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LearnCambridge97022025–2027Paper 4 · A Level Structured QuestionsCapacitance

Paper 4 · Module

Capacitance

3 subtopics≈ 105 min in total

Start the module: Capacitors and capacitance Open graphing calculator

Capacitors and capacitance
A capacitor stores separated charge: $+Q$ on one plate, $-Q$ on the other. Its capacitance is the charge stored per unit p.d.: $C=\dfrac QV$ , measured in farads (F). An isolated sphere also has capacitance, $C=4\pi\varepsilon_0r$ . Capacitors in parallel add: $C=C_1+C_2$ . In series, reciprocals add: $\dfrac1C=\dfrac1{C_1}+\dfrac1{C_2}$ , the opposite of resistors.
≈ 35 min
Energy stored in a capacitor
As a capacitor charges, each new bit of charge is pushed onto the plates against a rising p.d., so the p.d.–charge graph is a straight line through the origin. The energy stored is the area under it: $W=\tfrac12QV=\tfrac12CV^2=\dfrac{Q^2}{2C}$ . A battery charging a capacitor supplies $QV$ , but only half is stored; the other half is dissipated in the circuit resistance.
≈ 30 min
Discharging a capacitor
When a capacitor discharges through a resistor, the current is proportional to the charge remaining, so charge, p.d. and current all decay exponentially: $x=x_0e^{-t/RC}$ . The time constant $\tau=RC$ is the time for any of them to fall to $\dfrac1e$ ( $37\%$ ) of its starting value. A graph of $\ln V$ against $t$ is a straight line with gradient $-\dfrac1{RC}$ .
≈ 40 min