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(B) The impedance $Z$ of a series $LCR$ circuit is given by the formula: $Z = \sqrt{R^2 + (2 \pi v L - \frac{1}{2 \pi v C})^2}$.At very low frequencie

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$(B)$

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(B) The impedance $Z$ of a series $LCR$ circuit is given by the formula: $Z = \sqrt{R^2 + (2 \pi v L - \frac{1}{2 \pi v C})^2}$.At very low frequencies $(v 	o 0)$,the capacitive reactance $X_C = \frac{1}{2 \pi v C}$ approaches infinity,so $Z 	o \infty$.At the resonant frequency $v_r = \frac{1}{2 \pi \sqrt{LC}}$,the inductive reactance $X_L$ equals the capacitive reactance $X_C$,making the net reactance zero. Thus,$Z = R$,which is the minimum value of impedance.For frequencies higher than the resonant frequency $(v > v_r)$,the inductive reactance $X_L = 2 \pi v L$ dominates,and $Z$ increases as $v$ increases.Therefore,the graph of $Z$ versus $v$ starts from a high value,decreases to a minimum value $R$ at $v_r$,and then increases again. This behavior is correctly represented by graph $(B)$.

Which one of the following graphs correctly represents the variation of impedance $(Z)$ of a series $LCR$ circuit with the frequency $(v)$ of the applied $a.c.$?

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