Explain what happens to the charge stored and the energy stored in a capacitor when the potential difference across it is doubled.

AQA A-Level Physics (7408) — 3.7.4 Capacitance · Explain · 5 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

A capacitor is connected to a power supply. The potential difference across the capacitor is increased.

Model answer (5 marks)

The charge stored on the capacitor doubles, because Q = CV and the capacitance C is constant.
The energy stored in the capacitor increases by a factor of four, because E = ½CV² and the energy is proportional to the square of the potential difference.
The capacitance itself does not change; it is a fixed property of the capacitor.

Examiner tips

Use the equations Q = CV and E = ½CV² explicitly. Show the proportionality steps (doubling V → Q doubles, V² → energy quadruples).
Mention that C remains constant; the change is only in V.
Use UK spelling (e.g., ‘potential difference’).

Common mistakes

Confusing the change in charge with a change in capacitance. Failing to square the potential difference when calculating the energy change. Using the wrong formula for energy (e.g., E = CV² instead of ½CV²).

Mark scheme (5 marks)

Charge stored doubles (when potential difference is doubled)
Because charge is directly proportional to potential difference / Q = CV and C is constant
Energy stored increases by a factor of four / energy quadruples
Because energy stored is proportional to V² / E = ½CV² so doubling V multiplies energy by 2² = 4
The capacitance itself does not change / capacitance is a fixed property of the capacitor

Key terms in this question

potential difference · charge stored · energy stored