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?
Answer & explanation
Correct answer: option 4
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 -
$\cos\phi=\frac{Z}{R}=\frac{R}{R}=1$