An $L-C$ circuit containing an $90\mathrm{.}0-mH$ inductor and a $1\mathrm{.}70-nF$ capacitor oscillates with a maximum current of $0\mathrm{.}710$ A $.$

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Part A

Calculate the maximum charge on the capacitor.

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IDENTIFY: Apply energy conservation.

SET UP: If I is the maximum current, $\frac{1}{2}L{I}^2=\frac{Q^2}{2C}.$

EXECUTE: $\frac{1}{2}L{I}^2=\frac{Q^2}{2C}$ gives $Q=I\sqrt[\phantom{2}]{LC}=(0\mathrm{.}710A)\sqrt[\phantom{2}]{(90\mathrm{.}0mH)(1\mathrm{.}70nF)}=8\mathrm{.}78{10}^{-6}C.$

Part B

Calculate the oscillation frequency of the circuit.

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$=\frac{1}{\sqrt[\phantom{2}]{LC}}=\frac{1}{\sqrt[\phantom{2}]{(90\mathrm{.}0mH)(1\mathrm{.}70nF)}}=8\mathrm{.}085{10}^{4}ra\frac{d}{s}$~~$8\mathrm{.}08{10}^{4}ra\frac{d}{s}.f=\frac{}{2}=1\mathrm{.}29{10}^{4}Hz$

Part C

Assuming the capacitor had its maximum charge at time $t=0,$ calculate the energy stored in the inductor after $2\mathrm{.}55$ ms of oscillation.

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