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In a circuit, a capacitor of capacitance 2C holds charge q0 and a capacitor of capacitance C is initially uncharged. Two inductors of inductances L and 2L carry no initial current. A switch S is open initially. The capacitors discharge and at the instant the current in the inductors is maximum, switch S is instantly closed. If the maximum current through switch S after closing is q0 / sqrt(alpha * L * C), find the value of alpha.

1. 1
2. 2
3. 3
4. 4

Correct answer: 2

Solution

Initial energy: q0²/(4C). At max current: 3L*I0²/2 = q0²/(4C), giving I0 = q0/sqrt(6LC). After closing S, redistribution leads to maximum switch current q0/sqrt(2LC), so alpha = 2.

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