Q 12-07-077JEE MainJEE Main 2023 (24 Jan, Shift 1)Hard
In the circuit shown in the figure, the ratio of the quality factor and the band width is ______ s.
Numerical value type. Enter your answer.
Answer: 10
$\omega_0=\dfrac1{\sqrt{LC}}=\dfrac1{\sqrt{3\times27\times10^{-6}}}=\dfrac{1}{9\times10^{-3}}=\dfrac{1000}{9}\ \text{rad s}^{-1}$.
Bandwidth $\Delta\omega=\dfrac RL=\dfrac{10}{3}\ \text{rad s}^{-1}$, quality factor $Q=\dfrac{\omega_0}{\Delta\omega}=\dfrac{1000/9}{10/3}=\dfrac{100}{3}$.
$$\frac{Q}{\Delta\omega}=\frac{100/3}{10/3}=10\ \text{s}$$
Solution by Sreeraj P, M.Sc Physics