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(C) The power factor $(\cos \phi)$ of an $LR$ series circuit is given by $\cos \phi = \frac{R}{Z}$, where $R$ is the resistance and $Z$ is the impedan

Vedclass · Accepted Answer

$1: \sqrt{3}$

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(C) The power factor $(\cos \phi)$ of an $LR$ series circuit is given by $\cos \phi = \frac{R}{Z}$, where $R$ is the resistance and $Z$ is the impedance.Given, $\cos \phi = 0.5 = \frac{1}{2}$.We know that $Z = \sqrt{R^2 + X_L^2}$, where $X_L$ is the inductive reactance.So, $\frac{R}{\sqrt{R^2 + X_L^2}} = \frac{1}{2}$.Squaring both sides, we get $\frac{R^2}{R^2 + X_L^2} = \frac{1}{4}$.$4R^2 = R^2 + X_L^2$.$3R^2 = X_L^2$.Taking the square root, $\sqrt{3}R = X_L$.Therefore, the ratio of resistance to reactance is $\frac{R}{X_L} = \frac{1}{\sqrt{3}}$.

An inductor and a resistor are connected in series to an $AC$ source. If the power factor of the circuit is $0.5$, the ratio of the resistance of the resistor and the reactance of the inductor is:

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