Total impedance of a series $L-C-R$ circuit varies with angular frequency of the $\mathrm{AC}$ source connected to it as shown in the graph. The quality factor $Q$ of the series $L-C-R$ circuit is

• A

  $0.4$
• Correct answer
  B

  $2.5$
• C

  $5$
• D

  $1$

Solution

According to given diagram, $\begin{aligned} & \omega_1=400 \mathrm{rad} / \mathrm{s} ; \omega_r=500 \mathrm{rad} / \mathrm{s} \\ & \omega_2=600 \mathrm{rad} / \mathrm{s}\end{aligned}$
Quality factor, $\begin{aligned} Q & =\frac{\omega_r}{\omega_2-\omega_1} \\ & =\frac{500}{600-400}=\frac{500}{200}=2.5\end{aligned}$

Hence, the correct answer is option: 'B'.