In an electrical circuit R, L, C, and an AC voltage source are all connected in series. When L is removed from

Question

In an electrical circuit R, L, C, and an AC 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 π/3. If instead, C is removed from the circuit, the phase difference is again π/3. The power factor of the circuit is:

Accepted Answer

In a series AC circuit, the phase difference $\phi$ is determined by the reactance and resistance. 
1. **Case 1 (L removed):** The circuit acts as an RC circuit. The phase angle is given by $	an \phi = X_C / R$. With $\phi = \pi/3$ ($60^\circ$), we have $X_C = R 	an(60^\circ) = R\sqrt{3}$.
2. **Case 2 (C removed):** The circuit acts as an RL circuit. The phase angle is given by $	an \phi = X_L / R$. With $\phi = \pi/3$, we have $X_L = R 	an(60^\circ) = R\sqrt{3}$.
3. **Combined LCR Circuit:** Since $X_L = X_C = R\sqrt{3}$, the net reactance $X = X_L - X_C$ is zero. This is the condition for electrical resonance .
4. **Power Factor:** At resonance, the circuit is purely resistive, the phase difference $\phi$ is $0$, and the power factor is $\cos \phi = \cos(0) = 1$ .

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