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The power factor of an AC circuit having resistance \(R\) and inductance \(L\) connected in series and angular frequency \(\omega\) is

1. \(\dfrac{L}{R\omega}\)
2. \(\dfrac{R}{\sqrt{R^2+(L\omega)^2}}\)
3. \(\dfrac{R}{L\omega}\)
4. \(\dfrac{R}{\sqrt{R^2-(L\omega)^2}}\)

Correct answer: \(\dfrac{R}{\sqrt{R^2+(L\omega)^2}}\)

Solution

For a series RL circuit, the impedance is \(Z=\sqrt{R^2+(\omega L)^2}\). The power factor is \(\cos\phi=R/Z\), so it becomes \(R/\sqrt{R^2+(\omega L)^2}\).

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