KCET · Physics · Alternating Current
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 \(0.4\)
- B \(2.5\)
- C \(5\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(2.5\)
Step-by-step Solution
Detailed explanation
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,
\(\begin{aligned} Q & =\frac{\omega_r}{\omega_2-\omega_1} \\ & =\frac{500}{600-400}=\frac{500}{200}=2.5\end{aligned}\)
\(\begin{aligned} & \omega_1=400 \mathrm{rad} / \mathrm{s} ; \omega_r=500 \mathrm{rad} / \mathrm{s} \\ & \omega_2=600 \mathrm{rad} / \mathrm{s}\end{aligned}\)
Quality factor,
\(\begin{aligned} Q & =\frac{\omega_r}{\omega_2-\omega_1} \\ & =\frac{500}{600-400}=\frac{500}{200}=2.5\end{aligned}\)
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