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(C) In an $LC$ circuit, the total energy is conserved. The initial energy stored in the capacitor is $U_E = \frac{1}{2} C V^2$.When the current in the

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(C) In an $LC$ circuit, the total energy is conserved. The initial energy stored in the capacitor is $U_E = \frac{1}{2} C V^2$.When the current in the coil is maximum $(I_{max})$, the energy stored in the inductor is $U_B = \frac{1}{2} L I_{max}^2$.Since there is no resistance, the total energy remains constant, so the initial electrical energy is converted into maximum magnetic energy:$\frac{1}{2} C V^2 = \frac{1}{2} L I_{max}^2$$I_{max}^2 = \frac{C V^2}{L}$$I_{max} = V \sqrt{\frac{C}{L}}$Given: $C = 1 \, \mu F = 1 	imes 10^{-6} \, F$, $V = 50 \, V$, $L = 10 \, mH = 10 	imes 10^{-3} \, H = 10^{-2} \, H$.$I_{max} = 50 	imes \sqrt{\frac{1 	imes 10^{-6}}{10^{-2}}}$$I_{max} = 50 	imes \sqrt{10^{-4}}$$I_{max} = 50 	imes 10^{-2} \, A = 0.5 \, A$.

$A$ $1 \, \mu F$ capacitor is charged to $50 \, V$. The charging battery is then disconnected and a $10 \, mH$ coil is connected across the capacitor so that $LC$ oscillations occur. What is the maximum current in the coil (in $, A$)? Assume that the circuit contains no resistance.

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