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  4. A capacitor of capacitance 500 μ F is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in LC circuit will be A.

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Q. A capacitor of capacitance $500\, \mu F$ is charged completely using a dc supply of $100\, V$. It is now connected to an inductor of inductance $50 \,mH$ to form an LC circuit. The maximum current in LC circuit will be ____ $A$.

JEE MainJEE Main 2022Alternating Current

Solution:

Energy stored in capacitor
$ =\frac{1}{2} CV ^2=\frac{1}{2} 500 \times 10^{-6} \times 10^4$
$ =\frac{5}{2} J$
Current will be maximum when whole energy of capacitor becomes energy of inductor.
$ \frac{1}{2} LI ^2=\frac{5}{2} $
$ I =\sqrt{\frac{5}{ L }}=\sqrt{\frac{5}{50 \times 10^{-3}}}=10 A .$