1 Find vxt using superposition 5 cos 15001 V 500 Solution1 c

1- Find vx(t) using superposition, 5 cos 15001 V 500

1) conider 5cos1500t voltage source:

w=1500 rd/sec

xc=1/(jwc)=1/(j1500*2*10^-6)=-j333.33 ohms

vx(t)=-j333.33*5<0/(500-j333.33)=2.77<-56.3 volts

vx(t)=2.77cos(1500t-56.3) volts

consider 10cos500t voltage ssourrce:

w=500 rad/sec

xc=1/(jwc)=1/(j500*2*10^-6)=-j1000 ohms

vx(t)=-j1000*5<0/(500-j1000)=4.472<-26.56 volts

vx(t)=4.472cos(500t-26.56) volts

total voltage=4.472cos(500t-26.56)+ 2.77cos(1500t-56.3)