A series circuit consists of an ac source of variable frequency, a 120? resistor

ID: 1297147 • Letter: A

Question

A series circuit consists of an ac source of variable frequency, a 120? resistor, a 1.25?Fcapacitor, and a 4.50mH 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.

Resonant angular frequency

Wo=1/sqrt(LC)=1/sqrt[1.25*10-6*4.5*10-3)] =13,333.33 rad/s

at resonance ,inductive reactance equals capacitive reactance i.e XL=XC

So Impedance

Z=sqrt[R2+(XL-XC)2]=R

Z=R=120 ohms

W=2Wo=26,666.67 rad/s

Inductive reactance

XL=WL =26,666.67*4.5*10-3=120 ohms

Capacitive reactance

XC=1/WC =1/26,666.67*1.25*10-6=30 ohms

Impedance

Z=sqrt[1202+(120-30)2]

Z=150 ohms

Given

W=Wo/2=6666.67 rad/s

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

XC=1/6666.67*1.25*10-6 =120 ohms

Impedance

Z=sqrt[1202+(30-120)2]=150 ohms

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.