Quality factor in LCR

Advanced

Sharpness of resonance.

Key relationQ = ω₀L/R

Q = ω₀L/R = 1/(ω₀RC) measures the sharpness of resonance; large Q means narrow bandwidth. It's the voltage magnification across L or C.

Worked example

L = 1 mH, R = 10 Ω, ω₀ = 10⁶: Q = 100.

Common mistake

High Q needs low resistance.

In more detail

The quality factor of a series LCR circuit is Q = ω0L/R, which measures the sharpness of resonance. High Q gives narrow peaks and strong selectivity.

High-Q circuits select a single radio station out of many.
Low-Q circuits are used for broadband applications.
Engineers designing filters choose the Q factor to balance selectivity and bandwidth in a radio receiver.

What does high Q mean?

The resonance is sharp, so the circuit responds strongly only near the resonant frequency.

How can Q be increased?

Reduce the resistance or increase the inductance relative to it.

Does a higher Q mean narrower resonance?

Yes. A high Q means the resonance peak is sharp, so only frequencies very close to the resonant frequency pass.