In a series LCR circuit, the angular frequencies ${\mathrm{\omega }}_1$ and ${\mathrm{\omega }}_2$ at which the current amplitude falls to $\left(\frac{1}{\sqrt{2}}\right)$ of the current amplitude at resonance are separated by frequency interval $\frac{\mathrm{R}}{\mathrm{xL}}$. The value of ‘x’ is:

The bandwidth (BW) of a resonant circuit is defined as the total number of cycles below and above the resonant frequency for which the current is equal to 70.7%$\left[\left(\frac{1}{\sqrt{2}}\right) \mathrm{times}\right]$ of its resonant value.

And it is  denoted by change in $\mathrm{\Delta \omega }=\frac{\mathrm{R}}{\mathrm{L}}$.