A series circuit consists of an ac source of variable frequency, a 150 resistor,

Question

A series circuit consists of an ac source of variable frequency, a 150 resistor, a 1.40 Fcapacitor, and a 4.88 mH inductor. Part A Find the impedance of this circuit when the angular frequency of the ac source is adjusted to the resonance angular frequency

Part B Find the impedance of this circuit when the angular frequency of the ac source is adjusted to twice the resonance angular frequency

Part 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

given

R = 150 ohms

C = 1.4 micro F

L = 4.88 mH

A) at resosnat frequency, impedance, z = R

= 150 ohms

B) resonant angular frequency, wo = 1/sqrt(L*C)

= 1/sqrt(4.88*10^-3*1.4*10^-6)

= 12098 rad/s

at w = 2*wo

= 2*12098

so, inductive reacatnce, XL = w*L = 2*12098*4.8*10^-3 = 116.1 ohms

capative reacatnce, Xc = 1/(w*c) = 1/(2*12098*1.4*10^-6) = 29.5 ohms

so, z = sqrt(R^2 + (XL - XC)^2)

= sqrt(150^2 + (116.1 - 29.5)^2)

= 173 ohms

c) at w = wo/2 = 12098/2

inductive reacatnce, XL = w*L = 12098*4.8*10^-3/2 = 29 ohms

capative reacatnce, Xc = 1/(w*c) = 1/(12098*1.4*10^-6/2) = 118 ohms

so, z = sqrt(R^2 + (XL - XC)^2)

= sqrt(150^2 + (29 - 118)^2)

= 173 ohms

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