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(C) In the given $LCR$ series circuit,the inductive reactance is $X_L = 100 \ \Omega$,the capacitive reactance is $X_C = 50 \ \Omega$,and the resistan

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$1/\sqrt{2}$

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(C) In the given $LCR$ series circuit,the inductive reactance is $X_L = 100 \ \Omega$,the capacitive reactance is $X_C = 50 \ \Omega$,and the resistance is $R = 50 \ \Omega$.The impedance $Z$ of the circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Substituting the values,$Z = \sqrt{50^2 + (100 - 50)^2} = \sqrt{50^2 + 50^2} = \sqrt{2 	imes 50^2} = 50\sqrt{2} \ \Omega$.The power factor is defined as $\cos \phi = \frac{R}{Z}$.Therefore,$\cos \phi = \frac{50}{50\sqrt{2}} = \frac{1}{\sqrt{2}}$.

The power factor of the circuit shown in the figure is:

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