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(D) In an $LCR$ series circuit,the impedance $Z$ is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$,where $X_L = 2\pi fL$ and $X_C = 1/(2\pi fC)$.At resonan

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(D) In an $LCR$ series circuit,the impedance $Z$ is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$,where $X_L = 2\pi fL$ and $X_C = 1/(2\pi fC)$.At resonance frequency $f_r$,$X_L = X_C$,so $Z$ is minimum $(Z = R)$ and the current $I = V/Z$ is maximum.For frequencies $f  X_L$,so $Z$ decreases as $f$ increases towards $f_r$,causing the current $I$ to increase.For frequencies $f > f_r$,$X_L > X_C$,so $Z$ increases as $f$ increases beyond $f_r$,causing the current $I$ to decrease.Thus,the graph of current $I$ versus frequency $f$ shows a peak at $f_r$,which corresponds to the shape shown in graph $D$.

An $ac$ source of variable frequency $f$ is connected to an $LCR$ series circuit. Which one of the graphs represents the variation of current $I$ in the circuit with frequency $f$?

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