Energy stored in a capacitor

Why a capacitor stores energy

Charging a capacitor requires moving electric charges against the electric field that builds up between the plates: this work provided by the generator is stored as electric potential energy, which can later be released back to the circuit.

Energy formula

The energy E_C stored in a capacitor of capacitance C charged under a voltage U is written:

E_C = 1/2 * C * U^2

It is expressed in joules (J) when C is in farads and U in volts. It can also be written E_C = 1/2 * q * U or E_C = q^2/(2C), using q = CU.

Example

A capacitor with C = 2200 uF charged under U = 9 V stores:

E_C = 0.5 * 2200x10^-6 * 9^2 = 0.5 * 2200x10^-6 * 81 = about 0.089 J

Comparison with a battery

Unlike a battery, which releases its energy slowly through a chemical reaction, a capacitor can release all its stored energy very quickly (within a few milliseconds), which explains its use in a camera flash: the capacitor charges slowly via the battery, then discharges almost instantaneously into the flash lamp to produce an intense burst of light.

Common pitfall

Energy varies as the square of the voltage (U^2), not proportionally to U: if you double the voltage, the stored energy is multiplied by 4, not by 2.