Topic: Network Theory
In an AC circuit, a resistor of $10~\Omega$ is in series with an inductor of reactance $10~\Omega$. What is the power factor of the circuit?
- A. 0.5 lagging
- B. 0.707 lagging
- C. 1.0 (unity)
- D. 0.866 leading
Answer: B. 0.707 lagging
Explanation: The impedance of the series RL circuit is $Z = R + jX_L = 10 + j10~\Omega$.
The magnitude of impedance is $|Z| = \sqrt{R^2 + X_L^2} = \sqrt{10^2 + 10^2} = 10\sqrt{2}~\Omega$.
The power factor is $\cos \phi = \frac{R}{|Z|} = \frac{10}{10\sqrt{2}} = \frac{1}{\sqrt{2}} \approx 0.707$.
Since the circuit is inductive, the current lags the voltage, so the power factor is 0.707 lagging.