Physics - EMI/AC Question with Solution | TestHub

In$\mathrm{LCR}$series, resonant frequency,

${\mathrm{f}}_{\mathrm{r}}=600 \mathrm{Hz}$

$\therefore {\mathrm{\omega }}_{\mathrm{r}}=2\mathrm{\pi }\times 600 \mathrm{Hz}$

Frequencies at half power are given as,

${\mathrm{f}}_1=550 \mathrm{Hz}$and${\mathrm{f}}_2=650 \mathrm{Hz}$

${\mathrm{\omega }}_1=2\mathrm{\pi }\times 550 \mathrm{Hz}$and${\mathrm{\omega }}_2=2\mathrm{\pi }\times 650 \mathrm{Hz}$

Quality factor,$\mathrm{Q}=\frac{{\mathrm{\omega }}_{\mathrm{r}}}{{\mathrm{\omega }}_2-{\mathrm{\omega }}_1}$

$=\frac{2\mathrm{\pi }\times 600}{2\mathrm{\pi }\times 650-2\mathrm{\pi }\times 550}$

$=\frac{2\mathrm{\pi }\times 600}{2\mathrm{\pi }\times 100}=6$