What is the value of inductance L for which t | vedclass

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(A) The current in an $LCR$ series circuit is given by $i = \frac{V}{\sqrt{R^2 + (X_L - X_C)^2}}$,where $V$ is the $rms$ voltage,$R$ is the resistance

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$100 \ mH$

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(A) The current in an $LCR$ series circuit is given by $i = \frac{V}{\sqrt{R^2 + (X_L - X_C)^2}}$,where $V$ is the $rms$ voltage,$R$ is the resistance,$X_L = \omega L$ is the inductive reactance,and $X_C = \frac{1}{\omega C}$ is the capacitive reactance.For the current to be maximum,the impedance must be minimum,which occurs when $X_L = X_C$.This condition is known as resonance,where $\omega L = \frac{1}{\omega C}$.Rearranging for $L$,we get $L = \frac{1}{\omega^2 C}$.Given $\omega = 1000 \ s^{-1}$ and $C = 10 \ \mu F = 10 	imes 10^{-6} \ F$.Substituting these values: $L = \frac{1}{(1000)^2 	imes 10 	imes 10^{-6}} = \frac{1}{10^6 	imes 10^{-5}} = \frac{1}{10} = 0.1 \ H$.Converting to millihenry: $0.1 \ H = 100 \ mH$.

What is the value of inductance $L$ for which the current is a maximum in a series $LCR$ circuit with $C=10 \mu F$ and $\omega=1000 \ s^{-1}$?

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