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A constant voltage source V is connected to a resistance R and two ideal inductors L1 and L2 in parallel through a switch S. Initially the switch is open. At t = 0, the switch is closed. Which of the following statements is/are correct?

1. The ratio of currents through L1 and L2 is fixed at all times (t > 0).
2. After a long time, the current through L1 will be V/R * (L2 / (L1 + L2)).
3. After a long time, the current through L2 will be V/R * (L1 / (L1 + L2)).
4. At t = 0, the current through resistance R is V/R.

Correct answer: The ratio of currents through L1 and L2 is fixed at all times (t > 0).

Solution

L1 and L2 are in parallel. Same voltage V_L across both. dI1/dt = V_L/L1, dI2/dt = V_L/L2. Since both start at 0: I1(t) = (1/L1)*integral(V_L dt) and I2(t) = (1/L2)*integral(V_L dt). So I1/I2 = L2/L1 = constant always. Statement 1: CORRECT. At t->inf, inductors act as short circuits. Total current = V/R. I1 = (V/R)*L2/(L1+L2) and I2 = (V/R)*L1/(L1+L2). Statements 2 and 3: CORRECT. At t=0, both inductors resist sudden current change, so I1=I2=0. Total current through R = 0, not V/R. Statement 4: INCORRECT.

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