Question

derive the expression for the energy stored in a capacitor

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 V dq, 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:  dU = Vdq = q/c dq.

Answer 2

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 V dq, 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:

If Q is the amount of charge stored when the whole battery voltage appears across the capacitor, then the stored energy is obtained from the integral: