Question 297: AC fundamentals

Question

Which one of the following graph represent correctly the variation of impedance $(\mathrm{Z})$ of a series LCR circuit with the frequency $(v)$ of applied a.c.?

Accepted Answer

$$\mathrm{Z}=\sqrt{\mathrm{R}^2+\left(2 \pi v L-\frac{1}{2 \pi v C}\right)^2}$$
From above equation at $v=0 \Rightarrow Z=\infty$
When $v=\frac{1}{2 \pi \sqrt{\mathrm{LC}}}$ (resonant frequency)
$$\Rightarrow \mathrm{Z}=\mathrm{R}$$
For $v>\frac{1}{2 \pi \sqrt{L C}} \Rightarrow Z$ starts increasing.
i.e., for frequency $0-v_r, Z$ decreases and for $v_r$ to $\infty, \mathrm{Z}$ increases. This is justified by graph (B).

Answer

A

Answer

B

Answer

C

Answer

D

AC fundamentals

Which one of the following graph represent correctly the variation of impedance (\mathrm{Z}) of a series LCR circuit with the frequency (v) of applied a.c.?

Choose the correct answer: