Question

Obtain an expression for energy stored in a charged condenser.

Answer 1

A charged condense works as a capacitor and 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$=\frac{q}{C}$

Work done in giving additional charge $aq$ to the capacitor$dW=\frac{q}{C}dq$

Total work done in giving a charge $Q$ to the capacitor is $q$

$W=\frac{1}{C}\times \frac{Q^2}{2}$

Energy stored in the capacitor

$U=W=\frac{1}{2}\times \frac{Q^2}{C}$

We know that $Q=CV$

$U=\frac{1}{2}\times \frac{(CV{)}^2}{C}$

$U=\frac{1}{2}\times C{V}^2$

$U=\frac{1}{2}\times QV$

where

Q in Coloumb

V in volt energy

U in joule