Let us discuss energy stored in a capacitor. Let us take a simple capacitor
with capacitance value C Farad. Let us also connect a suitable battery with a switch across the capacitor as DC
source. As soon as we switch on the source, the charge Q will start accumulating in the capacitor. Due to this charge accumulation
the voltage established across the capacitor is gradually increased. If at any instance the charge accumulated in the capacitor is Q Coulomb and for that
the voltage established across the capacitor is V volt, then we can write Q
equals to C into V. Again as per definition, the potential difference of
V volts across the capacitor means V joules of work has to be done in
transferring one Coulomb from one plate to the other. That means work done for transferring one Coulomb charge is V. Hence work done
for transferring dQ charge is V dQ. This work done can be written as dW. Then we
can write dW equals to V dQ equals to C into V dV. The total work done in raising
the potential of the capacitor from zero to the supply voltage of V volt can be
expressed as W equals to integral of C V dV from zero to V
And it is 1 by 2 into C V square. This work done is stored in the
electrostatic field set up between the plates of the capacitor in the form of
energy. Again C into V is total charge accumulated in capacitor during
charging. So this equation can be rewritten as where Q is the total charge accumulated in the capacitor during charging. Hope
you got the idea. Thank you