A series circuit consists of an ac source of variable frequency, a 130 resistor,
ID: 1644808 • Letter: A
Question
A series circuit consists of an ac source of variable frequency, a 130 resistor, a 1.50 F capacitor, and a 4.60 mH 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 = sqrt(R^2 + (XL - XC)^2)
XL = 2*pi*F*L
w = 2*pi*F
F = 60 Hz
in this case w = 2f = 2 x 60 = 120 Hz
XL = 2 x 3.14 x 60 x 4.60 x 10^-3
XL = 1.73 ohm
Z = sqrt(130^2 - 1.73^2)
Z = 129.9.ohm
resonance frequency =W = 1/2pi*sqrt(LC) = 1/(2pi*sqrt(4.60*10^-3*1.5*10^-6)) = 1916 Hz
impedance = R i + (WL - 1/WC) j = 130 i + j(1916*5*10^-3 - 1/(1916*1.5*10^-6) = 130 i -339.13 j
magnitude = sqrt ( 130^2 + -339.13^2) = 313. 22ohm
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