

parallel circuit.

11. In the circuit below:

(a) what is the total resistance of the circuit

(b) what is the resistance between X and Y

(c) find the readings on the ammeters

(d) calculate the p.d. between X and Y

(e) what power is supplied by the battery ?

12. The circuit opposite uses the 230 V

alternating mains supply. Find the

current flowing in each resistor when:

(a) switch S is open

(b) switch S is closed.

Answers


V

r

A

13. An electric cooker has two settings, high and low. It takes 1 A at the low setting and

3 A at the high setting.

(a) Find the resistance of R1 and R2.

(b) What is the power consumption at each setting ?

14. (a) Find the value of the series resistor which

would allow the bulb to operate at its

normal rating.

(b) Calculate the power dissipated in the resistor.

15. In the circuit below, r represents the internal resistance of the cell and R represents the

external resistance of the circuit.

When S is open, the voltmeter reads 2.0 V.

When S is closed, it reads 1.6 V and the

ammeter reads 0.8 A.

(a) What is the e.m.f. of the cell ?

(b) What is the terminal potential difference

when S is closed?

(c) Calculate the values of r and R.

(d) If R was halved in value, calculate the new readings on

the ammeter and voltmeter.

16. The cell in the diagram has an e.m.f. of 5 V. The current through the lamp is 0.2 A

and the voltmeter reads 3 V. Calculate the internal resistance of the cell.

17. A cell of e.m.f. 4 V is connected to a load resistor of 15 W. If 0.2 A flows round the

circuit, what must be the internal resistance of the circuit?

R1230 V R2

RS

V

r

A

Answers


18. A signal generator has an e.m.f. of 8 V and internal resistance of 4 . A load resistor

is connected to its terminals and draws a current of 0.5 A. Calculate the load

resistance.

19. (a) What will be the terminal p.d. across the cell in the circuit below.

(b) Will the current increase or decrease as R is increased?

(c) Will the terminal p.d. then increase or decrease ? Explain your answer.

20. A cell with e.m.f. 1.5 V and internal resistance 2 is connected to a 3 Ω resistor.

What is the current?

21. A pupil is given a voltmeter and a torch battery. When he connects the voltmeter

across the terminals of the battery it registers 4.5 V, but when he connects the battery

across a 6 resistor, the voltmeter reading decreases to 3.0 V.

(a) Calculate the internal resistance of the battery.

(b) What value of resistor would have to be connected across the battery to reduce

the voltage reading to 2.5 V.

22. In the circuit shown, the cell has an e.m.f. of

6.0 V and internal resistance of 1 .

When the switch is closed, the reading on the

ammeter is 2 A. What is the corresponding

reading on the voltmeter ?

23. In order to find the internal resistance of a cell, the following sets of results were

taken.

Voltage (V) 1.02 0.94 0.85 0.78 0.69 0.60

Current (A) 0.02 0.04 0.06 0.08 0.10 0.12

(a) Draw the circuit diagram used.

(b) Plot a graph of these results and from it determine

(i) the e.m.f.

(ii) the internal resistance of the cell.

(c) Use the e.m.f. from part (b) to calculate the lost volts for each set of readings

and hence calculate 6 values for the internal resistance.

(d) Calculate the mean value of internal resistance and the approximate random

uncertainty.

Answers


R2

R1

+5 V

0 V

2 k

8 kR2

+5 V

0 V

4 k

1 kR2

+5 V

0 V

500

750

t

B B

+12 V

0V

3 k

3 k

V

9 k

3 k

A

+10 V

0V

3 k

2 k

V

6 k

4 k

A B

+5 V

0V

5 k

2 k

V

10 k

8 k

A

+9 V0 V

6 k

3 k

V

9 k

6 k

A

B

24. The voltage across a cell is varied and the corresponding current noted. The results are

shown in the table below.

Voltage (V) 5.5 5.6 5.7 5.8 5.9

Current (A) 5 4 3 2 1

Plot a graph of V against I.

