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A circuit has three parallel branches connected across a 24 V battery with a 1 ohm series resistor in the battery branch. The top branch has a 4 ohm resistor in series with an inductor L1 = 4 H. The middle branch has an inductor L2 = 3 H in series with a 3 ohm resistor. A switch S in the bottom branch is closed at t = 0. Find the current through the battery (i) just after closing the switch and (ii) a long time after closing the switch.

1. 3 A, 24 A
2. 24 A, 3 A
3. 3 A, 3 A
4. Insufficient information

Correct answer: 3 A, 24 A

Solution

At t = 0+: both inductor branches are open. The circuit reduces to the battery driving current through the series combination 1 ohm + 4 ohm + 3 ohm = 8 ohm. I = 24/8 = 3 A. At t = infinity: inductors are short circuits. Top branch has 4 ohm, middle branch has 3 ohm, and the battery branch has 1 ohm. The parallel combination of the three branches (viewed from battery) gives a very small effective resistance; total current = 24 A.

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