A) \[\pi \sqrt{LC}\]
B) \[\frac{\pi }{4}\sqrt{LC}\]
C) \[\frac{\pi }{2}\sqrt{LC}\]
D) \[\frac{\pi }{6}\sqrt{LC}\]
Correct Answer: B
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 \[\frac{q_{\max }^{2}}{2C}\] Energy will be equal when, \[\frac{1}{2}L{{I}^{2}}=\frac{1}{2}\frac{1}{2}LI_{\max }^{2}\Rightarrow I=\frac{{{I}_{\max }}}{\sqrt{2}}\] \[I={{I}_{\max }}\sin \omega t=\frac{1}{\sqrt{2}}{{I}_{\max }}\] \[\omega t=\frac{\pi }{4}\Rightarrow \frac{2\pi }{T}t=\frac{\pi }{4}\Rightarrow t=\frac{T}{8}\] \[t=\frac{1}{8}2\pi \sqrt{LC}=\frac{\pi }{4}\sqrt{LC}\] \[\Rightarrow \] \[t=\frac{\pi }{4}\sqrt{LC}\]
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