Question

An electronic test circuit produced a resonant curve of half power frequency points at $414Hz$ and $436Hz$. If Q factor be $10$, the resonant frequency of the circuit is:

• A. $220Hz$
• B. $22Hz$
• C. $2.2Hz$
• D. $0.22Hz$

Answer 1

The correct option is A $220Hz$

We have

$Q=\frac{f_r}{BW}$

Where

$Q=$ quality factor

$f_r=$ resonant frequency

$BW=$ Bandwidth

Also, bandwidth is the difference is half power frequencies.

So,

$Q=\frac{f_r}{f_2–f_1}$

Given

$f_1=414Hz,f_2=436Hz,Q=10$

So,

$f_r=Q(f_2–f_1)$

$f_r=10(436-414)=10\times 22=220Hz$

So the resonant frequency is $220Hz$