Alternating Current

JEE Main level, single correct, medium

153 of 190

Question 153 of 190

A fully charged capacitor CC with initial charge q0q_0 is connected to a coil of self inductance LL at t=0t=0. The time at which the energy is stored equally between the electric and the magnetic field is :

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Answer: (A) π4LC\frac{\pi}{4} \sqrt{L C}

Charge oscillates simple harmonic motion q=q0sin⁡ωt,U=12q2Cq=q_0 \sin \omega t, U=\frac{1}{2} \frac{q^2}{C}
q=q02⇒ωt=π4⇒t=T8=2π8LC=π4LC\begin{aligned} & q=\frac{q_0}{\sqrt{2}} \Rightarrow \omega t=\frac{\pi}{4} \\ & \Rightarrow t=\frac{T}{8}=\frac{2 \pi}{8} \sqrt{L C}=\frac{\pi}{4} \sqrt{L C} \end{aligned}

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