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(B) In an oscillating $LC$ circuit,the total energy is conserved,oscillating between the electric field of the capacitor and the magnetic field of the

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$9$

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(B) In an oscillating $LC$ circuit,the total energy is conserved,oscillating between the electric field of the capacitor and the magnetic field of the inductor.The maximum energy stored in the capacitor is equal to the maximum energy stored in the inductor:$\frac{1}{2} L I_{\max}^2 = \frac{1}{2} \frac{Q_{\max}^2}{C}$Rearranging for the maximum current $I_{\max}$:$I_{\max} = Q_{\max} \sqrt{\frac{1}{LC}}$Given values:$L = 75 	imes 10^{-3} \, H$$C = 1.2 	imes 10^{-6} \, F$$Q_{\max} = 2.7 	imes 10^{-6} \, C$Calculating the angular frequency $\omega = \frac{1}{\sqrt{LC}}$:$\omega = \frac{1}{\sqrt{75 	imes 10^{-3} 	imes 1.2 	imes 10^{-6}}} = \frac{1}{\sqrt{90 	imes 10^{-9}}} = \frac{1}{\sqrt{9 	imes 10^{-8}}} = \frac{1}{3 	imes 10^{-4}} = \frac{10^4}{3} \, rad/s$Now,$I_{\max} = Q_{\max} 	imes \omega$:$I_{\max} = (2.7 	imes 10^{-6}) 	imes \frac{10^4}{3} = 0.9 	imes 10^{-2} \, A = 9 	imes 10^{-3} \, A = 9 \, mA$.

An oscillating $LC$ circuit consists of a $75\,mH$ inductor and a $1.2\,\mu F$ capacitor. If the maximum charge on the capacitor is $2.7\,\mu C$,the maximum current in the circuit will be $...........\,mA$.

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