Question

A fully charged capacitor $C$ with initial charge $q_{0}$ is connected to a coil of self inductance $L$ at $t=0 .$ The time at which the energy is stored equally between the electric and the magnetic fields is

• A. $\sqrt{L C}$
• B. $\pi \sqrt{L C}$
• C. $\frac{\pi}{4} \sqrt{L C}$
• D. $2 \pi \sqrt{L C}$

Answer 1

Answer: (C)

$q=q_{0} \cos \omega t$
energy is halved when $q=\frac{q_{0}}{\sqrt{2}}$
$\Rightarrow \omega t=\frac{\pi}{4}$
$\Rightarrow \frac{1}{\sqrt{L c}} t=\frac{\pi}{4} $
$\Rightarrow t=\frac{\pi}{4} \sqrt{L c}$