A) \[\frac{\pi }{4}\sqrt{LC}\]
B) \[2\pi \sqrt{LC}\]
C) \[\sqrt{LC}\]
D) \[\pi \sqrt{LC}\]
Correct Answer: A
Solution :
[a] Energy stored in magnetic field = \[\frac{1}{2}\,L{{i}^{2}}\] Energy stored in electric field = \[\frac{1}{2}\,\frac{{{q}^{2}}}{C}\] \[\therefore \,\,\,\,\frac{1}{2}\,L{{i}^{2}}=\frac{1}{2}\,\frac{{{q}^{2}}}{C}\] Also \[q={{q}_{0}}\] cos \[\omega \,t\] and \[\omega =\frac{1}{\sqrt{LC}}\] On solving \[t=\frac{\pi }{4}\,\sqrt{LC}\]
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