1. Impedance of a series $R$-$L$ AC circuit

For a resistor $R$ and inductor $L$ in series, the inductive reactance is $X_L = \omega L$

Hence, the total impedance is $Z = \sqrt{R^2 + X_L^2} = \sqrt{R^2 + (\omega L)^2}$

2. Definition of power factor

The power factor is $\cos\phi = \frac{\text{resistance}}{\text{impedance}} = \frac{R}{Z}$

Substituting $Z$: $\cos\phi = \frac{R}{\sqrt{R^2 + \omega^2 L^2}}$

3. Match with the options

• A: $\dfrac{R}{\omega L}$ — incorrect
• B: $\dfrac{R}{\sqrt{R^2 + \omega^2 L^2}}$ — correct
• C: $\dfrac{\omega L}{R}$ — incorrect
• D: $\dfrac{R}{\sqrt{R^2 - \omega^2 L^2}}$ — incorrect

4. Final answer

The power factor is $\boxed{\frac{R}{\sqrt{R^2 + \omega^2 L^2}}}$ So, the correct option is B.