Q-factor is given by ______.

Asked in GSEB Board July 2022 · Power and bandwidth at resonance

Answer: (1) Q = 1/R√L/C

Step-by-step solution

Idea: Q measures the sharpness of resonance, Q = (ω₀L)/R: the inductive reactance at resonance divided by the resistance.

At resonance ω₀ = 1/(√LC).

So Q = L/(R√LC) = 1/R√L/C.

Check: √L/C is in ohm, so dividing by R leaves a pure number, as a quality factor must be.

(2) Inverts the ratio under the root. √C/L is in ohm⁻¹, so dividing it by R leaves ohm⁻², not the pure number a quality factor must be.
(3) Carries an extra factor L: it is L times the correct expression, so it has the unit of henry. Q is a ratio (reactance at resonance to resistance) and must be dimensionless.
(4) Puts R in the numerator. More resistance makes the resonance flatter, so Q must fall as R rises; this expression is not even dimensionless.

More Resonance in Series LCR questions

All Resonance in Series LCR questions →

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.