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(C) The impedance $Z$ of a series $LCR$ circuit is given by $Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}$.At resonance,the inductive reactance $X_{L}$ is e

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$I^{2} R$

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(C) The impedance $Z$ of a series $LCR$ circuit is given by $Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}$.At resonance,the inductive reactance $X_{L}$ is equal to the capacitive reactance $X_{C}$,i.e.,$X_{L} = X_{C}$.Substituting this into the impedance formula,we get $Z = \sqrt{R^{2} + 0} = R$.The power loss in an $AC$ circuit is given by $P = I^{2} R$,where $I$ is the $R.M.S.$ current.Since $Z = R$ at resonance,the circuit behaves as a purely resistive circuit,and the power loss is $I^{2} R$.

For a series $LCR$ circuit,the power loss at resonance is

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