Capacitors  Multiple Choice
Q1. A 1μF capacitor is charged using a constant current of 10 μA for 20 s. What is the energy finally stored by the capacitor?
A 2 × 10^{3} J
B 2 × 10^{2} J
C 4 × 10^{2} J
D 4 × 10^{1} J
Q2. A capacitor of capacitance 10 μF is fully charged through a resistor R to a p.d. of 20V using the circuit shown below.
Which one of the following statements is incorrect?
A The p.d. across the capacitor is 20V.
B The p.d. across the resistor is 0V.
C The energy stored by the capacitor is 2mJ.
D The total energy taken from the battery during the charging process is 2 mJ.
Q3. A 10 mF capacitor is charged to 10V and then discharged completely through a small motor. During this process, the motor lifts a weight of mass 0.10 kg. If 10 % of the energy stored in the capacitor is used to lift the weight, through what approximate height will the weight be lifted?
A 0.05 m
B 0.10 m
C 0.50 m
D 1.00 m
Q4. A capacitor of capacitance 15 μF is fully charged and the potential difference across its plates is 8.0V. It is then connected into the circuit as shown below.
The switch S is closed at time t = 0. Which one of the following statements is correct?
A The time constant of the circuit is 6.0 ms.
B The initial charge on the capacitor is 12 μC.
C After a time equal to twice the time constant, the charge remaining on the capacitor is Q_{0}e^{2}, where Q_{0} is the charge at time t = 0.
D After a time equal to the time constant, the potential difference across the capacitor is 2.9V.
Q5. A capacitor of capacitance C discharges through a resistor of resistance R. Which one of the following statements is not true?
A The time constant will increase if R is increased.
B The time constant will decrease if C increased.
C After charging to the same voltage, the initial discharge current will increase if R is decreased.
D After charging to the same voltage, the initial discharge current will be unaffected if C is increased.
Q6. In the circuit shown below, the capacitor C is charged to a potential difference V when the switch S is closed.
Which line, A to D, in the table gives a correct pair of graphs showing how the charge and current change with time after S is closed?

CHARGE 
CURRENT 
A 
graph 1 
graph 1 
B 
graph 1 
graph 2 
C 
graph 2 
graph 1 
D 
graph 2 
graph 2 
Q7. The graph shows how the charge stored by a capacitor varies with the potential difference across it as it is charged from a 6V battery.
Which one of the following statements is not correct?
A The capacitance of the capacitor is 5.0 μF.
B When the potential difference is 2V the charge stored is 10 μC.
C When the potential difference is 2V the energy stored is 10 μJ.
D When the potential difference is 6V the energy stored is 180 μJ.
Q8. A capacitor of capacitance C stores an amount of energy E when the pd across it is V. Which line, A to D, gives the correct stored energy and pd when the charge is increased by 50% ?

energy 
p.d. 
A 
1.5E 
1.5V 
B 
2.25E 
1.5V 
C 
1.5E 
2.25V 
D 
2.25E 
2.25V 
Q9. How many of the following four equations correctly represent the energy E stored by a capacitor of capacitance C when it is charged to a pd V and its charge is Q?
E = ½ Q^{2}/C 
E = ½ C/V^{2} 
E = ½ QC 
E = ½ CV^{2} 
A one
B two
C three
D four
Q10. A voltage sensor and a datalogger are used to record the discharge of a 10 mF capacitor in series with a 500Ω resistor from an initial pd of 6.0V. The datalogger is capable of recording 1000 readings in 10s.
Which line, A to D, in the table gives the pd and the number of readings made after a time equal to the time constant of the discharge circuit?

potential difference/V 
number of readings 
A 
2.2 
50 
B 
3.8 
50 
C 
2.2 
500 
D 
3.8 
500 
Q11. When switch S in the circuit is closed, the capacitor C is charged by the battery to a pd V_{0}.
The switch is then opened until the capacitor pd decreases to 0.5 V_{0}, at which time S is closed
again. The capacitor then charges back to V_{0}.
Which graph best shows how the pd across the capacitor varies with time, t, after S is opened?
Q12. A 2.0 mF capacitor, used as the backup for a memory unit, has a potential difference of 5.0V
across it when fully charged. The capacitor is required to supply a constant current of 1.0μA
and can be used until the potential difference across it falls by 10%.
How long can the
capacitor be used for before it must be recharged?
A 
10 s 
B 
100 s 
C 
200 s 
D 
1000 s 
Q13. When a capacitor discharges through a resistor it loses 50% of its charge in 10 s. What is the
time constant of the capacitorresistor circuit?
A 
0.5 s 
B 
5 s 
C 
14 s 
D 
17 s 
Q14. An uncharged capacitor of fixed capacitance is connected in series with a switch and battery. The switch is closed at time t = 0.
Which graph, A to D, shows how the energy, E, stored by the capacitor, changes with time, t, after the switch is closed?
Q15.The voltage across a capacitor falls from 10 V to 5 V in 48 ms as it discharges through a resistor. What is the time constant of the circuit?
A 
24 ms 
B 
33 ms 
C 
69 ms 
D 
96 ms 
Q16. The graph shows how the charge stored by each of two capacitors, X and Y, increases as the pd across them increases. Which one of the following statements is correct?
A 
The capacitance of X is equal to that of Y. 
B 
The capacitance of Y is greater than that of X. 
C 
The capacitance of Y is less than that of X. 
D 
The capacitances of both X and Y are increasing. 
Q17. A 1000 μF capacitor and a 10 μF capacitor are charged so that the potential difference across each of them is the same. The charge stored in the 1000 μF capacitor is Q_{1} and the charge stored in the 10 μF capacitor is Q_{2}.
What is the ratio Q_{1}/Q_{2}?
Q18. The graph shows how the potential difference across a capacitor varies with the charge stored by it.
Which one of the following statements is correct?
A The gradient of the line equals the capacitance of the capacitor.
B The gradient of the line equals the energy stored by the capacitor.
C The reciprocal of the gradient equals the energy stored by the capacitor.
D The reciprocal of the gradient equals the capacitance of the capacitor.
Q19. An initially uncharged capacitor of capacitance 10 μF is charged by a constant current of 200 μA. After what time will the potential difference across the capacitor be 2000V?
A 50 s
B 100 s
C 200 s
D 400 s
Q20. A 1000 μF capacitor, X, and a 100 μF capacitor, Y, are charged to the same potential difference.
Which row, A to D, in the table gives correct ratios of charge stored and energy stored by the capacitors?

charge stored by X / charge stored by Y 
energy stored by X /energy stored by Y 
A 
1 
1 
B 
1 
10 
C 
10 
1 
D 
10 
10 