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In an electrical circuit $R, L, C$ and $A C$ voltage source are all connected in series. When $L$ is removed from the circuit, the phase difference between the voltage and the current in the circuit is $\pi / 3$. If instead $C$ is removed from the circuit, the phase difference is again $\pi / 3$. The power factor of the circuit is
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Here, phase difference
$\tan \phi=\frac{X_L-X_C}{R} \Rightarrow \tan \frac{\pi}{3}=\frac{X_L-X_C}{R}$
When $L$ is removed, $\tan \frac{\pi}{3}=\frac{X_C}{R}=\sqrt{3}$
Similarly, when $C$ is removed
$\begin{aligned}
\tan \frac{\pi}{3} & =\frac{X_L}{R}=\sqrt{3} \\
\Rightarrow \quad X_L & =\sqrt{3} R
\end{aligned}$
$\begin{array}{lc}
\text { Now, } & \tan \phi=0 \\
\Rightarrow & \phi=0^{\circ}
\end{array}$
$\therefore$ Power factor, $\cos \phi=\cos 0^{\circ}=1$
$\tan \phi=\frac{X_L-X_C}{R} \Rightarrow \tan \frac{\pi}{3}=\frac{X_L-X_C}{R}$
When $L$ is removed, $\tan \frac{\pi}{3}=\frac{X_C}{R}=\sqrt{3}$
Similarly, when $C$ is removed
$\begin{aligned}
\tan \frac{\pi}{3} & =\frac{X_L}{R}=\sqrt{3} \\
\Rightarrow \quad X_L & =\sqrt{3} R
\end{aligned}$
$\begin{array}{lc}
\text { Now, } & \tan \phi=0 \\
\Rightarrow & \phi=0^{\circ}
\end{array}$
$\therefore$ Power factor, $\cos \phi=\cos 0^{\circ}=1$
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