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Q.
Which one of the following curves represents the variation of impedance $(Z)$ with frequency $f$ in series $L C R$ circuit?
Alternating Current
Solution:
$Z=\sqrt{R^{2}+\left(2 \pi f L-\frac{1}{2 \pi f C}\right)^{2}}$
From above equation at $f=0 \Rightarrow Z=\infty$
Wihen $f=\frac{1}{2 \pi \sqrt{L C}}$ (resonant frequency) $\Rightarrow Z=R$
For $f > \frac{1}{2 \pi \sqrt{L C}} \Rightarrow Z$ 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).