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  4. 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

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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 field is

KCETKCET 2022Electromagnetic Induction

Solution:

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