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Question:

A source of constant voltage V is connected to a resistance R and two ideal inductors L1 and L2 through a switch S as shown. There is no mutual inductance between the two inductors. The switch S is initially open. At t=0, the switch is closed and current begins to flow. Which of the following options is/are correct?

At t=0, the current through the resistance R is V/R

The ratio of the currents through L1 and L2 is fixed at all times (t>0)

After a long time, the current through L2 will be VR L1/(L1+L2)

After a long time, the current through L1 will be VR L2/(L1+L2)

Solution:

L = L1L2/(L1+L2)
I = V/R(1-e^(-t/τ)), I = L1L2R/(L1+L2)
IL2 = V × L1/(L1+L2)
IL1 = V × (L2/(L1+L2))
Applying KVL -IR -LdI/dt + V = 0 → 0∫1 dI/(V-IR) = V/R(1-e^(-Rt/L))
Hence B and C are correct.