(a) What is the open circuit p.d?

(b) Calculate the internal resistance.

(c) Calculate the short circuit current.

(d) A lamp of resistance 1.5 is connected across the terminals of this supply.

Calculate (i) the terminal p.d.

and (ii) the power delivered to the lamp.

25. Calculate the p.d. across R2 in each case.

(a) (b) (c)

26. Calculate the p.d. across AB (voltmeter reading) in each case.

(a) (b) (c)

27. (a) Calculate the reading on the voltmeter.

(b) What alteration could be made to

balance the bridge circuit ?

Answers


+1.5 V

5

10

G

10

5

A

B

+1.5 V

7

10

G

14

20

A

B

+1.5 V

9

12

12

16

A

B

G

5

10

G

20

X

+1.5 V

R

9

2 V

120

120

G

x

2 V

4 k

12 k

G

x

15 k

10 k 25 k

G

3.6 k x

2 V

28. Three pupils are asked to construct balanced Wheatstone bridges.

Their attempts are shown.

Pupil A Pupil B Pupil C

One of the circuits gives a balanced Wheatstone bridge, one gives an off - balance

Wheatstone bridge and one is not a Wheatstone bridge.

(a) Identify each circuit.

(b) How would you test that balance has been obtained ?

(c) In the off – balance Wheatstone bridge ;

(i) calculate the potential difference across the galvanometer.

(ii) in which direction will electron current flow through the galvanometer.

29. Calculate the value of the unknown resistor × in each case.

30. The circuit shown opposite is balanced.

(a) What is the value of resistance ×?

(b) Will the bridge be unbalanced if

(i) a 5 resistor is inserted next to the

10 resistor

(ii) a 3 V supply is used.

(c) What is the function of resistor R and what is the

disadvantage of using it as shown ?

Answers


31. The following Wheatstone bridge circuit

is used to monitor the mechanical strain

on a girder in an oil rig.

(a) Explain how the circuit can

be used to monitor the strain.

(b) Sketch the graph of current

through the galvanometer against the strain.

32. An automotive electrician needed to accurately measure the resistance of a resistor.

She set up a circuit using an analogue milliammeter and a digital voltmeter.

The two meter readings were:

(a) What are the readings?

(b) What is the nominal resistance calculated from these readings?

(c) Which reading is likely to cause the greatest uncertainty?

(d) What is the smallest division on the milliammeter?

(e) What is the absolute uncertainty on the milliammeter?

(f) What is the absolute uncertainty on the voltmeter?

(g) What is the percentage uncertainty on the milliammeter?

(h) What is the percentage uncertainty on the voltmeter?

(i) Which is the greatest percentage uncertainty?

(j) What is the percentage uncertainty in the resistance?

(k) What is the absolute uncertainty in the resistance?

(l) Express the final result as “(resistance ± uncertainty)Ω”

(m) Round both the result and the uncertainty to the relevant number of significant

figures or decimal places.

R3

G

+1.5 V

R4

Strain gauges

Answers


Alternating Current and Voltage

1. (a) What is the peak voltage of the 230 V mains supply?

(b) The frequency of the mains supply is 50 Hz. How many times does the

voltage fall to zero in one second.

2. The circuit below is used to compare the a.c. and d.c. supplies when the lamp is at the

same brightness with each supply. The variable resistor is used to adjust the

brightness of the lamp.

(a) Explain how the brightness of the lamp is changed using the variable resistor.

(b) What additional apparatus would you use to ensure the brightness of the lamp

was the same for each supply?

(c) In the oscilloscope traces shown below diagram 1 shows the voltage across the

lamp when the switch is in position B and diagram 2 shows the voltage when

the switch is in position A.

Y Gain set to 1 V cm-1

From the oscilloscope traces, how is the root mean square voltage numerically related

to the peak voltage.

(d) Redraw diagrams 1 and 2 to show what would happen to the traces if the time

base was switched on.

3. The root mean square voltage produced by a low voltage power supply is 10 V r.m.s.

(a) Calculate the peak voltage of the supply.

