First slide

Inductance

Question

A capacitor of capacitance C' has initial charge Q₀ and connected to inductor 'L' as shown, at t = 0 switch S is pressed. The current through the inductor when energy in the capacitor is three times of the energy of the inductor is

Moderate

A

$\frac{Q_{0}}{2 \sqrt{L C}}$
B

$\frac{Q_{0}}{\sqrt{L C}}$
C

$\frac{2 Q_{0}}{\sqrt{L C}}$
D

$\frac{4 Q_{0}}{\sqrt{L C}}$

Solution

$∵ total energy = \frac{Q_{0}^{2}}{2 C}$
$\frac{Q_{0}^{2}}{2 C} = \frac{Q^{2}}{2 C} + \frac{L i^{2}}{2} = \frac{Q^{2}}{2 C} + 3 (\frac{Q^{2}}{2 C})$
$\frac{Q_{0}^{2}}{2 C} = \frac{4 Q^{2}}{2 C} \Rightarrow Q = \frac{Q_{0}}{2}$
$Current at that instant = Q ω$
$i = \frac{Q_{0}}{2} ω = \frac{Q_{0}}{2 \sqrt{L C}}$

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