How Energy Stored in a Capacitor - QS Study
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The capacitor is a charge storage device. Work has to be done to store the charges in a capacitor. This work done is stored as electrostatic potential energy in the capacitor.

Let q be the charge and V be the potential difference between the plates of the capacitor. If dq is the additional charge given to the plate, then work done is, dw = Vdq

dw = q/C dq             (V = q/C)

Total work done to charge a capacitor is

w = ∫ dw = q0 q/C dq = ½ (q2/C)

This work done is stored as electrostatic potential energy (U) in the capacitor.

U = ½ (q2/C) = ½ CV2    (q = CV)

This energy is recovered if the capacitor is allowed to discharge.