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An inductor stores energy U when a steady current flows through it, and at that instant it dissipates power P. If this coil is connected across a battery of zero internal resistance, what is the time constant of the circuit?

1. 4U/P
2. U/P
3. 2U/P
4. 2P/U

Correct answer: 2U/P

Solution

U = (1/2)L*I² and P = I²*R. Then U/P = (1/2)L*I²/(I²*R) = L/(2R). So L/R = 2U/P, which is the time constant tau.

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