The lines of force in a capacitor start on one conductor and end on the other conductor. Electrical field is associated with the capacitor. Consider a parallel plate capacitor, Let F be the force of attraction between the plates. If the distance between plates is increased by a small amount dx, work F dx will be expended.
This work will be stored in the extended electric field in form of potential energy.
Let the potential difference between the plates be v. Then it represents the work done in moving a unit positive charge along one of the lines of force against the potential gradient. If the charge on the capacitor is increased by a small amount dq, the work done = v dq.
q is given by the relation, q = CV
Therefore, dq = C dv
Work done by increasing the charge by dq is given by v dq = Cv dv
Hence, the work done in increasing the potential difference from zero to V is
If V is expressed in volts, and capacitance C in farads, the work W is given in joules.
Example:- A capacitor having of 5microfarads is charged to a potential difference of 10,000 volts. Calculate the energy stored in the capacitor.
Energy stored W = ½ CV2
= ½ x 5 x 10-6 x (10000)²
= 250 joules.