Find all the currents I 1 , I 2 , and I 3 ? Please show ALL your work for points

Question

Find all the currents I1, I2, and I3?

Please show ALL your work for points and rating!!! I want to understand the problem, not just get the answer.

A circuit consists of a battery with emf V, an inductor with inductance L, a capacitor with capacitance C, and three resistors, each with resistance R, as shown in the sketch. The capacitor is initially uncharged and there is no current flowing anywhere in the circuit. The switch S has been open for a long time, and is then closed, as shown in the diagram. If we wait a long time after the switch is closed, the currents in the circuit are given by: Find all the currents I1,I2, and I3? Please show ALL your work for points and rating!!! I want to understand the problem, not just get the answer.

Explanation / Answer

after long time C becomes an open circuit and L is short circuit , hence i2 = 0

and i1 = i3 = i

KVL :

V = (R + R) * i = 2R i

=> i1 = i3 = V / (2R)

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