Energy Stored in a Capacitor:
Imagine the potential difference across a capacitor to be enhanced from V to (V + dv) volts in dt seconds.
We know i = C . (dv/ dt)
Instantaneous value of power to capacitor is
iv = vC . (dv / dt) watts
Energy supplied to capacitor during interval dt is
vC . (dv / dt ). dt = Cv . dv Joules
Hence, total energy when potential difference is increased from O to V volts is
∴ W =( ½) CV 2