Question

The values of $L$ and $R$ in $LCR$ circuit are $1mH$ and $10\Omega$ respectively. What is the value of its bandwidth?

• A. $\frac{10000}{2\pi }Hz$
• B. $\frac{1000}{\sqrt{3}}Hz$
• C. $\frac{100}{\pi }Hz$
• D. $\frac{100}{\sqrt{2}}Hz$

Answer 1

The correct option is A $\frac{10000}{2\pi }Hz$


At resonance frequency, $f_r=\frac{1}{2\pi \sqrt{LC}}$,
current $i=I_{max}$ (maximum currency)

And let $f_1$ and $f_2$ be the two frequencies between which the current $i>\frac{I_{max}}{\sqrt{2}}$.

Then $\Delta f=f_2-f_1$ is known as bandwidth.

$\Delta f=\frac{R}{2\pi L}=\frac{10}{2\pi (1\times {10}^{-3})}$
$=\frac{{10}^4}{2\pi }Hz$