Alternating Current: Practice Problem & Solution
22. 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 $\pi / 3$. If instead C is removed from the circuit, the phase difference is again $\pi / 3$ between current and voltage. The power factor of the circuit is: (2020)
Solution Explained:
To solve this problem, we apply the core principles of Alternating Current. Understanding the underlying formula is key to arriving at the correct answer below:
When L is removed (RC circuit): $\tan(\pi/3) = \frac{X_C}{R}$.
When C is removed (RL circuit): $\tan(\pi/3) = \frac{X_L}{R}$.
This implies $X_C = X_L$, meaning the circuit is in resonance and total impedance $Z = R$.
Power factor is $\cos\phi = \frac{R}{Z} = \frac{R}{R} = 1.0$.
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