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An LCR circuit has a resistance R = 20 ohm and inductive reactance X_L = 200 ohm at its resonant frequency. After how many oscillations does the ratio of current amplitude to its maximum value become 1/e?

1. 10
2. 10/pi
3. 100
4. 100/pi

Correct answer: 10/pi

Solution

Current decays as e^(-Rt/(2L)). For ratio 1/e: Rt/(2L) = 1 => t = 2L/R. Period T = 2*pi/omega. Oscillations = t/T = (2L/R)*(omega/(2*pi)) = omega*L/(pi*R) = X_L/(pi*R) = 200/(pi*20) = 10/pi.

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