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(D) In a series $LCR$ circuit,the impedance $Z$ is given by $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$.For the current $I = \frac{V}{Z}$ to

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$\frac{1}{\sqrt{LC}}$

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(D) In a series $LCR$ circuit,the impedance $Z$ is given by $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$.For the current $I = \frac{V}{Z}$ to be maximum,the impedance $Z$ must be minimum.This occurs when the inductive reactance equals the capacitive reactance,i.e.,$\omega L = \frac{1}{\omega C}$.Solving for $\omega$,we get $\omega^2 = \frac{1}{LC}$,which implies $\omega = \frac{1}{\sqrt{LC}}$.This frequency is known as the resonant frequency of the $LCR$ circuit.

The current in a series $LCR$ circuit will be maximum when $\omega$ is

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