What is the value of inductance L in mH for w | vedclass

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(C) In a series $LCR$ circuit,the current is maximum at resonance.At resonance,the inductive reactance equals the capacitive reactance,i.e.,$\omega L

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$100$

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(C) In a series $LCR$ circuit,the current is maximum at resonance.At resonance,the inductive reactance equals the capacitive reactance,i.e.,$\omega L = \frac{1}{\omega C}$.Therefore,the resonant frequency is given by $\omega = \frac{1}{\sqrt{LC}}$.Squaring both sides,we get $\omega^2 = \frac{1}{LC}$,which implies $L = \frac{1}{\omega^2 C}$.Given values: $\omega = 1000 \, rad/sec$ and $C = 10 \, \mu F = 10 	imes 10^{-6} \, F = 10^{-5} \, F$.Substituting these values into the formula:$L = \frac{1}{(1000)^2 	imes 10^{-5}} = \frac{1}{10^6 	imes 10^{-5}} = \frac{1}{10^1} = 0.1 \, H$.Converting to $mH$:$0.1 \, H = 0.1 	imes 1000 \, mH = 100 \, mH$.

What is the value of inductance $L$ in $mH$ for which the current is maximum in a series $LCR$ circuit with $C = 10 \, \mu F$ and $\omega = 1000 \, rad/sec$?

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