Engineering
Physics
L C Oscillation and LCR Damped Oscillation
Question

A fully charged capacitor C with initial charge q0 is connected to a coil of self inductance L at t = 0. The time at which the energy is stored equally between the electric and magnetic fields is :

\(\frac{\pi }{4}\sqrt {LC} \)

\(2\pi \sqrt {LC} \)

\(\sqrt {LC} \)

\(\pi \sqrt {LC} \)

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Solution

In LC oscillation energy is transferred C to L

or L to C maximum energy in L is \( = \frac{1}{2}LI_{\max }^2\)

Maximum energy in C is \( = \frac{{q_{\max }^2}}{{2C}}\)

Equal energy will be when

\(\frac{1}{2}L{I^2} = \frac{1}{2}\frac{1}{2}LI_{\max }^2\)

\(I = \frac{1}{{\sqrt 2 }}{I_{\max }}\)

\(I = {I_{\max }}\sin \omega t = \frac{1}{{\sqrt 2 }}{I_{\max }}\)

\(\omega t = \frac{\pi }{4}\)

or    \(\frac{{2\pi }}{T}t = \frac{\pi }{4}\)   or   \(t = \frac{\pi }{8}\)

\(t = \frac{\pi }{8}2\pi \sqrt {LC} = \frac{\pi }{4}\sqrt {LC} \)