Question

An a.c source of variable frequency f is connected to an LCR series circuit. Which of the graphs in figure represents the variation of current I in the circuit with frequency f?

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

$Z=\sqrt{R^2+{\left(2\pi fL-\frac{1}{2\pi fC}\right)}^2}$
From the above equation at $f=0,Z=\infty$
when, $f=\frac{1}{2\pi \sqrt{LC}}$ (resonant frequency)
$\Rightarrow Z=R$
For $f>\frac{1}{2\pi \sqrt{LC}}$
$\Rightarrow$ Z starts increasing
$\therefore$ For frequency $0>f,Z$ decreases and for $f_r\to \infty ,Z$
increases.
Hence $\left(I=\frac{V}{Z}\right)$ increases and for frequency $f_r\to \infty ,Z$
increases, hence I decreases.