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PhysicsEMI/ACLC oscillationMedium2 minPYQ_2020

PhysicsMediumsingle choice

A fully charged capacitor $C$ with initial charge $Q_{0}$ is connected to an ideal inductor of self-inductance $L$ at $t = 0$ . The time at which energy is stored equally between the electric and the magnetic fields is

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Answer:

Solution:

The charge on the capacitor at any instant of time is

$Q = Q_{0} \cos (ω t)$

$\Rightarrow i = \frac{d Q}{d t} = - ω Q_{0} \sin (ω t)$

$\frac{1}{2} L i^{2} = \frac{Q^{2}}{2 C}$

${\Rightarrow \frac{1}{2} L [ω Q_{0} \sin (ω t)]}^{2} = \frac{{[Q_{0} \cos (ω t)]}^{2}}{2 C}$

$ω = \frac{1}{\sqrt{L C}}$

$\Rightarrow \tan (ω t) = 1$

$ω t = \tan^{- 1} (1) = \frac{π}{4}$

$t = \frac{π}{4 ω} = \frac{π}{4} \sqrt{L C}$

Stream:JEESubject:PhysicsTopic:EMI/ACSubtopic:LC oscillation

⏱ 2mℹ️ Source: PYQ_2020

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