St Ivo School 1

1. In the circuit shown, the battery has negligible internal resistance.

A

6.0 V

30 Ω

60 Ω

X

Y

Calculate the current in the ammeter when

(a) the terminals X and Y are short-circuited i.e. connected together,

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(b) the terminals X and Y are connected to a 30 Ω resistor.

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(Total 6 marks)

St Ivo School 2

2. (a) Using the axes below, sketch the characteristic of a silicon semiconductor diode for

forward bias and reverse bias.

Indicate approximate values on the voltage axis.

I

V0

(4)

(b) Describe, with reference to the characteristic you have drawn, how the resistance of the

diode changes with the voltage across the diode.

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(Total 7 marks)

3. (a) A cell of emf ∈ and internal resistance r is connected in series to a resistor of resistance R

as shown. A current I flows in the circuit.

r

R

RV

∈

I

St Ivo School 3

(i) State an expression which gives ∈ in terms of I, r and R.

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(ii) Hence show how VR, the potential difference across the resistor, is related to ∈, I

and r.

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(b) A lamp, rated at 30 W, is connected to a 120 V supply.

(i) Calculate the current in the lamp.

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(ii) If the resistor in part (a) is replaced by the lamp described in part (b), determine

how many cells, each of emf 1.5 V and internal resistance 1.2 Ω, would have to be

connected in series so that the lamp would operate at its proper power.

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(Total 7 marks)

St Ivo School 4

4. A heating element, as used on the rear window of a car, consists of three strips of a resistive

material, joined, as shown in the diagram, by strips of copper of negligible resistance. The

voltage applied to the unit is 12 V and heat is generated at a rate of 40 W.

+ 12 V 0 V

copper

resistive material

(a) (i) Calculate the total resistance of the element.

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(ii) Hence show that the resistance of a single strip is about 11 Ω.

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(b) If each strip is 2.6 mm wide and 1.1 mm thick, determine the length of each strip.

resistivity of the resistive material = 4.0 × 10–5

Ω m

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(Total 8 marks)

St Ivo School 5

5. A sinusoidal alternating current (ac) source of frequency 50 Hz, is connected to a resistor of

resistance 2.0 kΩ and an oscilloscope, as shown. The rms current through the resistor is

5.0 mA.

oscilloscope2.0 kΩR50Hz

(a) Calculate the peak value of the voltage across R.

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..................................................................................................................................... (2)

(b) The grid represents the screen of the oscilloscope, each square being 1 cm × 1 cm. The

time base of the oscilloscope is set at 5 ms cm–1

and the voltage sensitivity is

4.0 V cm–1.

(i) Calculate the period of the ac signal.

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St Ivo School 6

(ii) Draw, on the grid, the signal you would expect to see on the oscilloscope. (4)

(Total 6 marks)

6. In the circuit shown, the battery has negligible internal resistance.

V

I

R

R

9.0 V

1

2

(a) (i) If the emf of the battery = 9.0 V, Rl = 120 Ω and R2 = 60 Ω, calculate the current I

flowing in the circuit.

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(ii) Calculate the voltage reading on the voltmeter.

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St Ivo School 7

(b) The circuit shown in the diagram acts as a potential divider. The circuit is now modified

by replacing R1 with a temperature sensor, whose resistance decreases as the temperature

increases.

Explain whether the reading on the voltmeter increases or decreases as the temperature

increases from a low value.

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(Total 7 marks)

St Ivo School 8

7. (a) The characteristic shown below is that of a filament lamp.

I

0 V

Explain why, as the voltage is increased either positively or negatively from zero, the

characteristic has the form shown in the figure.

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(b) At a certain point on the characteristic, the power developed in the lamp is 20 W and the

current is 90 mA. Calculate the resistance of the filament at this point on the

characteristic.

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(Total 7 marks)

St Ivo School 9

8. (a) The resistivity of a material in the form of a uniform resistance wire is to be measured.

The area of cross-section of the wire is known.

The apparatus available includes a battery, a switch, a variable resistor, an ammeter and a

voltmeter.

(i) Draw a circuit diagram using some or all of this apparatus, which would enable

you to determine the resistivity of the material.

(ii) Describe how you would make the necessary measurements, ensuring that you

have a range of values.

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St Ivo School 10

(iii) Show how a value of the resistivity is determined from your measurements.

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(b) A sheet of carbon-reinforced plastic measuring 80 mm × 80 mm × 1.5 mm has its two

large surfaces coated with highly conducting metal film. When a potential difference of

240V is applied between the metal films, there is a current of 2.0 mA in the plastic.

Calculate the resistivity of the plastic.

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St Ivo School 11

(c) If four of the units described in part (b) are connected as shown in the diagram, calculate

the total resistance of the combination.

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(Total 14 marks)

9. (a) The diagram shows the apparatus required for a simple experiment to measure the speed

of sound.