(b) If the supply was connected to an oscilloscope, Y-gain set to 5 V cm-1

with the

time base switch off, describe what you would see on the screen.

BA

Answers


4. (a) A transformer has a peak output voltage of 12 V. What is the r.m.s. output

voltage?

(b) A vertical line 6 cm long appears on an oscilloscope screen when the Y gain is

set to 20 V cm-1

. Calculate:

(i) the peak voltage of the input

(ii) the r.m.s. voltage of the input.

5. The following trace appears on an oscilloscope screen when the time base is set at

2.5 ms cm-1

.

(a) What is the frequency of the input including the uncertainty to the nearest Hz?

(b) Sketch what you would see on the screen if the time base was changed to

(i) 5 ms cm-1

(ii) 1.25 ms cm-1

6. An a.c. input of frequency 20 Hz is connected to an oscilloscope with time base set at

0.01 s cm-1

. What would be the wavelength of the waves appearing on the screen?

Capacitance

7. A 50 µF capacitor is charged till the voltage across its plates reaches 100 V.

(a) How much charge has been transferred from one plate to the other?

(b) If it was discharged in 4 milliseconds, what would be the average current?

8. A capacitor holds a charge of 3 × 10-4

C when it is charged to 600 V.

What is the value of the capacitor?

9. A 30 µF capacitor holds a charge of 12 × 10-4

C.

(a) What is the voltage that it is charged to?

(b) If the tolerance of the capacitor is ± 5 µF, express this uncertainty as a

percentage.

(c) What is the greatest voltage which could occur across the plates of the

capacitor?

10. A 15 µF capacitor is charged from a 1.5 V battery. What charge will be stored on the

plates?

11. (a) A capacitor has a voltage of 12 V across its plates and stores a charge of

1.2 × 10-5

C. Calculate its capacitance.

(b) A 0.1 µF capacitor is connected to a 8 volt direct supply. How much charge

will it store?

Answers


12. Using the circuit below a capacitor is charged at a constant charging current of

2.0x10-5

A.

The time taken to charge the capacitor is 30 s and during this time the voltage across

the capacitor rises from 0 V to 12 V.

What is the capacitance of the capacitor?

13. A 100 µF capacitor is charged from a 20 V supply.

(a) How much charge is stored?

(b) How much energy is stored in the capacitor?

14. A 30 µF capacitor stores 6 × 10-3

C of charge. How much energy is stored in the

capacitor?

15. The circuit below is used to investigate the charging of a capacitor.

(a) What is the response of the ammeter when switch S is closed?

(b) How can you tell when the capacitor is fully charged?

(c) What would be a suitable range for the ammeter?

(d) If the 10 k resistor is replaced by a larger resistor, what will be the effect on

the maximum voltage across the capacitor?

A

10 k

12 V

2000 µF

Answers


16. In the circuit below the neon lamp flashes at regular intervals. The neon lamp

requires a potential difference of 100 V across it before it will conduct and flash. It

continues to glow until the potential difference across it drops to 80 V. While lit, its

resistance is very small compared with R.

(i) Explain why the neon bulb flashes.

(ii) Suggest two methods of decreasing the flash rate.

17. In the circuit below the capacitor C is charged with a steady current of 1mA by

carefully adjusting the variable resistor R.

The voltmeter reading is taken every 10 seconds. The results are shown in the table.

Time 0 10 20 30 40

p.d.(V) 0 1.9 4 6.2 8.1

(a) Plot a graph of charge against voltage for the capacitor and hence find its

capacitance (use graph paper).

(b) Calculate the capacitance for each of the readings (ignoring readings for t = 0).

(c) Calculate the mean capacitance and the approximate random uncertainty in the

mean to two decimal places.

120 V dc

R

C

9 V dc C

A

V

Answers


18. The circuit below is used to charge and discharge the capacitor

(a) What position should the switch be set (i) to charge and (ii) to discharge the

capacitor?

