Question

If the band stop filters is to reject a 200 Hz Sinusoid, while passing other frequencies calculate the values of L and C. Take $R=150\Omega$ and bandwidth as 100 Hz.

• A. $0.5H,2.66\mu F$
• B. $0.2387mH,2.66F$
• C. $0.2387H,2.66F$
• D. $0.2387H,2.66\mu F$

Answer 1

The correct option is D $0.2387H,2.66\mu F$

We use formula for a series resonant circuit,

$B=2\pi \left(100\right)=200\pi rad/s$

But,
$B=\frac{R}{L}\Rightarrow L=\frac{R}{B}=\frac{150}{200\pi }=0.2387H$

Rejection of the 200 Hz sinusoid means that $f_o$ is 200 Hz, so that ${\omega }_o$ is

${\omega }_o=2\pi f_o=2\pi \left(200\right)=400\pi rad/s$

Since,
${\omega }_0=1/\sqrt{LC}$

$C=\frac{1}{{\omega }_o^{2}L}=\frac{1}{\left(400\pi {)}^2\right(0.2387)}=2.66\mu F$