A series circuit consists of an ac source of variable frequency, a 125 ? resisto
ID: 2244013 • Letter: A
Question
A series circuit consists of an ac source of variable frequency, a 125? resistor, a 1.40?F capacitor, and a 4.30mH inductor.
(A) Find the impedance of this circuit when the angular frequency of the ac source is adjusted to the resonance angular frequency.
(B) Find the impedance of this circuit when the angular frequency of the ac source is adjusted to twice the resonance angular frequency.
(C) Find the impedance of this circuit when the angular frequency of the ac source is adjusted to half the resonance angular frequency
Explanation / Answer
a)
Z = ?(R^2 + (2?fL - 1/2?fC)^2)
resonance frequency ==> Z = R = 125?
b)w = 1/ sqrt(LC)
w = 1/sqrt(0.0043*1.4*10^-6)
w =2 pi f =12888.5
f_resonance =12888.5/2pi = 2052.3 Hz
f = 2 f_resonance =4104.6 Hz
Z = ?(R^2 + (2?fL - 1/2?fC)^2)
Z = sqrt ( 125^2 + { (2pi*4104.6*0.0043) - 1/(2pi *4104.4*1.4*10^-6)
Z = 150.11 ?
c)
f_resonance = 2052.3Hz
f = 0.5 * f_resonance = 1026.15 Hz
Z = ?(R^2 + (2?fL - 1/2?fC)^2)
Z = 150.11 ?
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