Question

Write expression for capacitance and energy of a parallel plate capacitor .

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.

Potential of capacitor =q/C

Work done in giving additional charge dq to capacitor is 

dW=q/C *dq

total work done in giving a charge Q to the capacitor is q.

Q=Q

W=1/C Q2/2

Energy stored in the capacitor

U=W=1/2 Q2/C

We know that Q=CV

U=1/2 (CV)2/C =1/2 CV2

Now CV=Q

U=1/2 QV

Thus,                    U=1/2 Q2/C =1/2 CV2=1/2 QV

Where Q=Coloumb, V=Volt Energy U is in joule