A) \[\frac{\pi }{4}\sqrt{LC}\]
B) \[2\pi \sqrt{LC}\]
C) \[\sqrt{LC}\]
D) \[\pi \sqrt{LC}\]
Correct Answer: A
Solution :
[a] As \[={{\omega }^{2}}\frac{1}{LC}=\] or \[\omega =\frac{1}{\sqrt{LC}}\] Maximum energy stored in capacitor\[=\frac{1}{2}\frac{Q_{0}^{2}}{C}\] Let at any instant t, the energy be stored equally between electric and magnetic field. Then energy stored in electric field at instant t is \[\frac{1}{2}\frac{{{Q}^{2}}}{C}=\frac{1}{2}\left[ \frac{1}{2}\frac{Q_{0}^{2}}{C} \right]\] or \[{{Q}^{2}}=\frac{Q_{0}^{2}}{2}\] or \[Q=\frac{{{Q}_{0}}}{\sqrt{2}}\] \[\Rightarrow \]\[{{Q}_{0}}\cos \omega t=\frac{{{Q}_{0}}}{\sqrt{2}}\] or \[\omega t=\frac{\pi }{4}\] or \[t=\frac{\pi }{4\omega }=\frac{\pi }{4\times (1/\sqrt{LC})}\] \[=\frac{\pi \sqrt{LC}}{4}\]
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