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 field is

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

Answer 1

Answer: (B)

$\frac{1}{2}L{I}_{\max }^2=\frac{q^2}{2C}$
$\frac{1}{2}L{I}^2=\frac{1}{2}\times \frac{1}{2}L{I}_{\max }^2$
$I=\frac{I_{\max }}{\sqrt{2}}$
$I_{\max }\sin \omega t=\frac{I_{\max }}{\sqrt{2}}$
$\omega t=\frac{\pi }{4}$
$t=\frac{\pi }{4}\sqrt{LC}$