An LC circuit containing an 735mH inductor and a 105nF capac

An L-C circuit containing an 73.5-mH inductor and a 1.05-nF capacitor oscillates with a maximum current of 0.824 A.

(a) Calculate the maximum charge on the capacitor.

C

(b) Calculate the oscillation frequency of the circuit.
Hz

(c) Assuming the capacitor had its maximum charge at time t = 0, calculate the energy stored in the inductor after2.50 ms of oscillation.

J

Solution

a) U_max = L I²_max / 2 = Q² / 2 C

Q_max = I_max * sqrt [L C]

= 0.824 * sqrt [73.5 * 10^-3 * 1.05 * 10^-9]

= 7.24 * 10^-6 C

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f = w / 2 pi = 1 / 2 pi * sqrt [L C]

= 1 / 2 pi * sqrt [73.5 * 10^-3 * 1.05 * 10^-9]

f = 1.81 * 10⁴ Hz

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c) U_max = L I² / 2

I = I_max * sin wt = I_max * sin [t / sqrt[L C]]

U_max = L I_max² / 2 * sin [t / sqrt[L C]]²

= 73.5 * 10^-3 * 0.824² / 2 * sin [2.5 * 10^-3 / sqrt[73.5 * 10^-3 * 1.05 * 10^-9]]²

= 0.0065 J