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A capacitor is first charged fully through switch S1. Then S1 is opened and S2 is closed so that the charged capacitor is connected in series with an inductor (forming an LC loop). Which statement is correct about the resulting behaviour?

1. At t = 0 the energy in the circuit is stored entirely as magnetic energy.
2. For all times t > 0 the current keeps flowing in the same direction.
3. For t > 0 there is no exchange of energy between the inductor and the capacitor.
4. At any time t > 0 the instantaneous current can be as large as V*sqrt(C/L).

Correct answer: At any time t > 0 the instantaneous current can be as large as V*sqrt(C/L).

Solution

At t = 0 the energy is entirely electric (in the capacitor), so option A is false. In an LC loop the current is sinusoidal and reverses direction each half-cycle, so option B is false. Energy continuously oscillates between inductor and capacitor, so option C is false. The maximum current is found from energy conservation: (1/2)C*V² = (1/2)L*I_max² => I_max = V*sqrt(C/L). The instantaneous current reaches this peak value, so option D is correct.

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