Capacitors and capacitance

Physics A2 · Capacitance. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A capacitor stores charge. A parallel plate capacitor has two metal plates with an insulator between them. When it is connected to a supply, one plate gains charge +Q and the other −Q.

Capacitance is the charge stored per unit potential difference. For a parallel plate capacitor, Q is the charge on one plate and V is the p.d. between the plates. For an isolated sphere, Q is the charge on the sphere and V is its potential.

Capacitors in parallel share the same p.d. and their charges add. Capacitors in series carry the same charge and their p.d.s add. This is why the combination rules are the opposite of those for resistors.

Rules to remember

Common mistake

Students use the resistor rules. For capacitors it is the other way round: add directly in parallel, add reciprocals in series. In series, remember to turn 1/C upside down at the end.

Worked example

A 10 μF capacitor and a 15 μF capacitor are in series. A 4.0 μF capacitor is in parallel with this pair. The combination is connected to a 6.0 V supply. What is the total charge stored?

  1. Series pair: 1/C = 1/10 + 1/15 = 5/30, so C = 6.0 μF.
  2. Add the parallel capacitor: C = 6.0 + 4.0 = 10 μF.
  3. Q = CV = 10 × 10−6 × 6.0 = 6.0 × 10−5 C.

Answer: 60 μC

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