Question

Let the enery stored "in the capacitor" be U. Show that U is given by the expression: U=½Q²/C

Answer 1

A charged Capacitor is a store of electrical potential energy.

To find the energy stored in a capacitor, let us consider a capacitor of capacitance C, with a potential difference V between the plates.

There is a charge +q on one plate and –q on the other.

Suppose the capacitor is charged gradually. At any stage ,the charge on the capacitor is q.

Potential of capacitor $=\dfrac{q}{C}$

Small amount of work done in giving an additional charge $dq$ to the capacitor is:

$dW=\dfrac{q}{C} .dq$

Integrating both sides,

$\int dW = \dfrac{1}{C}\int_{0}^{Q}qdq$

$W = \dfrac{Q^2}{2C}$ $= U$