 # 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 Q0e2, where Q0 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 Q2/C E = ½ C/V2 E = ½ QC E = ½ CV2

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 V0.
The switch is then opened until the capacitor pd decreases to 0.5 V0, at which time S is closed
again. The capacitor then charges back to V0. 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 capacitor-resistor 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 Q1 and the charge stored in the 10 μF capacitor is Q2.

What is the ratio Q1/Q2?

 A 100 B 10 C 1 D 0.01

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 