(b) Draw graphs of VR against time for the capacitor charging and discharging,

and of VC against time for the capacitor charging and discharging.

(c) If the capacitor has capacitance of 4.0 µF and the resistor has resistance of 2.5

M calculate:

(i) the maximum charging current in the circuit above

(ii) the maximum charge stored by the capacitor when fully charged in the

above circuit.

19.

(a) For the above circuit draw graphs of

(i) VC against time during charging and

(ii) VA against time during charging.

(b) Calculate the final voltage across the capacitor and the final charged stored by

it.

20. For each of the circuits below state what happens to the current flowing when the

frequency is (i) increased and (ii) decreased.

3 V

3 M

3 µF

Answers


21. In the circuit below the signal generator is set at 6.0 Vr.m.s., 1000 Hz.

The lamp operates normally.

(a) Explain why the lamp can operate normally when the plates of the capacitor

are separated by an insulator.

(b) What happens to the brightness of the lamp when the frequency of the signal

generator is increased. Why does this happen?

22. For each of the following circuits sketch a graph of current against frequency.

23.

The supply frequency to the above circuit is increased from a very low frequency,

while the supply voltage remains constant.

What will happen to the brightness of lamp A and B?

Signalgenerator

Diagram A Diagram B

Signalgenerator

A B

A A

Answers


Vs

R1

R2 V2

V1

4 V

R1

5 k

V1

3 V

2 V

R1

1 k

V1

1.5 V

12 V

R1

1 k

V1

8.5 V

+1.5 V

8.2 k

V1

0 V

V2

4.7 k

+5 V

3.3 k

V1

0 V

V2

2.2 k

+1.5 V

15 k

V1

0 V

V2

3 k

Analogue Electronics

1. Calculate the values of V1 and V2 in the circuit shown for the following situations.

(a) VS = 12 V R1 = 40 k R2 = 20 k

(b) VS = 6 V R1 = 150 k R2 = 30 k

(c) VS = 10 V R1 = 3 k R2 = 5 k

2. Calculate the values of R1 in the following circuits.

(a) (b) (c)

3. Calculate the values of V1 and V2 in the circuits shown.

(a) (b) (c)

4. Explain what happens to the value of V1 in each of the following situations -

(a) brightness increasing (b) temperature increasing (c) brightness decreasing.

V1

+1.5 V

0 V

V1

+1.5 V

0 V

tV1

+1.5 V

0 V

Answers


5. The thermistor shown has a resistance of 31 k at 30 °C and 35 k at 25 °C.

(a) If the variable resistor is set at 5 k, calculate the input voltage to the

transistor in each case.

(b) Hence, explain how the circuit shown works.

(c) Explain the purpose of the variable resistor.

(d) Suggest a possible use for the circuit.

(e) Why is the relay switch necessary?

6. Draw a circuit diagram similar to the circuit of Question 5 that would switch on a

mains voltage lamp when the ambient light level drops below a certain level.

7. The circuits shown in questions 5 & 6 could use a different type of transistor called an

n-channel enhancement MOSFET. Draw the symbol for this transistor and label each

terminal.

8. The following signals are fed into an inverting amplifier with a gain of 5.

Draw the expected output trace.

(a) (b) (c)

(d) (e) (f)

Answers


9. (a) In what mode is the op-amp being used in the circuit below.

(b) State the relationship between V1, R1, Rf, and V0.

(c) Find the unknown values in the table shown. All calculations should be set out

clearly.

10. (a) Which of the following values of Rf

will produce saturation of the output

voltage?

(i) 15 k (ii) 25 k (iii) 35 k

(b) What is the approximate value of the

saturation voltage?

