Energy in a capacitor

Intermediate

Energy stored in the field.

Key relationU = ½CV²

The stored energy U = ½CV² = Q²/2C = ½QV. It sits in the electric field between the plates.

Worked example

100 μF at 12 V: 7.2 mJ.

Common mistake

Not QV, which is twice the energy.

In more detail

A charged capacitor stores energy U = ½CV² = ½QV = Q²/(2C). This energy is held in the electric field between the plates.

Defibrillators use stored capacitor energy to shock the heart.
Flash units store energy in capacitors for bright, brief light.
Defibrillators store energy in a capacitor, which is released as a short pulse through the heart.

Why is there a half in the formula?

Because the voltage rises steadily from zero to V as charge builds up, so the average voltage is V/2.

Where is the energy stored?

In the electric field between the plates.

Why use ½CV² and not Q times V?

Both are correct, but the ½ comes from the average voltage as the capacitor charges from zero.