Resonance, Bandwidth & Q Factor question from MHT CET 2026 (13 Apr, Shift 2)

Answer: (a)

1. Quality factor $Q = \frac{\omega_0 L}{R} = \frac{1}{R}\sqrt{\frac{L}{C}}$; bandwidth $= \frac{R}{L}$.
2. $\frac{Q}{\text{BW}} = \frac{1}{R}\sqrt{\frac{L}{C}}\cdot\frac{L}{R} = \frac{L}{R^2}\sqrt{\frac{L}{C}}$
3. $\frac{L}{R^2}\sqrt{\frac{L}{C}} = \frac{L^2}{R^2}\cdot\frac{1}{\sqrt{LC}}$
4. So the answer is (a) $\sqrt{\frac{1}{LC}}\,\frac{L^2}{R^2}$.