Question

A resonance circuit having inductance and resistance $2 \times 10^{-4} H$ and $6.28 \Omega$ respectively oscillates at $10 MHz$ frequency. The value of quality factor of this resonator is ________. $[\pi=3.14]$

Answer 1

Given : $L =2 \times 10^{-4} H$
$R =6.28 \Omega $
$f =10 MHz =10^{7} Hz$
Since quality factor,
$Q =\omega_{0} \frac{ L }{ R }=2 \pi f \frac{ L }{ R }$
$\therefore Q =2 \pi \times 10^{7} \times \frac{2 \times 10^{-4}}{6.28} $
$Q =2 \times 10^{3}=2000 $