Question

A capacitance of a charged capacitor is C and the energy stored in it is U . What is the value of charge on the capacitor ?

Answer 1

We know that the electrostatic energy stored in a capacitor is given by,

$U=\frac{1}{2}C{V}^2$ ..........(1)

Where,

$V=$ potential difference across capacitor

$C=$ Cpacitance of capacitor

We know that, charge in capacitor

$Q=CV$

Substituting value of $Q$ in equation (1)

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

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

$=Q^2=2CU$

$Q=\sqrt{2CU}$

Hence the value of charge in terms of capacitance $C$ and electrostatic energy $U$ is $\sqrt{2CU}$.