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An arc lamp needs a direct current of 10 A at 80 V to operate. If it is run from a 220 V (rms), 50 Hz AC supply, the inductor to be connected in series for proper operation is closest to:

1. 0.065 H
2. 80 H
3. 0.08 H
4. 0.044 H

Correct answer: 0.065 H

Solution

The lamp needs 10 A and behaves as R = 80/10 = 8 ohm. For 10 A rms from 220 V, total impedance Z = 220/10 = 22 ohm. The inductive reactance X_L = sqrt(Z² - R²) = sqrt(22² - 8²) = sqrt(484 - 64) = sqrt(420) = 20.49 ohm. Then L = X_L/(2*pi*f) = 20.49/(2*pi*50) = 20.49/314.16 = 0.065 H.

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