Question

Which one of the following curves represents the variation of impedance $(Z)$ with frequency $f$ in series $LCR$ circuit?

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

$Z=\sqrt{R^2+{\left(2\pi fL-\frac{1}{2\pi fC}\right)}^2}$
From above equation at $f=0\Rightarrow Z=\infty$
Wihen $f=\frac{1}{2\pi \sqrt{LC}}$ (resonant frequency) $\Rightarrow Z=R$
For $f>\frac{1}{2\pi \sqrt{LC}}\Rightarrow Z$ starts increasing.
i.e., for frequency $0-f_r,Z$ decreases and for $f_r$ to $\infty ,Z$ increases. This is justified by graph (c).