A battery connected to a capacity \(20 \mu \mathrm{F}\) is charged to a potential of \(35 \mathrm{~V}\). The battery is disconnected. A pure inductor coil of \(200 \mathrm{mH}\) is connected across the capacitor so that LC oscillations are set up.The maximum current in the coil is

Capacitance, \(\mathrm{C}=20 \mu \mathrm{F}\)
Voltage applied to capacitor, \(\mathrm{V}=35\) volts
Inductance connected to the capacitor, \(\mathrm{L}=200 \mathrm{mH}\)
To find: The maximum current in the inducting coil.
The charge stored in the capacitor is given by:
\(\mathrm{Q}_0=\mathrm{CV}\)
The maximum current flowing in the series LC circuit is:
\(I_{\text {max }}=Q_{\text {ow }}\)
The frequency of a series LC circuit is given by:
\(\omega=\frac{1}{\sqrt{\mathrm{LC}}}\)
Substitute the values in equation of maximum current.
\(\begin{aligned} & \Rightarrow I_{\max }=(\mathrm{CV}) \times \frac{1}{\sqrt{\mathrm{LC}}}=\sqrt{\frac{\mathrm{C}}{\mathrm{L}}} \mathrm{V} \\ & \therefore \mathrm{I}_{\max }=\sqrt{\frac{20 \times 10^{-6}}{200 \times 10^{-3}}} \times 35=0.35 \mathrm{~A}\end{aligned}\)