Consider an LC circuit in which L = 490 mH and C = 0.108 µF. (a) What is the res
ID: 1646332 • Letter: C
Question
Consider an LC circuit in which L = 490 mH and C = 0.108 µF.
(a) What is the resonance frequency 0?
4.35 krad/s
(b) If a resistance of 1.08 k is introduced into this circuit, what is the frequency of the damped oscillations?
4.20 krad/s
(c) By what percentage does the frequency of the damped oscillations differ from the resonance frequency?
-3.448 %
The first two are correct, the last one is incorrect. I get this response:
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.%
Can someone please explain how to do part c?
Explanation / Answer
(A) w0 = 1/ sqrt(LC) = 4347 rad/s
(B) w = sqrt[ 1/LC - R^2 / 4L^2]
w = 4205 rad/s
(C) % = ( (w0 - w) / w0) x 100
= ( ( 4347 - 4205) / 4347) x 100
= 3.27 %
{ only three significant figures have to use to only as in every given value there are only three significant values}