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Concepts Of Physics MCQ Edition [Volume 2]PhysicsAlternating Current

A coil with an inductance of 0.4 henry and a resistance of 10 is connected to an AC source of 6.5 V , 30 Hz . Determine the average power consumed in the circuit.

Options

  1. A13 8 W
  2. B3 2 W
  3. C5 8 W
  4. D5 4 W

Correct answer

C. 5 8 W

Step-by-step solution

Given L = 0.4 H , R = 10 , V_ rms = 6.5 V , f = 30 Hz . The angular frequency is = 2 f = 2 30 = 60 rad/s . The inductive reactance is X_L = L = 60 0.4 = 24 . The impedance of the circuit is Z = R^2 + X_L^2 = 10^2 + 24^2 = 100 + 576 = 676 = 26 . The rms current in the circuit is I_ rms = V_ rms Z = 6.5 26 = 1 4 A . The average power consumed is P_ avg = I_ rms ^2 R = ( 1 4 )^2 10 = 10 16 = 5 8 W .

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