The frequencies at which the current amplitude in an LCR series circuit becomes $\frac{1}{\sqrt{2}}$ times its maximum value, are $212 \mathrm{rad} \mathrm{s}^{-1}$ and $232 \mathrm{rad} \mathrm{s}^{-1}$. The value of resistance in the circuit is $\mathrm{R}=5 \Omega$. The self inductance in the circuit is \_\_\_\_ mH .

JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Alternating Current

The frequencies at which the current amplitude in an LCR series circuit becomes

\frac{1}{2}

times its maximum value, are

212 rad s^{- 1}

and

232 rad s^{- 1}

. The value of resistance in the circuit is

R = 5Ω

. The self inductance in the circuit is ____ mH .

Answer: 250

The bandwidth (difference between half-power frequencies) is

Δ ω = ω_{2} - ω_{1} = 232 - 212 = 20

rad/s. For an LCR circuit, bandwidth =

\frac{R}{L}

. Thus

L = \frac{R}{Δ ω} = \frac{5}{20} = 0.25

H = 250 mH.

JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Integer answer