Energy stored in capacitor

#)Energy stored in capacitor”:
The work done in charging the condenser is store in it in the form of potential energy.
It is denoted by U. It is scalar quantity.

#Derivation of expression:

Initially when condenser is uncharged then the potential difference between two plates is (V1 = 0) on charging the plates the potential difference between gradually increases. The amount of charge +Q is given to the condenser for full charging then potential difference become (V2 = V). let the capacitance of condenser be C .

Initial potential difference, V1 = 0
Final potential difference, V2 = V

Hence, Average potential difference:
V(av) = (V1 + V2)/2
V(av) = (0 + V)/2
V(av) = V/2

By the definition:
Average pot. diff. = Work done/ charge
V/2 = W/Q
W = 1/2×V×Q --------(1)

By the theory of condenser
C = Q/V
Q = C×V

Putting this value of Q in eqn1

W = 1/2×V(C.V)

W = 1/2×C×V²
This work done is stored in condenser in the form of potential energy
Thus,
U = W
U = 1/2 CV²