Assertion (A): If the frequency of the applie | vedclass

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(C) The power factor of a series $R-L$ circuit is given by $\cos 	heta = \frac{R}{Z} = \frac{R}{\sqrt{R^2 + \omega^2 L^2}}$, where $\omega = 2 \pi f$

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If Assertion is true but Reason is false.

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(C) The power factor of a series $R-L$ circuit is given by $\cos 	heta = \frac{R}{Z} = \frac{R}{\sqrt{R^2 + \omega^2 L^2}}$, where $\omega = 2 \pi f$.If the frequency $f$ is doubled, $\omega$ increases, which means the impedance $Z = \sqrt{R^2 + \omega^2 L^2}$ increases.Since $\cos 	heta = \frac{R}{Z}$, as $Z$ increases, the power factor $\cos 	heta$ decreases. Thus, the Assertion $(A)$ is true.The formula provided in the Reason $(R)$ is $\cos 	heta = \frac{2R}{\sqrt{R^2 + \omega^2 L^2}}$, which is incorrect because the factor $2$ in the numerator is wrong. The correct formula is $\cos 	heta = \frac{R}{\sqrt{R^2 + \omega^2 L^2}}$. Thus, the Reason $(R)$ is false.Therefore, the correct option is $(c)$.

Assertion $(A):$ If the frequency of the applied $AC$ is doubled, then the power factor of a series $R-L$ circuit decreases.
Reason $(R):$ Power factor of a series $R-L$ circuit is given by $\cos \theta = \frac{2R}{\sqrt{R^2 + \omega^2 L^2}}$.

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Assertion $(A):$ If the frequency of the applied $AC$ is doubled, then the power factor of a series $R-L$ circuit decreases.Reason $(R):$ Power factor of a series $R-L$ circuit is given by $\cos \theta = \frac{2R}{\sqrt{R^2 + \omega^2 L^2}}$.