A capacitor of capacity ' $\mathrm{C}$ ' is charged to a potential ' $\mathrm{V}$ '. It is connected in…

A capacitor of capacity ' $\mathrm{C}$ ' is charged to a potential ' $\mathrm{V}$ '. It is connected in parallel to an inductor of inductance ' $L$ '. The maximum current that will flow in the circuit is
  1. $V \sqrt{\frac{L}{C}}$
  2. $\mathrm{V} \sqrt{\mathrm{LC}}$
  3. $\mathrm{V} \sqrt{\frac{\mathrm{C}}{\mathrm{L}}}$
  4. $\frac{\mathrm{VC}^2}{\mathrm{~L}}$

Solution

The charge oscillates according to the equations $\begin{aligned} & \mathrm{q}=\mathrm{q}_0 \cos \omega \mathrm{t} \\ & \mathrm{i}=-\frac{\mathrm{dq}}{\mathrm{dt}}=\omega \mathrm{q}_0 \sin \omega \mathrm{t}=\mathrm{i}_0 \sin \omega \mathrm{t} \\ & \text { where } \mathrm{i}_0=\omega \mathrm{q}_0, \omega=\frac{1}{\sqrt{\mathrm{LC}}}, \mathrm{q}_0=C V \\ & \therefore \mathrm{i}_0=\frac{1}{\sqrt{\mathrm{LC}}} \cdot \mathrm{CV}=\mathrm{V} \sqrt{\frac{\mathrm{C}}{\mathrm{L}}} \end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 2)

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