A resistor R, an inductor L, and a capacitor | vedclass

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(D) In an $LCR$ 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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(D) In an $LCR$ 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 $RC$ circuit. The phase difference is $	an(\pi/3) = \frac{X_C}{R} = \sqrt{3}$, so $X_C = R\sqrt{3}$.When $C$ is removed, the circuit becomes an $RL$ circuit. The phase difference is $	an(\pi/3) = \frac{X_L}{R} = \sqrt{3}$, so $X_L = R\sqrt{3}$.Since $X_L = X_C$, the circuit is in resonance when all three components are connected.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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