Question

If a battery is used to charge a capacitor, work done by the battery is $W$ and energy stored in the capacitor is $E$. How these two are related ?

Answer 1

The energy stored on a capacitor can be expressed in terms of the work done by the battery. Voltage represents energy per unit charge, so the work to move a charge element dq from the negative plate to the positive plate is equal to$Vdq$ , where $V$ is the voltage on the capacitor. The voltage $V$ is proportional to the amount of charge which is already on the capacitor.

Element of energy stored: $dE=dW=Vdq$

Hence, relation is $E=W$