Physics - EMI/AC Question with Solution | TestHub

In resonance condition, maximum current flows in the circuit.

Current in the LCR circuit is given by

$i=\frac{V}{\sqrt{R^2+{\left(X_L-X_C\right)}^2}}$

For current to be maximum denominator should be minimum.

${\left(X_L-X_C\right)}^2=0$

$\Rightarrow X_L=X_C$

$\Rightarrow \omega L=\frac{1}{\omega C}$

$\therefore L=\frac{1}{{\omega }^{2}C}$

$=\frac{1}{{\left(1000\right)}^2\times 10\times {10}^{-6}}$

$=\frac{1}{10} \mathrm{H}$

$\therefore L=0.1\mathrm{ }\mathrm{H}=100\mathrm{ }\mathrm{mH}$