M

glass tube

1.5 m

A pulse of sound is sent down a hollow glass tube and is reflected at the sealed end of the

tube. A microphone, M, placed at the open end detects the initial pulse and, at a later

time, the reflected pulse. The microphone is connected to an oscilloscope which gives a

signal when the microphone detects a pulse of sound.

St Ivo School 12

The signal displayed on the oscilloscope screen is shown below.

initial pulse reflected pulse

If the time base of the oscilloscope is set to 2.0 ms per division, estimate the speed of

sound in air.

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..................................................................................................................................... (3)

St Ivo School 13

(b) Describe how the frequency of a sinusoidal alternating (ac) voltage source is measured

using an oscilloscope.

Your answer should include a sketch of the trace seen on the oscilloscope screen and

explain how the frequency is obtained from this trace.

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(Total 8 marks)

St Ivo School 14

10. A battery of emf 24 V and negligible intemal resistance is connected to a resistor network as

shown in the circuit diagram in the diagram below.

A B

30 Ω 40 Ω

60 Ω 120 Ω

24 VR1

(a) Show that the resistance of the single equivalent resistor that could replace the four

resistors between the points A and B is 50 Ω.

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(b) If R1 is 50 Ω, calculate

(i) the current in R1,

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St Ivo School 15

(ii) the current in the 60 Ω resistor.

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........................................................................................................................... (4)

(Total 8 marks)

11. (a) In the circuit shown in Figure 1, the battery has an emf of 12 V and negligible internal

resistance.

PQ is a potential divider, S being the position of the sliding contact. In the position

shown, the resistance between P and S is 180 Ω and the resistance between S and Q is 60

Ω.

V

12 V

I

P

S

Q

Figure 1

(i) Calculate the current, I, in the circuit, assuming that there is no current through the

voltmeter V.

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St Ivo School 16

(ii) What property of the voltmeter allows us to assume that no current flows through

it?

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(iii) What is the reading on the voltmeter?

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........................................................................................................................... (4)

(b) The circuit in Figure 1 is modified as shown in Figure 2, by exchanging the voltmeter

for a load R, whose resistance is about the same as the resistance of section SQ of the

potential divider.

12 V

I

P

S

Q R

Figure 2

St Ivo School 17

Explain, without calculation, why the current through the battery increases in value from

that in part (a).

You may be awarded marks for the quality of written communication in your answer.

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(Total 6 marks)

12. (a) The circuit shown in Figure 1 may be used to determine the internal resistance of a

battery. An oscilloscope is connected across the battery as shown. Figure 2 represents the

screen of the oscilloscope.

S

S

2

1

battery

14 Ω

oscilloscopeB

C

A

Figure 1 Figure 2

St Ivo School 18

The time base of the oscilloscope is switched off throughout the experiment. Initially the

switches S1 and S2 are both open. Under these conditions the spot on the oscilloscope

screen is at A.

(i) Switch S1 is now closed, with S2 remaining open. The spot moves to B. State what

the deflection AB represents.

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(ii) Switch S1 is kept closed and S2 is also closed. The spot moves to C. State what the

deflection AC represents.

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(iii) The vertical sensitivity of the oscilloscope is 0.50 V div–1. Calculate the current

through the 14 Ω resistor with both switches closed.

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(iv) Hence, calculate the internal resistance of the battery.

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........................................................................................................................... (6)

(b) The oscilloscope is now connected to an alternating voltage source of rms value 3.5 V.

(i) Calculate the peak value of the alternating voltage.

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St Ivo School 19

(ii) Draw on Figure 3 what you would expect to see on the oscilloscope screen, if the

time base is still switched off and the voltage sensitivity is altered to 2.0 V div–1

.

Figure 3 (3)

(Total 9 marks)

13. (a) A metal wire of length 1.4 m has a uniform cross-sectional area = 7.8 × 10–7 m2.

Calculate the resistance, R, of the wire.

resistivity of the metal = 1.7 × 10–8

Ωm

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St Ivo School 20

(b) The wire is now stretched to twice its original length by a process that keeps its volume

constant. If the resistivity of the metal of the wire remains constant, show that the

resistance increases to 4R.

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(Total 4 marks)

14. (a) On the axes in Figure 1 draw I –V characteristics for two components, A and B, both of

which obey Ohm’s law. Component B has a lower resistance than component A. Label

your characteristics clearly as A and B.

I

0V

Figure 1 (2)

St Ivo School 21

(b) On the axes in Figure 2 draw the I – V characteristic for a silicon semiconductor diode,

giving any relevant voltage values.

I

0V

Figure 2 (3)

St Ivo School 22

(c) Figure 3 shows the I – V characteristic of a filament lamp. Explain the shape of this

characteristic.

I

0V

Figure 3

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(Total 9 marks)

St Ivo School 23

15. Columns A and B show some of the results from an experiment in which the current I through a

component X was measured for various values of the potential difference V applied across it.

column A column B column C column D

potential difference V / V current I/ mA (V – 0.55) / V In (I / mA)

0.70 12.5

0.75 17.0

0.80 22.0

0.85 29.0

0.90 39.0

0.95 51.5

(a) Draw a diagram of a circuit which could have been used to obtain these results.

