A capacitor with capacitance C is connected in parallel to two inductors: induct

Question

A capacitor with capacitance C is connected in parallel to two inductors: inductor 1 with inductance L, and inductor 2 with inductance 2L, as shown in the figure. The capacitor is charged up to a voltage V, at which point it has a charge q. There is no current in the inductors. Then the switch is closed. (Figure 1)

A.) Since the two inductors are in parallel, the voltage across them is the same at any time. Hence, V1=V2=X1I1=X2I2, where X1 and X2 are the reactances of inductors 1 and 2, and I1 and I2 are the currents through them. Use this equality to express I1 in terms of I2. Express your answer in terms of I2

B.) What is the effective inductance Leff of the inductors 1 and 2 in the circuit?

C.) Find the maximum current I1max through inductor 1. Express your answer in terms of C, L, and V.

Explanation / Answer

A) X1 I1 = X2 I2

=> I2 = X1 I1 / X2 = L I1 /2L = I1/2

B) effective inductance in parallel

1/Leff = 1/L + 1/2L

=> Leff = 2/3 L

C) I1 max x X1 = V = q/C

I1 MAX = q/X1C

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