Alternating Current

JEE Main level, numerical answer, medium

90 of 190

Question 90 of 190

The frequencies at which the current amplitude in an LCR series circuit becomes 12\dfrac{1}{\sqrt{2}} times its maximum value, are 212rads−1212rad{s}^{-1} and 232rads−1232rad{s}^{-1}. The value of resistance in the circuit is R=5ΩR=5\Omega. The self inductance in the circuit is _____ mHmH.

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Answer: 250

Bandwidth of RLC circuit is BW=f2−f1BW={f}_{2}-{f}_{1}=R2πL=\dfrac{R}{2\pi L}
Or, BW=ω2−ω1=RLBW={\omega }_{2}-{\omega }_{1}=\dfrac{R}{L}
BW=232−212=RLBW=232-212=\dfrac{R}{L}
Thus, self inductance in the circuit is L=520=250mHL=\dfrac{5}{20}=250mH

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