Question 213: AC fundamentals

Question

In the circuit shown in the figure, the ratio of the quality factor and the band width is ___________ s.

Accepted Answer

Bandwidth $\Delta \omega=\frac{R}{L}$
Quality factor $Q=\frac{1}{R} \sqrt{\frac{L}{C}}$
So $\frac{Q}{\Delta \omega}=\frac{\frac{1}{R} \sqrt{\frac{L}{C}}}{\frac{R}{L}}$
$$
\begin{aligned}
& =\frac{L^{\frac{3}{2}}}{R^{2} \sqrt{C}} \\
& =\frac{3^{\frac{3}{2}}}{10^{2}\left(27 	imes 10^{-6}ight)^{\frac{1}{2}}} \\
& =\frac{3 \sqrt{3}}{100\left(3 \sqrt{3} 	imes 10^{-3}ight)} \\
& =10
\end{aligned}
$$

AC fundamentals

In the circuit shown in the figure, the ratio of the quality factor and the band width is ___________ s.

Integer / Numeric Answer Type