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% ?

 

 

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?

 

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?

 

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?

 

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?

 

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?

 

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?