P.3.7.4.4 Capacitor charge and discharge

A capacitor of capacitance 120 μF is charged and then discharged through a 20 kΩ resistor. What fraction of the original charge remains on the capacitor 4.8 s after the discharge begins?

• 0.14

• 0.37

• 0.63

• 0.86

A 500 µF capacitor is charged to a pd of 10.0 V. It is then discharged through a 100 kΩ resistor.

What is the time taken for the pd to fall from 10.0 V to 5.0 V?

• 35 s

• 50 s

• 72 s

• 100 s

A voltage sensor and a datalogger are used to record the discharge of a 10 mF capacitor in series with a 500 Ω resistor from an initial pd of 6.0 V. The datalogger is capable of recording 1000 readings in 10 s.

After a time equal to the time constant of the discharge circuit, which one of the rows gives the pd and the number of readings made?

• Potential difference / V: 2.2

  Number of readings: 50

• Potential difference / V: 3.8

  Number of readings: 50

• Potential difference / V: 3.8

  Number of readings: 500

• Potential difference / V: 2.2

  Number of readings: 500

The capacitor in the circuit is initially uncharged. The switch S is closed at time t = 0.

Which pair of graphs, A to D, correctly shows how the pd across the capacitor and the current in the circuit change with time?

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• 
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When fully charged the 2.0 mF capacitor used as a backup for a memory unit has a potential difference of 5.0 V across it. The capacitor is required to supply a constant current of 1.0 μA and can be used until the potential difference across it falls by 10%. For how long can the capacitor be used before it must be recharged?

• 10 s

• 100 s

• 200 s

• 1000 s

Switch S in the circuit is held in position 1, so that the capacitor C becomes fully charged to a pd V and stores energy E. The switch is then moved quickly to position 2, allowing C to discharge through the fixed resistor R. It takes 36 ms for the pd across C to fall to V/2.

What period of time must elapse, after the switch has moved to position 2, before the energy stored by C has fallen to E/16?

• 51 ms

• 72 ms

• 432 ms

• 576 ms

In the circuit shown the capacitor C charges when switch S is closed. Which line, A to D, in the table gives a correct pair of graphs showing how the charge on the capacitor and the current in the circuit change with time after S is closed?

• A

• B

• C

• D

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?

• 24 ms

• 33 ms

• 69 ms

• 96 ms

A voltage sensor and a datalogger are used to record the discharge of a 10 mF capacitor in series with a 500 Ω resistor from an initial pd of 6.0 V. The datalogger is capable of recording 1000 readings in 10 s. Which line gives the pd and the number of readings made after a time equal to the time constant of the discharge circuit?

• potential difference/V: 2.2

  number of readings: 50

• potential difference/V: 3.8

  number of readings: 50

• potential difference/V: 3.8

  number of readings: 500

• potential difference/V: 2.2

  number of readings: 500

When a 220 μF capacitor is discharged through a resistor R, the capacitor pd decreases from 6.0 V to 1.5 V in 92 s.

What is the resistance of R?

• 210 kΩ

• 300 kΩ

• 420 kΩ

• 440 kΩ