In a series LCR circuit an ac voltage source is connected. When inductor is removed from the circuit, the phase difference between the voltage and the current in the circuit is $\frac{π}{3}$. If capacitor is removed from the cirrcuit instead of inductor, the phase difference is again $\frac{π}{3}$. What is the power factor of the circuit?

1

The correct answer is Option (4) → 1

When the inductor is removed, the circuit become a simple RC circuit.

$\tan θ=\frac{X_C}{R}$

$⇒\tan\left(\frac{π}{3}\right)=\frac{X_C}{R}$

$⇒X_C=\sqrt{3}R$

When the capacitor is removed, circuit becomes a simple RL circuit.

$\tan θ=\frac{X_L}{R}$

$⇒\tan\left(\frac{π}{3}\right)=\sqrt{3}$

$⇒X_C=\sqrt{3}R$

and,

$X_L=X_C$

Impedance, $Z=\sqrt{R^2(X_L-X_C)^2}$

$⇒Z=R$

Hence, Power factor is -

$\cos\phi=\frac{Z}{R}=\frac{R}{R}=1$