Question

An alternating voltage \( V = 200\sin(100t) \) is applied to a series combination of \( R = 30\Omega \) and an inductor of \( 400 \, \text{mH} \). The power factor of the circuit is,

• A. \( 0.01 \)
• B. \( 0.6 \)
• C. \( 0.05 \)
• D. \( 0.042 \)

Hint:

For RL circuits, the power factor is given by \( \cos\phi = \frac{R}{Z} \). Use reactance \( X_L = \omega L \) and then compute total impedance.

Answer 1

The Correct Option is B

The angular frequency \( \omega = 100 \, \text{rad/s} \)
The inductive reactance is given by: \[ X_L = \omega L = 100 \times 0.4 = 40 \, \Omega \] The impedance of the RL circuit is: \[ Z = \sqrt{R^2 + X_L^2} = \sqrt{30^2 + 40^2} = \sqrt{900 + 1600} = \sqrt{2500} = 50 \, \Omega \] The power factor \( \cos\phi = \frac{R}{Z} = \frac{30}{50} = 0.6 \)