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Question:

A $100 \Omega$ resistance, a $0.1 \mu \mathrm{F}$ capacitor and an inductor are connected in series across a $250 \mathrm{~V}$ supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is $60 \mathrm{~Hz}$.

  1. 0.70 H 

  2. 70.3 mH 

  3. $7.03 \times 10^{-5} \mathrm{H}$

  4. 70.3 H


Correct Option: , 4

Solution:

$\mathrm{C}=0.1 \mu \mathrm{F}=10^{-7} \mathrm{~F}$

Resonant frequency = 60 Hz

$\omega_{0}=\frac{1}{\sqrt{L C}}$

$2 \pi \mathrm{f}_{0}=\frac{1}{\sqrt{\mathrm{LC}}} \Rightarrow \mathrm{L}=\frac{1}{4 \pi^{2} \mathrm{f}_{\mathrm{o}}^{2} \mathrm{C}}$

by putting values $L \simeq 70.3 \mathrm{~Hz}$. 

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