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JEE Main 2011
Exam
JEE Main
Year
2011
Subject
Physics
Chapter
Alternating Current

JEE Main 2011 · Physics · Alternating Current

A fully charged capacitor C with initial charge q_0 is connected to...

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 :

Options

  1. Aπ4LC\frac{\pi}{4} \sqrt{L C}
  2. B2πLC2 \pi \sqrt{L C}
  3. CLC\sqrt{L C}
  4. DπLC\pi \sqrt{L C}

Correct answer

A. π4LC\frac{\pi}{4} \sqrt{L C}

Step-by-step solution

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⇒\omegat=π4⇒t=T8=2π8LC=π4LC\begin{aligned}& q=\frac{q_0}{\sqrt{2}} \Rightarrow \omegat=\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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