What is the power factor of an ac circuit having resistance R and Inductance L connected in series? (\( \omega \) is the angular frequency)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( R/(R^2+\omega^2L^2)^{\frac{1}{2}} \)
The power factor of an ac circuit is \( \cos\phi \), where \( \phi \) is the phase difference between voltage and current. For a series circuit it equals the resistance divided by the impedance.
\( \displaystyle \cos\phi = \frac{R}{Z} \)
In a series LR circuit the voltages across R and L are at right angles, so the impedance adds as squares:
\( \displaystyle Z = \sqrt{R^{2} + X_L^{2}} = \sqrt{R^{2} + \omega^{2}L^{2}} \)
\( \displaystyle \cos\phi = \frac{R}{(R^{2} + \omega^{2}L^{2})^{1/2}} \)
Note: A similar question was also asked in CUET (UG) 2023 on 30-05-2023 (Slot 2).