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Safari File Edit View History Bookmarks Window Help 4) Wed 5:20 PM 2120 Homework-10 VM http://www.webassign.net/web/student/Assignment-Responses/submit?dep 8800110 c Q Webassign O Ga m EEEE Question on...cminds.com Potatoes Pl...ome Recipes peanut butte...ing) Recipe Bodybuildin...Fitness.com Frequently ...d Questions verified W ..sonFire.com osneaker Ni...s and shoes Please Be Clear For Full Credit C... 2120 Homework-10 4. +-10 points. My Notes The figure shows the current and voltage graphs for a series RLC circuit. Voltage 10 V 2 A Current 100 50 2 A 100 V (a) What is the impedance (Z) of the circuit? (b) What is the phase angle between the current and voltage (positive if the the current lags, negative if it leads)? (c) What is the resistance (R) of the circuit? (d) If L 190 uH, what is the resonance frequency of this circuit? Hz da 212 nointe L Previous Answers u Nata L Kniaht 24

Explanation / Answer

a)

From the graph

Peak Voltage

Vp=10 V

Peak Current

Ip=2 A

so Impedance

Z=Vp/Ip =10/2

Z=5 ohms

b)

I=Imax*cos(Wt+phi)

at t=0 =>I =Imax/2

so

Imax/2 =Imax*cos(phi)

phi=cos^-1(1/2) =60 degrees

c)

since

tan(phi)=XL-XC/R

XL-XC=R*tan60

Impedance

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

Z=sqrt[R^2+(R*tan60)^2]

=>R =Z/sqrt[1+(tan60)^2]

R=5/sqrt[1+3]

R=2.5 ohms

d)

From the graph ,Time period is

T=100 us

angular frequency

W=2pi/T =2pi/100*10^-6

W=62831.85 rad/s

since

XL-Xc=Rtan60 =2.5*tan60

XL-Xc=4.33

at W=62831.85

WL-1/WC =4.33

62831.85*(190*10^-3)-1/62831.85*C=4.33

C=1.334*10^-9 F

so resonant frequency

f=1/2pi*sqrt(LC)

f=1/2pi*sqrt[190*10^-3*1.334*10^-9)

f=9998.2 Hz

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