Electro Magnetic Induction And Alternating Currents Question 203
Question: A fully charged capacitor C with initial charge $ q_{0} $ 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 the magnetic fields is:
Options:
A) $ \frac{\pi }{4}\sqrt{LC} $
B) $ 2\pi \sqrt{LC} $
C) $ \sqrt{LC} $
D) $ \pi \sqrt{LC} $
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Answer:
Correct Answer: A
Solution:
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Energy stored in magnetic field = $ \frac{1}{2},Li^{2} $
Energy stored in electric field = $ \frac{1}{2},\frac{q^{2}}{C} $
$ \therefore \frac{1}{2},Li^{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} $
