In a series L-C-R circuit,the inductive react | vedclass

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(C) In an $L-C-R$ circuit,we are given:$X_L = 2R$ and $X_C = \frac{X_L}{3}$.Substituting $X_L = 2R$ into the expression for $X_C$,we get $X_C = \frac{

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$0.6$

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(C) In an $L-C-R$ circuit,we are given:$X_L = 2R$ and $X_C = \frac{X_L}{3}$.Substituting $X_L = 2R$ into the expression for $X_C$,we get $X_C = \frac{2R}{3}$.The impedance $Z$ of the $L-C-R$ circuit is given by the formula:$Z = \sqrt{R^2 + (X_L - X_C)^2}$.Substituting the values of $X_L$ and $X_C$:$Z = \sqrt{R^2 + (2R - \frac{2R}{3})^2} = \sqrt{R^2 + (\frac{4R}{3})^2} = \sqrt{R^2 + \frac{16R^2}{9}} = \sqrt{\frac{25R^2}{9}} = \frac{5R}{3}$.The power factor is defined as $\cos \phi = \frac{R}{Z}$.Substituting the value of $Z$:$\cos \phi = \frac{R}{5R/3} = \frac{3}{5} = 0.6$.

In a series $L-C-R$ circuit,the inductive reactance is twice the resistance and the capacitive reactance is $1/3$ rd of the inductive reactance. The power factor of the circuit is

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