In a series LCR circuit at resonance, what is the power factor of the circuit?

Solution

1. In a series LCR circuit at resonance, the inductive reactance $X_L$ equals the capacitive reactance $X_C$.
2. The total impedance $Z$ of the circuit is given by $Z=\sqrt{R^2+(X_L-X_C{)}^2}$, which simplifies to $Z=R$.
3. The power factor is defined as $\cos (\varphi )=\frac{R}{Z}$, which becomes $\frac{R}{R}=1$.
4. Hence the answer is (C).