Question

Derive an expression for energy stored in a capacitor. In which form energy is stored?

Answer 1

Let us consider a capacitor of capacitance C and potential difference V between the plates.

Let the charge on one plate be +q and -q on the other.

Suppose the capacitor is being charged gradually.

Now,at any stage the charge on capacitor is q.

Therefore, the potential difference = $\frac{q}{C}$

Small amount of work doe in giving n additional charge dq to the capacitor is
dW= $\frac{q}{C}\ast dq$

Total work done in giving a charge Q to the capacitor is
W=$\int dW$

W= ${\int }_0^Q\frac{Q}{C}dq$

W = $\frac{Q^2}{C}$

Energy = E
E= $\frac{Q^2}{2C}$ = $\frac{C{V}^2}{2}$ = $\frac{QV}{2}$
The energy is stored in the form of potential energy.