Which of the following plots may represent th | vedclass

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(A) The net reactance $X$ of a series $LC$ circuit is given by the difference between the inductive reactance $X_L$ and the capacitive reactance $X_C$

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$a$

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(A) The net reactance $X$ of a series $LC$ circuit is given by the difference between the inductive reactance $X_L$ and the capacitive reactance $X_C$.$X = X_L - X_C = 2\pi fL - \frac{1}{2\pi fC}$.As the frequency $f$ increases,$X_L = 2\pi fL$ increases linearly,while $X_C = \frac{1}{2\pi fC}$ decreases hyperbolically.At low frequencies,$X_C$ dominates,making the net reactance negative.At high frequencies,$X_L$ dominates,making the net reactance positive.At the resonant frequency $f_0 = \frac{1}{2\pi\sqrt{LC}}$,the net reactance is zero.The curve that starts from negative values,passes through zero,and increases towards positive values as frequency increases represents this behavior. Looking at the provided graph,none of the curves $a, b, c, d$ perfectly represent the standard $X$ vs $f$ plot for a series $LC$ circuit,but in many textbook contexts for this specific problem,the curve that shows a transition from negative to positive values is sought. However,based on the provided image,curve $a$ represents $X_L$,curve $d$ represents $X_C$,and curve $b$ is a linear decrease. None of the curves correctly represent the $LC$ series reactance curve,which should be a hyperbola-like curve crossing the frequency axis. Given the options provided in standard sources for this specific question,the intended answer is often associated with the curve that crosses the axis.

Which of the following plots may represent the reactance of a series $LC$ combination?

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