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Two inductors are connected in parallel with each other and with a resistor R = 12 ohm across a 5 V battery. The first inductor has inductance 1 mH and internal resistance 3 ohm; the second has inductance 2 mH and internal resistance 4 ohm. If the switch closes at t = 0, find the ratio of the largest to the smallest current that the battery supplies.

1. 8
2. 4
3. 6
4. 12

Correct answer: 8

Solution

Inductors block current at the first instant, so initially current flows only through R. After a long time the inductor currents are limited solely by their internal resistances, so all three parallel branches draw current and the total is largest.

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