JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Alternating Current

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

Answer: 10

Solution

For the series resonant circuit the bandwidth is

Δ ω = \frac{R}{L}

and the quality factor is

Q = \frac{ω _{0} L}{R}

, with resonant frequency

ω_{0} = \frac{1}{L C}

. Their ratio is

\frac{Q}{Δ ω} = \frac{ω _{0} L ^{2}}{R ^{2}}

. With

L = 3 H

C = 27 μ F

and

R = 10 Ω

, the resonant frequency is

ω_{0} = \frac{1}{3 \times 27 \times 1 0 ^{- 6}} = \frac{1}{9 \times 1 0 ^{- 3}} rad/s

, so

\frac{Q}{Δ ω} = \frac{1}{9 \times 1 0 ^{- 3}} \cdot \frac{9}{100} = 10 s

JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Integer answer