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)

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