Xl/Xc = 5.54
frequency f' = ?
frequency resonant f = 220Hz
For resonant frequencies, Xl = Xc
Xl = 2pi*f*L = wL
Xc = 1/( 2pi*f*C ) = 1/wC
wL = 1/wC
moving w to one side,
w^2 = 1/LC
Now for non resonant.
The same thing applies but with a different frequency, so w is the only difference.
w'L = w'C
w'^2 = 1/LC
the ration between these two is the same.
w'^2/w^2 = 5.54
sub in 2pi*f for omega (w)
(2pi*f')^2 / (2pi * f)^2 = 5.54
f'^2/f^2 = 5.54
solve for f'
f' = sqrt(5.53*220Hz^2)
= 517.351 Hz
In a series RCL circuit the generator is set to a frequency that is not the resonant frequency. This nonresonant frequency is such that the ratio of the inductive reactance to the capacitive reactance of the circuit is observed to be 5.53. The resonant frequency is 220 Hz. What is the frequency of the generator?
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