Question

A resistor of $R=6\Omega$ an inductor of $L=1\text{H}$ and a capacitor of $C=17.36\mu \text{F}$ are connected in series with an $AC$ source. Find the quality factor.

• A. $3.72$
• B. $40$
• C. $2.37$
• D. $80$

Answer 1

The correct option is B $40$

We know that the quality factor is given by:

$Q=\frac{{\omega }_{0}L}{R}$

Here, ${\omega }_0=\frac{1}{\sqrt{LC}}$

$\Rightarrow Q=\frac{1}{\sqrt{LC}}\times \frac{L}{R}=\frac{1}{R}\sqrt{\frac{L}{C}}$

From the data given in the question:

$Q=\frac{1}{6}\times \sqrt{\frac{1}{17.36\times {10}^{-6}}}$

$\therefore Q\approx 40$

Hence, $\left(B\right)$ is the correct answer.