11. Calculate the value of VO for the following situations.

V1

-

+V0

R1

Rf

R1(k) V1(V)

10 100 0.5

5 8 -1.4

5.4 0.4

1000 1.5

-1.8

-0.6

(i)

(ii)

(iii)

(iv)

Rf(k) V0(V)

+1.5V-

+V0

4 k

Rf

0 V

+12 V

-12 V

-15 V

-

+

+15 V

RA

R1

Rf

+5 V

V0

RA(k)

1 4 10 20

1.2 4.7 1.5 10

5 2 8.2 27

5 1 1 4

(a)

(b)

(c)

(d)

RB(k) R1(k) Rf(k)

RB

0 V

Answers


-

+

R1

Rf+5 V

0 V

V0V1

10 20 30 400

0.5

Time (ms)

-

+

-0.8 V

0 V

8 k

80 k

+15 V

-15 VV1

V0

-

+

10 k

100 k

+9 V

-9 VV1

V0

-

+

1 k

100 k

+15 V

-15 VV1

V0

Voltage (V)

12. Describe 3 ways to increase the

magnitude of the output voltage in

the circuit shown.

13. (a) Calculate the value of the

output voltage in the circuit

shown.

(b) If the value of Rf is doubled,

what would be the output

voltage?

14. (a) An operational amplifier can be

connected in different modes.

State the operating mode of the

amplifier shown.

(b) Calculate the gain of the circuit.

The graph shows how the voltage applied

to the input of the circuit varies with time.

(c) Using square ruled paper, draw a graph

showing how the output voltage varies with

time.

(d) Describe the output signal if the input voltage

is increased to 2 V.

(e) Both resistors have an uncertainty of ± 0.01 kΩ.

Which resistor will introduce the greatest

uncertainty into the gain calculation?

(f) What is the uncertainty in the gain?

15. (a) Calculate the gain of the circuit shown.

(b) Calculate the output voltage V0

for an input voltage of 15 mV.

(c) What happens to the gain of the circuit

if the feedback resistor is reduced.

Answers


-

+

+15 V

-15 VV1

V2V0

R1

R2

Rf

R3

V1 (V) Rf = R3

(k)

R1 = R2

(k)

2.5

1.5

0.4

6.0

4.5

3.0

1.3

0.4

7.2

100

30

10

40

10

5

100

3

5

6.6

-8.0

(a)

(b)

(c)

(d)

(e)

V2 (V) V0 (V)

-

+

V5 k

40 k

16 k

R

100 k

+1.5 V

0 V

10 k

A

B

-

+

V

LDR

10

k

10

k

0-10 k

10 k

10 k

100 k

100 k

+9 V

0 V

V2

V1

16. The circuit below shows an operational amplifier in the differential mode.

(a) What is the function of this circuit ?

(b) State the relationship that applies to this

circuit, giving the condition for this to

hold.

(c) Find the value of VO when

Rf = 10 M R1 = 10 k

R2 = 10 k R3 = 10 M

V1 = 480 mV V2 = 500 mV.

17. Calculate the unknown values in

the table for a differential

amplifier circuit.

18. (a) In the circuit below, what value should be chosen for R for it to operate as a

differential amplifier?

(b) Determine the reading on the voltmeter with the slider at position A.

(c) If the contact is moved to a position midway between A and B calculate the

voltmeter reading.

(d) Where should the contact be to produce an output voltage of

(i) -1.25 V (ii) 0 V.

19. The circuit opposite can be

shown to monitor the level

of brightness.

(a) Explain how it operates,

mentioning why the

voltmeter reading changes.

(b) What is the purpose of the

variable resistor?

Answers


20. (a) Calculate the gain of the circuit shown.

(b) At what value of (i) V0 (ii) V1 will the transistor switch on ?

(c) Write down a rule which will allow you to predict whether a transistor is on or

off. Remember the polarity of the base-emitter voltage is important.

21. State if the transistors below are switched on or off.

-

+

1 M

100

k

VVV1

V0

c

e

b

0 V

+6 V-Vs

(a)

-5 V

0 V

(e)

-5 V

-3 V

(c)

-5 V

0 V

(g)

-5 V

-2 V

(b)

+5 V

0 V

(f)

+5 V

+9 V

(d)

+5 V

0V

(h)

-5 V

-9 V

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