Q 12-07-013NEETNEET 2020Top questionMedium
A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is $\dfrac{\pi}{3}$. If instead C is removed from the circuit, the phase difference is again $\dfrac{\pi}{3}$ between current and voltage. The power factor of the circuit is :
Answer: (C) $1.0$
Concept. Each two-element case gives a reactance in terms of $R$; with all three present the power factor is $\dfrac{R}{Z}$.
Step 1. L removed. $\tan\dfrac{\pi}{3} = \dfrac{X_C}{R}$.
Step 2. C removed. $\tan\dfrac{\pi}{3} = \dfrac{X_L}{R}$.
Step 3. Full circuit. $X_L = X_C$: resonance, $Z = R$, $\cos\phi = 1$.
Answer. $1.0$ (Option C).
Solution by Sreeraj P, M.Sc Physics