1. The graph below shows the current/voltage characteristics of a filament lamp.
24
16
–3
Current / × 10 A
8
0
0 2 4 6 8 10
Voltage / V
The resistance of the filament at 4.0 V is
A. 250 Ω.
B. 4 000 Ω.
C. 8 000 Ω.
D. 64 000 Ω.
(1)
2. The variation with potential difference V of the current I in an electric lamp is shown below.
P
Ip
0
0 Vp V
1
At point P, the current is Ip, the potential difference is Vp and the gradient of the tangent to the
curve is G. What is the resistance of the lamp at point P?
1
A.
G
B. G
Ip
C.
Vp
Vp
D.
Ip
(1)
2
3. A cell of emf E and internal resistance r is connected to a variable resistor. A voltmeter is
connected so as to measure the potential difference across the terminals of the cell. Which one
of the following is the correct circuit diagram of the arrangement?
A. E B. E r
C. E r D. E r
V V
(1)
4. This question compares the electrical properties of two 12 V filament lamps.
A lamp is designed to operate at normal brightness with a potential difference of 12 V across its
filament. The current in the filament is 0.50 A.
(a) For the lamp at normal brightness, calculate
(i) the power dissipated in the filament.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
3
(ii) the resistance of the filament.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
In order to measure the voltage-current (V-I) characteristics of a lamp, a student sets up the
following electrical circuit.
12 V battery
(b) On the circuit above, add circuit symbols showing the correct positions of an ideal
ammeter and an ideal voltmeter that would allow the V-I characteristics of this lamp to be
measured.
(2)
The voltmeter and the ammeter are connected correctly in the previous circuit.
(c) Explain why the potential difference across the lamp
(i) cannot be increased to 12 V.
...........................................................................................................................
...........................................................................................................................
(2)
4
(ii) cannot be reduced to zero.
...........................................................................................................................
...........................................................................................................................
(2)
An alternative circuit for measuring the V-I characteristic uses a potential divider.
(d) (i) Draw a circuit that uses a potential divider to enable the V-I characteristics of the
filament to be found.
(3)
(ii) Explain why this circuit enables the potential difference across the lamp to be
reduced to zero volts.
...........................................................................................................................
...........................................................................................................................
(2)
5
The graph below shows the V-I characteristic for two 12 V filament lamps A and B.
Potential
lamp A lamp B
difference 12
/V
0
0 0.5 1.0
current / A
(e) (i) Explain why these lamps do not obey Ohm’s law.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii) State and explain which lamp has the greater power dissipation for a potential
difference of 12 V.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
6
The two lamps are now connected in series with a 12 V battery as shown below.
12 V battery
lamp A lamp B
(f) (i) State how the current in lamp A compares with that in lamp B.
...........................................................................................................................
...........................................................................................................................
(1)
(ii) Use the V-I characteristics of the lamps to deduce the total current from the battery.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(4)
(iii) Compare the power dissipated by the two lamps.
...........................................................................................................................
...........................................................................................................................
(2)
(Total 25 marks)
7
5. Which one of the following shows a correct circuit, using ideal voltmeters and ammeters, for
measuring the I-V characteristic of a filament lamp?
A. B.
A
A
V V
C. D.
A A
V V
(1)
6. This question is about electrical energy and associated phenomena.
Current electricity
A cell of electromotive force (emf) E and internal resistance r is connected in series with a
resistor R, as shown below.
E r
The cell supplies 8.1 × 103 J of energy when 5.8 × 103 C of charge moves completely round the
circuit. The current in the circuit is constant.
8
(i) Calculate the emf E of the cell.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii) The resistor R has resistance 6.0 Ω. The potential difference between its terminals is
1.2 V. Determine the internal resistance r of the cell.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(iii) Calculate the total energy transfer in the resistor R.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(iv) Describe, in terms of a simple model of electrical conduction, the mechanism by which
the energy transfer in the resistor R takes place.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(5)
(Total 12 marks)
7. In the circuit shown, the voltmeter has a resistance of 20 kΩ and the battery has an emf of 6.0 V
and negligible internal resistance.
9
6.0 V
10 k 20 k
V
20 k
The reading on the voltmeter is
A. 2.0 V.
B. 3.0 V.
C. 4.0 V.
D. 6.0 V.
(1)
10
8. This question is about electric circuits.
Susan sets up the circuit below in order to measure the current-voltage (I-V) characteristic of a
small filament lamp.
3.0 V
V
The supply is a battery that has an emf of 3.0 V and the ammeter and voltmeter are considered
to be ideal. The lamp is labelled by the manufacturer as “3 Volts, 0.6 Watts”.
(a) (i) Explain what information this labelling provides about the normal operation of the
lamp.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
11
(ii) Calculate the current in the filament of the lamp when it is operating at normal
brightness.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
Susan sets the variable resistor to its maximum value of resistance. She then closes the switch S
and records the following readings.
Ammeter reading = 0.18 A Voltmeter reading = 0.60 V
She then sets the variable resistor to its zero value of resistance and records the following
readings.
Ammeter reading = 0.20 A Voltmeter reading = 2.6 V
(b) (i) Explain why, by changing the value of the resistance of the variable resistance, the
potential difference across the lamp cannot be reduced to zero or be increased to
3.0 V.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
12
(ii) Determine the internal resistance of the battery.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(c) Calculate the resistance of the filament when the reading on the voltmeter is
(i) 0.60 V.
...........................................................................................................................
...........................................................................................................................
(1)
(ii) 2.6 V.
...........................................................................................................................
...........................................................................................................................
(1)
(d) Explain why there is a difference between your answers to (c)(i) and (c)(ii).
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
13
(e) Using the axes below, draw a sketch-graph of the I-V characteristic of the filament
of the lamp. (Note: this is a sketch-graph; you do not need to add any values to the
axes.)
0
0 V
(1)
The diagram below shows an alternative circuit for varying the potential difference across the
lamp.
Y
3.0 V
The potential divider XZ has a potential of 3.0 V across it. When the contact is at the position
Y, the resistance of XY equals the resistance of YZ which equals 12 Ω. The resistance of the
lamp is 4 Ω.
14
(f) Calculate the potential difference across the lamp.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(4)
(Total 18 marks)
9. This question is about emf and internal resistance.
A dry cell has an emf E and internal resistance r and is connected to an external circuit. There is
a current I in the circuit when the potential difference across the terminals of the cell is V.
E
I
(a) State expressions, in terms of E, V, r and I where appropriate, for
(i) the total power supplied by the cell;
...........................................................................................................................
(1)
(ii) the power dissipated in the cell;
...........................................................................................................................
(1)
15
(iii) the power dissipated in the external circuit.
...........................................................................................................................
(1)
(b) Use your answers to (a) to derive a relationship between V, E, I and r.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
16
The graph below shows the variation of V with I for the dry cell.
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.90
0.80
V/V
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.0
0.0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.0 1.1 1.2 1.3
I/A
17
(c) Complete the diagram below to show the circuit that could be used to obtain the data
from which the graph was plotted.
(3)
(d) Use the graph, explaining your answers, to
(i) determine the emf E of the cell;
...........................................................................................................................
...........................................................................................................................
(2)
(ii) determine the current in the external circuit when the resistance R of the external
circuit is very small;
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
18
(iii) deduce that the internal resistance r of the cell is about 1.2 Ω.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(e) The maximum power dissipated in the external circuit occurs when the resistance of the
external circuit has the same value as the internal resistance of the cell. Calculate the
maximum power dissipation in the external circuit.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(Total 18 marks)
19
