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In a series LCR circuit the resistance is R = 20 ohm and the inductive reactance is X_L = 200 ohm. After how many complete oscillations does the ratio of instantaneous current to its maximum value fall to 1/e?

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

Correct answer: 10/pi

Solution

The damping condition e^(-Rt/2L) = 1/e gives t = 2L/R. The number of oscillations n = t/T = (2L/R)*(omega/(2*pi)) = omega*L/(pi*R) = X_L/(pi*R) = 200/(20*pi) = 10/pi.

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