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(A) In an $LCR$ series circuit,the amplitude of the current is given by $I_0 = \frac{E_0}{Z}$,where $Z = \sqrt{R^2 + (X_L - X_C)^2}$.For the current a

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$\frac{100}{\pi^2}$

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(A) In an $LCR$ series circuit,the amplitude of the current is given by $I_0 = \frac{E_0}{Z}$,where $Z = \sqrt{R^2 + (X_L - X_C)^2}$.For the current amplitude to be maximum,the impedance $Z$ must be minimum.This occurs at resonance,where $X_L = X_C$.Given the $emf$ equation $e = 200 \sin(100 \pi t) \ V$,the angular frequency is $\omega = 100 \pi \ rad/s$.The condition for resonance is $\omega L = \frac{1}{\omega C}$.Substituting the given values: $100 \pi 	imes L = \frac{1}{100 \pi 	imes 1 	imes 10^{-6}}$.$L = \frac{1}{(100 \pi)^2 	imes 10^{-6}} = \frac{1}{10000 \pi^2 	imes 10^{-6}} = \frac{1}{10^{-2} \pi^2} = \frac{100}{\pi^2} \ H$.

An $LCR$ series circuit is connected to an external $emf$,$e = 200 \sin(100 \pi t) \ V$. The values of capacitance and resistance in the circuit are $1 \ \mu F$ and $100 \ \Omega$ respectively. The amplitude of current in the circuit is maximum when the inductance is (in henry):

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