A series circuit consists of an ac source of variable frequency, a 140 resistor,

ID: 1446839 • Letter: A

Question

A series circuit consists of an ac source of variable frequency, a 140 resistor, a 1.15 F capacitor, and a 4.12 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.

Impedence of RLC ckt is given by Z^2 = R^2 + (XL-Xc)^2

Xl = wL

and Xc = 1/wL

W = angular frequency = 1/sqrt(LC)

part A:

at resonance XL = Xc

Impedence Z = R = 140 ohms

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at W' = 2W0 = 2*(1/sqrt(1.15*10^ -6 * 4.12 *10^ -3)

W' = 29055.77 Rad/s

Xl = wL = 29055.77 * 4.12 *10^-3 = 119.7 ohms

Xc = 1/WC = 1/(29055.77 * 1.15 *10^-6) = 29.92 ohms

Impedence Z^2 = (140^2 ) + (119.7 - 29.92)^2

Z = 166.31 ohms

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part C: W' = W0/2 = 29055.7/2 = 14527.885 ohms

XL = wL = 14527.885 * 4.12 *10^-3 = 59.85 ohms

Xc = 1/wC = 1/(14527.885*1.15*10^-6) = 59.85 ohms

so Z^2 = R^2 + 0^2

Z = R = 140 ohms

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