A series circuit consists of an ac source of variable frequency, a 115 ohm resis

Question

A series circuit consists of an ac source of variable frequency, a 115 ohm resistor, a 1.25 microfarad capacitor, and a 4.50 mH inductor.

a) Find the impedance of this circuit when the angular frequency of the ac source is adjusted to the resonance angular frequency. (answer is in ohms)

b)Find the impedance of this circuit when the angular frequency of the ac source is adjusted to twice the resonance angular frequency. (answer is in ohms)

c)Find the impedance of this circuit when the angular frequency of the ac source is adjusted to half the resonance angular frequency. (answer is in ohms)

Explanation / Answer

a)

when angular frequency =resonance frequency

XL=Xc

so

Z=R =115 ohms

b)

Resonace angular frequency

Wo =1/sqrt(LC) =1/sqrt(1.25*10^-6*4.5*10^-3)

Wo=13333.33 rad/s

given W=2Wo =26,666.67 rad

XL=WL =26666.67*4,5*10^-3 =120 ohms

Xc=1/WC =1/26666.67*1.25*10^-6

Xc=30 ohms

so

Z=sqrt[R^2+(XL-Xc)^2] =sqrt[115^2+(120-30)^2]

Z=146.03 ohms

c)

W=Wo/2 =6666.67 rad

XL=WL =6666.67*4.5*10^-3 =30 ohms

Xc =1/WC =1/6666.67*1.25*10^-6 =120 ohms

Z=sqrt[R^2+(XL-Xc)^2]=sqrt[115^2+(30-120)^2]

Z=146 .03 ohms

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