The Q-factor of a resonant LCR series AC circuit is given by

The correct answer is Option (2) → \( \displaystyle Q=\frac{1}{R}\sqrt{\frac{L}{C}} \)

The quality factor of a series LCR circuit measures the sharpness of resonance. It is the ratio of the reactance of the inductor at the resonant angular frequency \( \omega_0 \) to the resistance.

    \( \displaystyle Q = \frac{\omega_0 L}{R},\qquad \omega_0 = \frac{1}{\sqrt{LC}} \)

    \( \displaystyle Q = \frac{1}{\sqrt{LC}}\times\frac{L}{R} = \frac{1}{R}\sqrt{\frac{L}{C}} \)

Shortcut: Q is a pure number. \( \sqrt{L/C} \) has the dimensions of a resistance (ohm), so only \( \frac{1}{R}\sqrt{L/C} \) is dimensionless. In the other options, \( \sqrt{LC} \) is a time, \( R\sqrt{L/C} \) is ohm squared and \( R/\sqrt{LC} \) is ohm per second.

Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.

NCERT (2026-27):
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