The power factor of an R-L circuit is frac{1} | vedclass

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(B) The power factor of an $R-L$ circuit is given by $\cos \phi = \frac{R}{Z} = \frac{R}{\sqrt{R^2 + X_L^2}}$.Given $\cos \phi = \frac{1}{\sqrt{2}}$,w

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$\frac{1}{\sqrt{5}}$

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(B) The power factor of an $R-L$ circuit is given by $\cos \phi = \frac{R}{Z} = \frac{R}{\sqrt{R^2 + X_L^2}}$.Given $\cos \phi = \frac{1}{\sqrt{2}}$,we have $\frac{R}{\sqrt{R^2 + X_L^2}} = \frac{1}{\sqrt{2}}$.Squaring both sides,$\frac{R^2}{R^2 + X_L^2} = \frac{1}{2}$,which implies $2R^2 = R^2 + X_L^2$,so $R^2 = X_L^2$ or $X_L = R$.Since $X_L = \omega L = 2\pi f L$,if the frequency $f$ is doubled,the new inductive reactance $X_L'$ becomes $2X_L = 2R$.The new power factor is $\cos \phi' = \frac{R}{\sqrt{R^2 + (X_L')^2}} = \frac{R}{\sqrt{R^2 + (2R)^2}} = \frac{R}{\sqrt{R^2 + 4R^2}} = \frac{R}{\sqrt{5R^2}} = \frac{1}{\sqrt{5}}$.

The power factor of an $R-L$ circuit is $\frac{1}{\sqrt{2}}$. If the frequency of $AC$ is doubled,the power factor will now be

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