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In an AC circuit, alternating voltage of amplitude U0 = 100 V is applied. The phase difference between current and voltage is phi = pi/4. The resistance R = 100 ohm and the inductor is ideal (no resistance). The angular frequency omega = 100 rad/s. Which statement(s) is/are correct? (A) The amplitude of current is sqrt(2) A (B) The average power dissipated is 50 W (C) The inductance is 1 H (D) The amplitude of current through the inductance is 0.5 A

1. (A) The amplitude of current is √2 amp.
2. (B) The average power dissipated is 50 W
3. (C) The inductance is 1H
4. (D) The amplitude of current through the inductance is 0.5 A

Correct answer: (C) The inductance is 1H

Solution

phi = pi/4 => tan(pi/4) = X_L/R = 1 => X_L = R = 100 ohm => L = X_L/omega = 100/100 = 1 H (C correct). Z = 100*sqrt(2), I0 = 100/(100*sqrt(2)) = 1/sqrt(2) ≈ 0.707 A (not sqrt(2), so A is wrong). Avg power = (1/2)*I0²*R = (1/2)*(1/2)*100 = 25 W (not 50, so B wrong). D is wrong as I0 = 1/sqrt(2) ≠ 0.5 A.

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