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. 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 series $R-L$ circuit is given by $\cos \theta = \frac{R}{\sqrt{R^2 + \omega^2 L^2}}$.

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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 series $R-L$ circuit is given by $\cos \theta = \frac{R}{\sqrt{R^2 + \omega^2 L^2}}$.