(2)

(b) (i) Calculate the resistance of X when the potential difference is 0.70 V.

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St Ivo School 24

(ii) By considering one other value of potential difference, explain whether or not X is

an ohmic conductor.

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........................................................................................................................... (3)

(c) It is suggested that for potential differences greater than 0.55 V, the current voltage

relationship for X is of the form.

I = A ek(V–0.55)

where A and k are constants.

(i) Complete column C and column D in the abive

(ii) Plot a graph of 1n (I /mA ) on the y-axis against (V – 0.55) on the x-axis.

(Allow one sheet of graph paper)

(iii) Use your graph to determine the constants k and A.

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St Ivo School 25

(iv) On the basis of your graph, discuss the validity of the above relationship.

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(Total 15 marks)

16. Four resistors, each having resistance of 50 Ω, are connected to form a square. A resistance

meter measured the resistance between different corners of the square. Determine the resistance

the meter records when connected between the following corners.

(a) Between A and C, as in Figure 1.

A

B

C

D

50Ω

50Ω

50Ω

50Ω

Figure 1

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..................................................................................................................................... (2)

St Ivo School 26

(b) Between A and B, as in Figure 2.

A

B

C

D

50Ω

50Ω

50Ω

50Ω

Figure 2

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(Total 5 marks)

17. In the circuit shown, the battery has an emf of 12 V and an internal resistance of 2.0 Ω. The

resistors A and B each have resistance of 30 Ω.

12 V2.0Ω

P QA B

Calculate

(i) the total current in the circuit,

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St Ivo School 27

(ii) the voltage between the points P and Q,

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(iii) the power dissipated in resistor A,

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(iv) the energy dissipated by resistor A in 20 s.

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18. (a) X and Y are two lamps. X is rated at 12 V, 24 W and Y at 6.0 V, 18 W. Calculate the

current through each lamp when it operates at its rated voltage.

X: ................................................................................................................................

Y: ................................................................................................................................ (2)

St Ivo School 28

(b) The two lamps are connected in the circuit shown. The battery has an emf of 27 V and

negligible internal resistance. The resistors R1 and R2 are chosen so that the lamps are

operating at their rated voltage.

R

R

1

2

Y

X27 V

V high resistancevoltmeter

(i) What is the reading on the voltmeter?

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(ii) Calculate the resistance of R2.

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(iii) Calculate the current through R1.

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(iv) Calculate the voltage across R1.

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St Ivo School 29

(v) Calculate the resistance of R1.

........................................................................................................................... (7)

(Total 9 marks)

19. (a) A student wishes to measure the resistance of a fixed length of uniform constantan wire.

The apparatus available includes a battery, a switch, a milliammeter and a voltmeter.

You may be awarded marks for the quality of written communication in your answer.

(i) Draw a circuit diagram using the apparatus listed above. Include in your diagram

an extra piece of apparatus which will enable a range of measurements to be made.

(ii) State how the student should make the necessary measurements, ensuring that a

range of readings is recorded.

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St Ivo School 30

(iii) Describe how the results would be used to determine an accurate value for the

resistance of the wire.

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(b) A heating element for an electric fire consists of a single strand of nichrome wire wound

around an insulator. The heater is required to produce 1.2 kW when connected to the

230 Vrms ac mains.

(i) Calculate the working resistance of the nichrome wire.

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(ii) Calculate the length of nichrome wire required to make the element.

cross-sectional area of the wire = 9.4 × 10–8

m2

resistivity of nichrome = 1.1 × 10–6 Ω m

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(Total 13 marks)

St Ivo School 31

20. (a) In the circuit in Figure 1, the battery, of emf 15 V and the negligible internal resistance,

is connected in series with two lamps and a resistor. The three components each have a

resistance of 12 Ω.

15 V 12 Ω

12 Ω12 Ω

Figure 1

(i) What is the voltage across each lamp?

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(ii) Calculate the current through the lamps.

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....................................................................................................................... (3)

(b) The two lamps are now disconnected and reconnected in parallel as shown in Figure 2.

12 Ω

12 Ω

15 V 12 Ω

Figure 2

St Ivo School 32

(i) Show that the current supplied by the battery is 0.83 A.

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(ii) Hence show that the current in each lamp is the same as the current in the lamps in

the circuit in Figure 1.

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(c) How does the brightness of the lamps in the circuit in Figure 1 compare with the

brightness of the lamps in the circuit in Figure 2?

Explain your answer.

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(Total 8 marks)

St Ivo School 33

21. The graph shows the I - V characteristics for two conductors, the tungsten filament of a lamp

and a length of constantan wire.

3.0

2.0

1.0

00 2 4 6 8 10 12

V/V

I/A

tungsten filament

constantan wire

(a) State, with a reason, which conductor obeys Ohm’s law across the full voltage range.

conductor: ..............................................................................................................

reason: .................................................................................................................... (2)

(b) (i) Calculate the resistance of the tungsten filament when V = 1 V and V = 10 V.

