(B) In an $ac$ series $LR$ circuit,the impedance $(Z)$ is given by $Z = \sqrt{R^2 + X_L^2}$.Here,$X_L = \omega L$ is the inductive reactance.So,$Z = \

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(B) In an $ac$ series $LR$ circuit,the impedance $(Z)$ is given by $Z = \sqrt{R^2 + X_L^2}$.Here,$X_L = \omega L$ is the inductive reactance.So,$Z = \sqrt{R^2 + (\omega L)^2} = \sqrt{R^2 + \omega^2 L^2}$.The power factor $(\cos \phi)$ is defined as the ratio of resistance to impedance:$\cos \phi = \frac{R}{Z} = \frac{R}{\sqrt{R^2 + \omega^2 L^2}}$.

Class 12 Physics Alternating Current Power in AC and Power Factor

Medium

The power factor of an $ac$ circuit having resistance $(R)$ and inductance $(L)$ connected in series and an angular velocity $\omega$ is:

AIEEE 2002 All AIEEE

A
$R/\omega L$
B
$R/\sqrt{R^2 + \omega^2 L^2}$
C
$\omega L/R$
D
$R/\sqrt{R^2 - \omega^2 L^2}$

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Alternating Current

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Power in AC and Power Factor

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The power factor of an $ac$ circuit having resistance $(R)$ and inductance $(L)$ connected in series and an angular velocity $\omega$ is:

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