QUALITY factor Q is defined as the ratio of the resonant frequency to the bandwidth.\(Q=\frac{{{f}_{r}}}{BW}\)fr = resonant frequencyMathematically, for a COIL, the quality factor is given by:\(Q = \frac{{{\omega _o}L}}{R}=\frac{X_L}{R}\)Also, the bandwidth is defined as the difference in the upper and lower cut off frequencies, i.e.B.W. = fU - fLCalculation:Given fu = 2.2 kHz and fL = 1.8 kHz.The bandwidth will be:B.W. = 2.2 - 1.8 kHz = 0.4 kHzResonant frequency or notch frequency = 2 kHz∴ The quality factor will be:\(Q=\frac{{{f}_{r}}}{BW}=\frac{2k}{0.4k}\)Q = 5 The sharpness of the resonance in RLC series resonant circuit is measured by the quality factor and is explained in the figure shown below:Observations:Less the Bandwidth, more the Quality factor.More the Bandwidth, less is the Quality factor.For the above figure, B2 > B1, so Q2 < Q1