V = 1 V: ........................................................................................................

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V = 10 V: ......................................................................................................

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St Ivo School 34

(ii) Explain why the values of resistance, calculated in part (b)(i), differ from each

other.

You may be awarded marks for the quality of written communication in your

answer.

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....................................................................................................................... (4)

(c) Use the graph to determine the resistivity of constantan, given that the wire is 0.80 m long

with a uniform cross-sectional area of 6.8 × 10–8

m2.

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St Ivo School 35

(d) A student is required to obtain the I – V characteristic for a filament lamp using a

datalogger, so that the data can be fed into a computer to give a visual display of the

characteristic.

Draw a labelled circuit diagram for such an experiment.

(An account of the experiment is not required).

(3)

(Total 12 marks)

St Ivo School 36

22. An oscilloscope is connected to a sinusoidal ac source as shown in Figure 1.

The frequency and the voltage output of the ac source can be varied.

oscilloscopeac source

Figure 1

At a certain frequency the ac signal has an rms output of 7.1 V. Figure 2 shows the trace

obtained on the screen of the oscilloscope when one horizontal division corresponded to a time

of 5.0 ms.

5.0 ms

Figure 2

St Ivo School 37

(a) Calculate, for the signal shown in Figure 2,

(i) the peak voltage,

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(ii) the frequency.

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....................................................................................................................... (3)

(b) The voltage output and frequency of the signal are now changed so that the peak voltage

is 80 V and the frequency is 200 Hz.

State which two controls on the oscilloscope have to be altered so that four full cycles

again appear on the screen but the peak to peak distance occupies the full screen.

Determine the values at which these two controls have to be set.

control 1: ................................................................................................................

value of the setting: ................................................................................................

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control 2: ................................................................................................................

value of setting: ......................................................................................................

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................................................................................................................................. (5)

(Total 8 marks)

St Ivo School 38

23. In the circuit shown the battery has emf ∈ and internal resistance r.

2.4 Ω

V

S

r

(a) (i) State what is meant by the emf of a battery.

.......................................................................................................................

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(ii) When the switch S is open, the voltmeter, which has infinite resistance, reads 8.0

V. When the switch is closed, the voltmeter reads 6.0 V.

Determine the current in the circuit when the switch is closed.

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(iii) Show that r = 0.80 Ω.

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....................................................................................................................... (4)

(b) The switch S remains closed. Calculate

(i) the power dissipated in the 2.4 Ω resistor,

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St Ivo School 39

(ii) the total power dissipated in the circuit,

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(iii) the energy wasted in the battery in 2 minutes.

....................................................................................................................... (4)

(Total 8 marks)

24. A battery is connected across a uniform conductor. The current in the conductor is 40 mA.

(i) Calculate the total charge that flows past a point in the conductor in 3 minutes.

……….........................................................................................................................

……….........................................................................................................................

……….........................................................................................................................

(ii) Using data from the Data Sheet calculate the number of electron charge carriers passing

the same point in the conductor in this time.

……….........................................................................................................................

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(iii) If 8.6 J of energy are transferred to the conductor in this time, calculate the potential

difference across the conductor.

……….........................................................................................................................

……….........................................................................................................................

……….........................................................................................................................

St Ivo School 40

(iv) Calculate the resistance of the conductor.

……….........................................................................................................................

………......................................................................................................................... (Total 6 marks)

25. (a) Figure 1 shows two possible arrangements of connecting three resistors, each resistor

having a resistance of 40 Ω.

(i) (ii)

Figure 1

Calculate the equivalent resistance in each case.

(i) ...........................................................................................................................

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(ii) ...........................................................................................................................

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........................................................................................................................... (3)

St Ivo School 41

(b) The designer of a heating element for the rear window of a car decides to connect six

separate heating elements together as shown in Figure 2. Each element has a resistance of

6.0 Ω and the unit is connected to a 12 V dc supply having zero internal resistance.

12 V

Figure 2

(i) Calculate the current in each single element.

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(ii) With the aid of a similar calculation give a reason why the heater would not be as

effective if all six were connected in series.

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........................................................................................................................... (5)

(Total 8 marks)

3

St Ivo School 42

26. In the circuit shown, a battery of emf ∈ and internal resistance r is connected to a variable

resistor R. The current I and the voltage V are read by the ammeter and voltmeter respectively.

A

V

R

r∈

(a) The emf is related to V, I and r by the equation

∈ = V + Ir

Rearrange the equation to give V in terms of ∈, I and r.

................................................................................................................................… (1)

(b) In an experiment, the value of R is altered so that a series of values of V and the

corresponding values of I are obtained. Using the axes, sketch the graph you would

expect to obtain as R is changed.

V

I (2)

St Ivo School 43

(c) State how the values of ∈ and r may be obtained from the graph.

∈ .................................................................................................................................

r .................................................................................................................................. (2)

(Total 5 marks)

27. (a) Give an expression for the resistivity of a material in the form of a uniform wire.

