In the circuit shown in the figure, the ratio of the quality factor and the band width is ________ s. [2023]

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Solution

Q.
In the circuit shown in the figure, the ratio of the quality factor and the band width is ________ s. [2023]

Ans.
(10)

$Δ ω = \frac{R}{L}$

$Q = \frac{ω_{0}}{Δ ω} = ω_{0} \frac{L}{R}$

$ω_{0} = \frac{1}{\sqrt{3 \times 27 \times 10^{- 6}}} = \frac{1}{9 \times 10^{- 3}}$

$\frac{Q}{Δ ω} = \frac{ω_{0} \frac{L}{R}}{\frac{R}{L}} = ω_{0} \frac{L^{2}}{R^{2}} = \sqrt{\frac{1}{L C}} \frac{L^{2}}{R^{2}}$

$\Rightarrow \frac{Q}{Δ ω} = \frac{1}{9 \times 10^{- 3}} \times \frac{9}{100} = 10 s$

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