How a Capacitor Stores Energy | CAIE 9702 Paper 4 Notes

Chapters

Paper 4

Physics9702

How a Capacitor Stores Energy

The supply does work while it separates charge. That work becomes electric potential energy stored by the capacitor.

Store slowly, release quickly

An open camera shows a large cylindrical capacitor beside the circuit board while the flash emits light. — A camera flash needs a short, high-power pulse. The battery transfers energy to the capacitor over a longer time; the capacitor then transfers that energy to the lamp quickly.

The battery transfers energy to the capacitor over time.
The capacitor transfers the energy to the flash lamp in a much shorter time, giving a large power output.

Stored energy is an area

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V against Q is a straight line through the origin (gradient 1/C). The energy stored is the area under it — a triangle, which is where the ½ in W = ½QV comes from.

Potential difference rises in direct proportion to charge.
Work done is the area under the potential-difference–charge graph.
The area is a triangle, so it contains a factor of one half.

W=\dfrac{1}{2}QV

Your turnquick check

A capacitor reaches 12 V when its charge is 4.0 mC. Use the graph area to find its stored energy.

Show worked answer

W=\dfrac{1}{2}QV

W=\dfrac{1}{2}(4.0\times10^{-3})(12)

Answer

W=2.4\times10^{-2}\ \mathrm{J}