Define all the symbols used.

................................................................................................................................…

...............................................................................................................................…

................................................................................................................................… (2)

(b) A thin film of carbon may be used in some electronic systems. Typical dimensions of

such a film are shown in Figure 1.

I I8.0 × 10 m

30 × 10 m

2.0 × 10 m

–3

–3

–6

Figure 1

(i) Calculate the resistance of the carbon film to a current I passing through it as

shown in Figure 1.

resistivity of carbon = 4.0 × 10–5 Ω m

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St Ivo School 44

(ii) Without recalculating the resistance of the carbon film, explain how you would

expect the resistance to change if the current flowed as in Figure 2. You should

consider the numerical ratio or factor by which each dimension affecting the

resistance has changed.

You may be awarded marks for the quality of written communication in your

answer.

I

I

Figure 2

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........................................................................................................................... (4)

(Total 6 marks)

St Ivo School 45

28. A student carried out an experiment to investigate how the resistance of a coil made from iron

wire varied as its temperature changed. In the experiment, a constant potential difference of 2.00

V was maintained across the coil as the student measured the current through it at various

temperatures.

(a) Draw a circuit diagram to show how such measurements could be made using a 3.0 V

battery and other necessary apparatus.

(3)

(b) The results are shown in the table.

temperature θ/ °C p.d. across the

coil /V

current /mA resistance R / Ω

10 2.00 790

20 2.00 740

35 2.00 680

50 2.00 620

65 2.00 590

80 2.00 550

The resistance, R, of a metal wire varies with temperature according to the equation

R = R0 (1 + αθ)

where R0 is the resistance of the wire at 0 °C, θ is the temperature of the wire in °C, and α

is a constant which depends on the material from which the wire is made.

St Ivo School 46

(i) Complete the table to show the value of the resistance, R, of the iron coil at each

temperature.

(ii) Use the data to plot a graph to confirm the equation.

(One sheet of graph paper should be provided.) (6)

(c) (i) Use your graph to determine the value of the resistance of the coil at 0 °C (R0).

...........................................................................................................................

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(ii) Use your graph to determine the value of the constant α and state its unit.

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........................................................................................................................... (5)

St Ivo School 47

(d) Explain why the resistance of a metal wire changes when its temperature is increased.

You may be awarded marks for the quality of written communication in your answer.

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(Total 16 marks)

29. In the circuit shown in Figure 1, the battery, of emf 6.0V, has negligible internal resistance.

6.0 V

S

A

20 Ω

60 Ω

Figure 1

St Ivo School 48

(a) Calculate the current through the ammeter when the switch S is

(i) open,

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.............................................................................................................................

.............................................................................................................................

(ii) closed.

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............................................................................................................................. (3)

(b) The switch S is now replaced with a voltmeter of infinite resistance.

Determine the reading on the voltmeter.

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....................................................................................................................................... (2)

(Total 5 marks)

St Ivo School 49

30. (a) The graph in Figure 1 shows the I − V characteristic for a semiconductor diode.

B O

A

V

I

Figure 1

In order to produce this characteristic in the laboratory, a student is given suitable

apparatus, including a data logger. The output of the data logger is connected to a

computer to give a visual display.

(i) Draw a labelled circuit diagram of the apparatus that would be used to obtain the

characteristic from O to A in Figure 1.

St Ivo School 50

(ii) Describe how the apparatus would be used.

You may be awarded marks for the quality of written communication in your

answer.

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(iii) What change would have to be made to the circuit in order to obtain the

characteristic from O to B in Figure 1?

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............................................................................................................................. (6)

(b) On the axes in Figure 2 draw the characteristic for a filament lamp.

V

I

0

Figure 2

Explain why the I − V characteristic has the shape you have drawn.

St Ivo School 51

You may be awarded marks for the quality of written communication in your answer.

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(Total 11 marks)

31. The graph shows how the resistance, RR, of a metal resistor and the resistance, RTh, of a

thermistor change with temperature.

200

150

100

50

00 100 200 300

temperature/°C

resistance/Ω

resistor

thermistor

St Ivo School 52

(a) Give the values of the resistance RR and RTh at a temperature of 200°C.

RR ..............................................................RTh ....................................................................

(1)

(b) The resistor and thermistor are connected in series to a 12V battery of negligible internal

resistance, as shown in Figure 1.

12 V A

B

Figure 1

(i) Calculate the voltage across the terminals AB when both the resistor and thermistor

are at 200°C.

.............................................................................................................................

.............................................................................................................................

.............................................................................................................................

(ii) Assuming that the temperature of the resistor always equals the temperature of

the thermistor, deduce the temperature when the voltage across the resistor equals

the voltage across the thermistor.

.............................................................................................................................

.............................................................................................................................

............................................................................................................................. (4)

St Ivo School 53

(c) A lamp and a switch are now connected across the terminals AB, as shown in Figure 2.

