Question

A fully charged capacitor C with initial charge q₀ is connected to a coil of inductance L at time t = 0. The time after which the energy is stored equally between electric and magnetic fields is

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

Answer 1

The correct option is A $\frac{\pi }{4}\sqrt{LC}$

$\frac{1}{2}\left(\frac{1}{2}\frac{q_0^2}{L}\right)=\left(\frac{1}{2}\frac{q^2}{C}\right)$
$q=\frac{q_0}{\sqrt{2}}$
$q_{0}coswt=\frac{q_0}{\sqrt{2}}\Rightarrow wt=\frac{\pi }{4}\Rightarrow t=\frac{\pi }{4}\times \frac{1}{\sqrt{LC}}$