P.3.7.4.3 Energy stored by a capacitor

A capacitor of capacitance C has a charge of Q stored on the plates. The potential difference between the plates is doubled.

What is the change in the energy stored by the capacitor?

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The initial charge stored by a capacitor of capacitance 0.50 µF is 2.0 µC. The capacitor is then discharged through a resistor.

How much energy is stored by the capacitor after a time equal to one time constant?

• 0.06 µJ

• 0.54 µJ

• 1.0 µJ

• 4.0 µJ

Which of the following statements about a parallel plate capacitor is incorrect?

• The capacitance of the capacitor is the amount of charge stored by the capacitor when the pd across the plates is 1 V.

• A uniform electric field exists between the plates of the capacitor.

• The charge stored on the capacitor is inversely proportional to the pd across the plates.

• The energy stored when the capacitor is fully charged is proportional to the square of the pd across the plates.

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

A capacitor of capacitance 10 μF is charged through a resistor R to a potential difference (pd) of 20 V using the circuit shown. When the capacitor is fully charged which one of the following statements is incorrect?

• The energy stored by the capacitor is 2 mJ.

• The total energy taken from the battery during the charging process is 2 mJ.

• The pd across the capacitor is 20 V.

• The pd across the resistor is 0 V.

The diagram shows a rigidly-clamped straight horizontal current-carrying wire held mid-way between the poles of a magnet on a top-pan balance. The wire is perpendicular to the magnetic field direction. The balance, which was zeroed before the switch was closed, read 161 g after the switch was closed. When the current is reversed and doubled, what would be the new reading on the balance?

• −322 g

• −161 g

• zero

• 322 g

Initially a charged capacitor stores 1600 μJ of energy. When the pd across it decreases by 2.0 V, the energy stored by it becomes 400 μJ. What is the capacitance of this capacitor?

• 100 μF

• 200 μF

• 400 μF

• 600 μF

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

A nuclear fusion device is required to deliver at least 1 MJ of energy using capacitors. If the largest workable potential difference is 10 kV, what is the minimum capacitance of the capacitors that should be used?

• 0.01 F

• 0.02 F

• 2 F

• 100 F

An initially uncharged capacitor of capacitance 20 μF is charged by a constant current of 80 μA. Which line, A to D, in the table gives the potential difference across, and the energy stored in, the capacitor after 50 s?

• A

• B

• C

• D