Consider a capacitor of capacitance C farads being charged from a source or V volts.

Let at any instant of charging the charge attained by it and potential difference across its plates be q coulombs and v volts respectively.

Now by definition of capacitance C = q
                                                     v

                                         or   v = q
                                                    C

Now if the charge of the capacitor is raised by small amount dq coulombs, the work equivalent to vdq is done which appears as stored energy in the condenser.

Therefore energy stored during the interval of raising the charge by small amount dq.

dw = vdq = q   dq
                 C

Work done in giving the charge of Q coulombs to uncharged condenser.



Also W = Q . Q = 1  QV = 1 CV²
               2   C     2           2

Energy stored in a capacitor = W = Q² =1 QV = 1 CV²
                                                    2C   2          2

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