SSE JE Electrical Engineering 24 March 2021 Shift 1 Paper

The quality factor Q is defined as the ratio of the resonant frequency to the bandwidth.
$\mathrm{Q}=\frac{{\mathrm{f}}_{\mathrm{r}}}{\mathrm{BW}}$
${\mathrm{f}}_{\mathrm{r}}=$ resonant frequency
For a series RLC circuit, the resonance frequency is calculated as:
${\mathrm{f}}_{\mathrm{r}}=\frac{1}{\sqrt{\mathrm{LC}}}$
Also, the bandwidth of a series RLC circuit is calculated as:
$\mathrm{BW}=\frac{\mathrm{R}}{\mathrm{L}}$
Substituting this in Equation (1), we get:
$\mathrm{Q}=\frac{{\mathrm{f}}_{\mathrm{r}}}{\mathrm{B}\mathrm{W}}=\frac{1}{\mathrm{R}}\sqrt{\frac{\mathrm{L}}{\mathrm{C}}}$