Question

Define quality factor of resonance in series LCR circuit. What is its SI unit?

Answer 1

Quality factor of resonance is a dimensionless parameter that describes how underdamped an oscillator or resonator is, and characterizes a resonator bandwidth relative to its center frequency.

At resonance, $X_C=X_L$ $⟹w_o=\sqrt{\frac{1}{LC}}$

$\therefore$ Quality factor in series LCR circuit $Q=\frac{w_{o}L}{R}=\frac{1}{R}\sqrt{\frac{L}{C}}$

As quality factor is dimensionless, thus it has no SI unit.