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Two coils have self-inductances 8 mH and 2 mH. The current in each coil is increased at the same constant rate. At the instant when the power delivered to the two coils is equal, let I1, V1, W1 be the current, induced voltage and stored energy in the first coil, and I2, V2, W2 the corresponding quantities in the second. Which relation is correct?

1. I1/I2 = 1/4
2. I1/I2 = 4
3. W2/W1 = 4
4. V2/V1 = 1/4

Correct answer: I1/I2 = 1/4

Solution

Equal dI/dt makes V proportional to L, so V1/V2 = 8/2 = 4 (V2/V1 = 1/4 would be correct as a magnitude relation, but the listed option 'V2/V1 = 1/4' is actually true). Equal power P = V*I gives L1*I1 = L2*I2 -> 8*I1 = 2*I2 -> I1/I2 = 1/4. This is the intended correct single answer.

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