Whenever any conductor is charged, work has to be done by the external agency against the electrostatic forces of repulsion. The word done is stored as the electrostatic potential energy which is stored in the electrostatic field of the conductor.

Let us consider that charge is given in a step-wise manner to the conductor. If V be the potential of the conductor at the instant when it has a charge q, then

`V = q/C`

If `dq` is the additional infinitesimal charge that is to be given to the conductor and `dW` is the corresponding work done, then

`dW = Vdq => dW = q/C dq`

Total work done to charge the conductor to Q is

`W = int dW = (1/C) int_0^Q q dq = 1/C[q^2 /2]_0^Q`
`W = Q^2/(2C)`

If `V_0` is the potential that develops on the conductor finally on account of charge Q then

`V_0 = Q/C`

`W = 1/2 CV_0^2 = Q^2/(2C) = 1/2 QV_0`
As discussed above say capacitor is charged using a battery of EMF V. All the Q supplied to the capacitor is at a potential difference V
Hence work done by the battery in charging the capacitor W = QV
Energy stored in the capacitor U = 1/2 QV. This shows only 50% enerrgy stores and rest 50% lost in the form of heat through the connection wire.