For a series LCR circuit, at the condition of resonance, the value of power factor will be :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1.0
The power factor of a series LCR circuit is the ratio of the resistance to the impedance.
\( \displaystyle \cos\phi = \frac{R}{Z} = \frac{R}{\sqrt{R^{2} + (X_L - X_C)^{2}}} \)
At resonance \( X_L = X_C \), so the reactances cancel and \( Z = R \).
\( \displaystyle \cos\phi = \frac{R}{R} = 1 \)
The current is in phase with the voltage (\( \phi = 0 \)), and the circuit takes the maximum power.
NCERT (2026-27):
Power in AC Circuit: The Power Factor – “… The quantity \( \cos\phi \) is called the power factor.”
Power in AC Circuit: The Power Factor – “… Case (iv) Power dissipated at resonance in LCR circuit: At resonance \( X_C - X_L = 0 \), and \( \phi = 0 \). Therefore, \( \cos\phi = 1 \) and \( P = I^2 Z = I^2 R \). That is, maximum power is dissipated in a circuit (through R) at resonance.”