The temperature of the thermistor does not change from that obtained in part (b)(ii).

12 VA

B

lamp

S

Figure 2

(i) The lamp is rated at 2.0 W at a voltage of 6.0 V. Calculate the resistance of the

lamp at this rating.

.............................................................................................................................

.............................................................................................................................

(ii) The switch S is now closed. Explain, without calculation, why the voltage across

the thermistor will fall from the value in part (b)(ii).

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............................................................................................................................. (4)

(Total 9 marks)

St Ivo School 54

32. (a) For a conductor in the form of a wire of uniform cross-sectional area, give an equation

which relates its resistance to the resistivity of the material of the conductor.

Define the symbols used in the equation.

.......................................................................................................................................

.......................................................................................................................................

....................................................................................................................................... (2)

(b) (i) An electrical heating element, made from uniform nichrome wire, is required

to dissipate 500 W when connected to the 230 V mains supply.

The cross-sectional area of the wire is 8.0 × 10−8

m2. Calculate the length of

nichrome wire required.

resistivity of nichrome = 1.1 × 10−6

Ω m

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.............................................................................................................................

.............................................................................................................................

.............................................................................................................................

.............................................................................................................................

.............................................................................................................................

St Ivo School 55

(ii) Two heating elements, each rated at 230 V, 500 W are connected to the 230 mains

supply

(A) in series,

(B) in parallel.

Explain why only one of the circuits will provide an output of 1 kW.

.............................................................................................................................

.............................................................................................................................

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............................................................................................................................. (6)

(Total 8 marks)

33. A sinusoidal alternating voltage source of frequency 500 Hz is connected to a resistor of

resistance 2.0 kΩ and an oscilloscope, as shown in Figure 1.

2.0 kΩ500 Hz oscilloscope

Figure 1

(a) The rms current through the resistor is 5.3 mA. Calculate the peak voltage across the

resistor.

.......................................................................................................................................

.......................................................................................................................................

....................................................................................................................................... (2)

St Ivo School 56

(b) The settings on the oscilloscope are

timebase: 250 µs per division,

voltage sensitivity: 5.0 V per division.

Draw on the grid, which represents the screen of the oscilloscope, the trace that would

be seen.

.......................................................................................................................................

.......................................................................................................................................

(4)

(Total 6 marks)

St Ivo School 57

34. A student investigates the variation of electric potential with distance along a strip of

conducting paper of length l and of uniform thickness. The strip tapers uniformly from a

width 4w at the broad end to 2w at the narrow end, as shown in Figure 1. A constant pd is

applied across the two ends of the strip, with the narrow end at positive potential, Vl, and the

broad end at zero potential. The student aims to produce a graph of pd against distance x,

measured from the broad end of the strip.

4w 2wx

l

Figure 1

(a) Draw a labelled circuit diagram which would be suitable for the investigation.

(2)

(b) The student obtained some preliminary measurements which are shown below.

pd, V/V 0 2.1 4.5 7.2

Distance, x/m 0 0.100 0.200 0.300

St Ivo School 58

By reference to the physical principles involved, explain why the increase of V with x

is greater than a linear increase.

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.......................................................................................................................................

.......................................................................................................................................

....................................................................................................................................... (4)

(c) The potential, V, at a distance x from the broad end is given by

V = k − 1.44Vl ln (2l − x),

where Vl is the potential at the narrow end, and k is a constant.

(i) The student’s results are given below. Complete the table.

l = 0.400 m

distance x/m potential V/V (2l − x)/m 1n (2l − x)

0.100 2.1 0.700 − 0.357

0.200 4.5

0.270 6.4

0.330 8.3

0.360 9.3

0.380 10.1

St Ivo School 59

(ii) Plot a graph of V against ln (2l − x) and explain whether or not it confirms the

equation.

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(iii) Use the graph to calculate Vl.

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............................................................................................................................. (10)

(Total 16 marks)

35. (a) A set of decorative lights consists of a string of lamps. Each lamp is rated at 5.0 V,

0.40 W and is connected in series to a 230 V supply.

Calculate

(i) the number of lamps in the set, so that each lamp operates at the correct rating,

...........................................................................................................................

...........................................................................................................................

(ii) the current in the circuit,

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...........................................................................................................................

St Ivo School 60

(iii) the resistance of each lamp,

...........................................................................................................................

...........................................................................................................................

(iv) the total electrical energy transferred by the set of lights in 2 hours.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (5)

(b) When assembled at the factory, one set of lights inadvertently contains 10 lamps too

many. All are connected in series. Assume that the resistance of each lamp is the same as

that calculated in part (a) (iii).

(i) Calculate the current in this set of lights when connected to a 230 V supply.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(ii) How would the brightness of each lamp in this set compare with the brightness of

each lamp in the correct set?

........................................................................................................................... (3)

(Total 8 marks)

St Ivo School 61

36. (a) A student is given three resistors of resistance 3.0 Ω, 4.0 Ω and 6.0 Ω respectively.

