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

Question

Dr. Abubacker · Accepted Answer

(a) As initially charge is maximum,
$\ \ \ \ \ \ \ \ \ \ \ \ q = q_{0}\cos{\omega t}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ i = \frac{dq}{dt} = - \omega q_{0}\sin{\omega t}$
Given $\frac{1}{2}Li^{2} = \frac{q^{2}}{2C}$
${\Rightarrow \ \ \frac{1}{2}L\ (\omega q_{0}\sin{\omega t)}}^{2} = \frac{{(q_{0}\cos{\omega t)}}^{2}}{2C}$
$\ \ \ \ \ \ \ \ \ \ \ \ \omega = \frac{1}{\sqrt{LC}}$
$	herefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\ \ \ tan}{\omega t = 1}$
$\ \ \ \ \ \ \ \ \ \omega t = 	an\frac{\pi}{4}$
$\ t = \frac{\pi}{4\omega} = \frac{\pi}{4}\sqrt{LC}$

Q. 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

Explanation

Reviewed by Dr. Abubacker

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