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A coil of self-inductance 2.0 H carries a current that grows with time as I = 2*sin(t²) A. Find the energy stored in the coil during the interval in which the current rises from 0 to 2 A.

1. 2 J
2. 4 J
3. 8 J
4. 16 J

Correct answer: 4 J

Solution

Energy stored in an inductor is a state function of the instantaneous current: U = (1/2)*L*I². Although the current oscillates as 2*sin(t²), the question asks for the energy when the current first reaches 2 A. Plugging L = 2 H and I = 2 A gives U = (1/2)*2*4 = 4 J.

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