(i) Draw the arrangement, using all three resistors, which will give the largest

resistance.

(ii) Calculate the resistance of the arrangement you have drawn.

...........................................................................................................................

...........................................................................................................................

(iii) Draw the arrangement, using all three resistors, which will give the smallest

resistance.

(iv) Calculate the resistance of the arrangement you have drawn.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (5)

St Ivo School 62

(b) The three resistors are now connected to a battery of emf 12 V and negligible internal

resistance, as shown in Figure 1.

3.0 Ω

6.0 Ω

4.0 Ω

12 V

Figure 1

(i) Calculate the total resistance in the circuit.

...........................................................................................................................

...........................................................................................................................

(ii) Calculate the voltage across the 6.0 Ω resistor.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(Total 9 marks)

St Ivo School 63

37. (a) In the circuit shown in Figure 1, the battery has an emf of 6.0 V. With the switch closed

and the lamp lit, the reading on the voltmeter is 5.4 V.

= 6.0 V lampV

Figure 1

Explain without calculation, why the voltmeter reading is less than the emf of the battery.

You may be awarded marks for the quality of written communication in your answer.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(b) A torch is powered by two identical cells each having an emf of 1.5 V and an internal

resistance r. The cells are connected in series. The torch bulb is rated at 1.6 W and the

voltage across it is 2.5 V.

(i) Draw the circuit described.

St Ivo School 64

(ii) Calculate the internal resistance of each cell.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (5)

(c) In the circuit in Figure 2 the cell has emf ∈ and internal resistance r. The voltage V

across the cell is read on the voltmeter which has infinite resistance, and the current I

through the variable resistor R is read on the ammeter.

rcell

RV

A

Figure 2

St Ivo School 65

By altering the value of the variable resistor R, a set of values of V and I is obtained.

These values, when plotted, give the graph shown in Figure 3.

V

I0

Figure 3

Show how the values of ∈ and r may be obtained from this graph. Explain your method.

.....................................................................................................................................

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.....................................................................................................................................

..................................................................................................................................... (3)

(Total 11 marks)

St Ivo School 66

38. The graph shows how the current through a thermistor varies with the potential difference

across it.

0.6

0.4

0.2

00 5 10 15 20

potential difference/V

current/mA

(a) Draw the circuit of an experimental arrangement which could be used to collect the data

necessary to produce this graph. On your circuit diagram label clearly a component which

would enable the current to be changed continuously across the range.

(4)

(b) (i) Using information obtained from the graph, calculate the resistances of the

thermistor when the current is 0.10 mA and also when the current is 0.60 mA.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

St Ivo School 67

(ii) Using the results of part (b) (i) deduce how the resistance of the thermistor changes

as its temperature increases.

You may be awarded marks for the quality of written communication in your

answer.

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........................................................................................................................... (5)

(Total 9 marks)

39. (a) A steady current of 0.25 A passes through a torch bulb for 6 minutes.

Calculate the charge which flows through the bulb in this time.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

St Ivo School 68

(b) The torch bulb is now connected to a battery of negligible internal resistance. The battery

supplies a steady current of 0.25 A for 20 hours. In this time the energy transferred in the

bulb is 9.0 × 104

J. Calculate

(i) the potential difference across the bulb,

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(ii) the power of the bulb.

............................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 5 marks)

40. In the circuit shown in the figure below, the battery, of negligible internal resistance, is

connected to two resistors which form a potential divider.

A

12 V

110 Ω

X

Y

160 Ω

St Ivo School 69

(a) (i) Calculate the current through the ammeter.

...........................................................................................................................

(ii) A 20 Ω resistor is now connected between X and Y. State and explain, without

further calculation, whether the current through the ammeter will increase or

decrease.

You may be awarded marks for the quality of written communication in your

answer.

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........................................................................................................................... (4)

(b) The 20 Ω resistor is now removed and replaced with a voltmeter. Stating the assumption

made, show that the reading on the voltmeter is 4.9 V.

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.....................................................................................................................................

..................................................................................................................................... (2)

(c) The voltmeter is now removed and the terminals X and Y joined together with a wire.

Calculate the reading on the ammeter.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(Total 8 marks)

St Ivo School 70

41. (a) A student wishes to measure the resistivity of the material of a uniform resistance wire.

The available apparatus includes a battery, a switch, a variable resistor, an ammeter and a

voltmeter.

(i) Draw a circuit diagram which incorporates some or all of this apparatus and which

enables the student to determine the resistivity of the material.

(ii) State the measurements which must be made to ensure that a reliable value of the

resistivity is obtained.

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(iii) Explain how a value of the resistivity would be obtained from the measurements.

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........................................................................................................................... (10)

St Ivo School 71

(b) A wire made from tin with cross-sectional area 7.8 × 10–9 m2, has a pd of 2.0 V across it.

