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

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

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$π \sqrt{LC}$

$2 π \sqrt{LC}$

$\sqrt{LC}$

$\frac{π}{4} \sqrt{LC}$

answer is B.

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Detailed Solution

energy across the capacitor becomes half when energy across inductor and capacitor are equal i.e $\frac{Q^{2}}{4 C}$

$\frac{Q^{2}}{4 C} = \frac{Q^{2} \cos^{2} ω t}{2 C} \frac{1}{\sqrt{2}} = \cos ω t \frac{1}{\sqrt{L C}} t = \frac{π}{4} t = \frac{π}{4} \sqrt{L C}$

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