In an electrical circuit,R, L, C and an a.c. | vedclass

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(A) In an $R-L-C$ series circuit,the phase difference $\phi$ is given by $	an \phi = \frac{|X_L - X_C|}{R}$.When $L$ is removed,the circuit becomes a

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(A) In an $R-L-C$ series circuit,the phase difference $\phi$ is given by $	an \phi = \frac{|X_L - X_C|}{R}$.When $L$ is removed,the circuit becomes an $R-C$ circuit. The phase difference is $	an \phi = \frac{X_C}{R}$. Given $\phi = \pi/3$,we have $	an(\pi/3) = \sqrt{3} = \frac{X_C}{R}$,so $X_C = R\sqrt{3}$.When $C$ is removed,the circuit becomes an $R-L$ circuit. The phase difference is $	an \phi = \frac{X_L}{R}$. Given $\phi = \pi/3$,we have $	an(\pi/3) = \sqrt{3} = \frac{X_L}{R}$,so $X_L = R\sqrt{3}$.Since $X_L = X_C$,the original $R-L-C$ circuit is in resonance.At resonance,the impedance $Z = R$,and the phase difference $\phi = 0$.The power factor is $\cos \phi = \cos(0) = 1$.

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