2 3 determine the values of the resistance R and the inducta

2 mF 1002 vo(1) This circuit is at steady state. The input to t his circuit is the voltage source voltage, V(t), given by vs(1) = 40cos (351 + (-50°)) v The output voltage, Vo(t), can be expressed as volt) = Acos(351 + ) v where A and are constants such that A > 0 and-180°

Solution

1) vs(t)=40cos(35t-50) volts

vs(t)=40<-50 volts

w=35 rad/ssec

xc=1/(jwc)=1/(j35*2*10^-3)=-j14.285 ohmss

by using voltage divison forrmula

vo=[(40<-50*10)/(10-j14.285)]=22.9<5.006 volts.

vo(t)=22.9cos(35t+5.006) volts.

A=22.9, theta=5.006

2) vs(t)=30cos(50t-40) volts

vs=30<-40 volts.

w=50 rad/sec

xc=1/(jwc)=1/(j50*2*10^-3)=-j10 ohms.

vo=[(30<-40*24)/(24+[(16*-j10)/(16-j10)])]=24.49<-25.83 volts.

vo(t)=24.49cos(50t-25.83) volts.

A=24.49, theta=-25.83

3) v(t)=8.5292cos(21t+81.213) volts.

v=8.5292<81.213 volts

w=21 rad/sec

i(t)=210cos(21t+65) amps

i=210<65 amps

w=21 rad/sec

z=v/i=(8.5292<81.213)/(210<65)=0.0406<16.213 ohms.