A capacitor C is first charged fully with potential difference of and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In ts, 25% of the initial energy in the capacitor is transferr

Question

A capacitor C is first charged fully with potential difference of $V_{0}$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In ts, 25% of the initial energy in the capacitor is transferred to the inductor. The value of t is ________ s. [2026]

Smart Achievers · Accepted Answer

(4)

$U_{e_{r}} = 75 % U_{e_{i}}$

$Q_{F}^{2} = \frac{3}{4} Q_{i}^{2}$

$Q_{i} \cos ω t = \frac{\sqrt{3}}{2} Q_{i} \Rightarrow t = \frac{T}{12}$

$t = \frac{π}{6} \sqrt{L C}$

Solution

1 $\frac{π \sqrt{L C}}{2}$

2 $π \sqrt{\frac{L C}{2}}$

3 $\frac{π \sqrt{L C}}{3}$

4 $\frac{π \sqrt{L C}}{6}$

Ans.
(4)

$U_{e_{r}} = 75 % U_{e_{i}}$

$Q_{F}^{2} = \frac{3}{4} Q_{i}^{2}$

$Q_{i} \cos ω t = \frac{\sqrt{3}}{2} Q_{i} \Rightarrow t = \frac{T}{12}$

$t = \frac{π}{6} \sqrt{L C}$

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Solution

1 πLC2

2 πLC2

3 πLC3

4 πLC6