In a series LR circuit,X_{L} = R and the powe | vedclass

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(B) In an $LR$ circuit,the impedance $Z$ is given by $Z = \sqrt{X_{L}^{2} + R^{2}}$.Given $X_{L} = R$,we have $Z = \sqrt{R^{2} + R^{2}} = \sqrt{2}R$.T

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$\frac{1}{\sqrt{2}}$

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(B) In an $LR$ circuit,the impedance $Z$ is given by $Z = \sqrt{X_{L}^{2} + R^{2}}$.Given $X_{L} = R$,we have $Z = \sqrt{R^{2} + R^{2}} = \sqrt{2}R$.The power factor $P_{1} = \cos \phi = \frac{R}{Z} = \frac{R}{\sqrt{2}R} = \frac{1}{\sqrt{2}}$.When a capacitor is added such that $X_{L} = X_{C}$,the circuit becomes a series $LCR$ circuit at resonance.In resonance,the impedance $Z = R$.The power factor $P_{2} = \cos \phi = \frac{R}{Z} = \frac{R}{R} = 1$.Therefore,the ratio $\frac{P_{1}}{P_{2}} = \frac{1/\sqrt{2}}{1} = \frac{1}{\sqrt{2}}$.

In a series $LR$ circuit,$X_{L} = R$ and the power factor of the circuit is $P_{1}$. When a capacitor with capacitance $C$ such that $X_{L} = X_{C}$ is put in series,the power factor becomes $P_{2}$. The ratio $\frac{P_{1}}{P_{2}}$ is

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