Calculate the minimum length of wire needed so that the current through it does not

exceed 4.0 A.

resistivity of tin = 1.1 × 10–7 Ω m

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.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(Total 12 marks)

42. A battery of emf ∈ and internal resistance r is connected in series to a variable resistor R and

an ammeter of negligible resistance. A voltmeter is connected across R, as shown in the figure

below.

r

R

A

V

(a) (i) State what is meant by the emf of the battery.

...........................................................................................................................

...........................................................................................................................

(ii) The reading on the voltmeter is less than the emf. Explain why this is so.

...........................................................................................................................

........................................................................................................................... (2)

St Ivo School 72

(b) A student wishes to measure ∈ and r. Using the circuit shown in the figure above the

value of R is decreased in steps and at each step the readings V and I on the voltmeter and

ammeter respectively are recorded. These are shown in the table.

reading on voltmeter/V reading on ammeter/A

8.3 0.07

6.8 0.17

4.6 0.33

2.9 0.44

0.3 0.63

(i) Give an expression relating V, I, ∈ and r.

...........................................................................................................................

(ii) Draw a graph of V (on the y-axis) against I (on the x-axis) on graph paper.

(Allow one sheet of graph paper)

(iii) Determine the values of ∈ and r from the graph, explaining your method.

∈ : .....................................................................................................................

...........................................................................................................................

r: ........................................................................................................................

........................................................................................................................... (8)

(Total 10 marks)

St Ivo School 73

43. (a) On the axes below draw the I – V characteristic for a silicon semiconductor diode in both

forward bias and reverse bias. Indicate any relevant voltage values on the axis.

I

V

(4)

(b) The figure below shows the I – V characteristic for a filament lamp. Explain the shape of

the characteristic.

I

V

St Ivo School 74

You may be awarded additional marks to those shown in brackets for the quality of

written communication in your answer.

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..................................................................................................................................... (4)

(Total 8 marks)

44. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf

of 30 V. The pd across the lamp is 6.0 V and its resistance is 12 Ω.

10 Ω

18 Ω

15 Ω

30 V

12 Ω

A B

(a) Show that the total resistance of the circuit is 20 Ω.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

St Ivo School 75

(b) Calculate

(i) the current supplied by the battery,

...........................................................................................................................

...........................................................................................................................

(ii) the pd between the points A and B,

...........................................................................................................................

...........................................................................................................................

(iii) the current in the lamp.

...........................................................................................................................

........................................................................................................................... (4)

(c) (i) What is the power of the lamp, in W?

...........................................................................................................................

...........................................................................................................................

(ii) What percentage of the power supplied by the battery is dissipated in the lamp?

...........................................................................................................................

........................................................................................................................... (3)

(Total 10 marks)

St Ivo School 76

45. The battery of an electric car consists of 30 cells, connected in series, to supply current to the

motor, as shown in the figure below.

M

(a) Assume that the internal resistance of each cell is negligible and that the pd across each

cell is 6.0 V.

(i) State the pd across the motor.

...........................................................................................................................

(ii) The battery provides 7.2 kW to the motor when the car is running. Calculate the

current in the circuit.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(iii) The battery can deliver this current for two hours. Calculate how much charge the

battery delivers in this time.

...........................................................................................................................

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St Ivo School 77

(iv) Calculate the energy delivered to the motor in the two hour period.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (7)

(b) In practice, each cell has a small but finite internal resistance. Explain, without

calculation, the effect of this resistance on

• the current in the circuit, and

• the time for which the battery can deliver the current in part (a)(ii).

You may assume that the motor behaves as a constant resistance.

You may be awarded additional marks to those shown in brackets for the quality of

written communication in your answer.

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.....................................................................................................................................

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.....................................................................................................................................

..................................................................................................................................... (3)

(Total 10 marks)

St Ivo School 78

46. The circuit in Figure 1 shows a sinusoidal ac source connected to two resistors, R1 and R2,

which form a potential divider. Oscilloscope 1 is connected across the source and oscilloscope

2 is connected across R2.

Figure 1

oscilloscope 2R2

oscilloscope 1

R1

(a) Figure 2 shows the trace obtained on the screen of oscilloscope 1. The time base of the

oscilloscope is set at 10 m s per division and the voltage sensitivity at 15 V per division.

Figure 2

For the ac source, calculate

(i) the frequency,

...........................................................................................................................

...........................................................................................................................

St Ivo School 79

(ii) the rms voltage.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(b) The resistors have the following values: R1 = 450 Ω and R2 = 90 Ω.

Calculate

(i) the rms current in the circuit,

...........................................................................................................................

(ii) the rms voltage across R2.

............................................................................................................................. (2)

(c) Oscilloscope 2 is used to check the calculated value of the voltage across R2. The screen

of oscilloscope 2 is identical to that of oscilloscope 1 and both are set to the same time

base. Oscilloscope 2 has the following range for voltage sensitivity: 1 V per div., 5 V per

div., 10 V per div. and 15 V per div.

State which voltage sensitivity would give the most suitable trace. Explain the reasons for

your choice.

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........................................................................................................................................

........................................................................................................................................

........................................................................................................................................ (3)

(Total 9 marks)