The Q-factor of a series resonance circuit is defined as the ratio of resonant frequency to the difference in two frequencies taken on both sides of the resonant frequency such that each current amplitude becomes √2 times value of the resonant frequency.
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Q-factor= Resonant frequency/Band width
Resonant frequency=> ωr= 1/ √LC
Band width= higher frequency-lower frequency
Band width=ω2-ω1
(ω1=ωr-Δ ω) and (ω2=ωr+Δω)
Therefore , band width= 2Δω
Q-factor= ωr/2Δω
