Use AC analysis to find the complex voltage for vc shown in

Use AC analysis to find the complex voltage for vc shown in the circuit below for frequencies of co = 103 rad/s, 104 rad/s, and 105 rad/s. The amplitude of the sine-wave source is 1 V. Express your answers in magnitude and phase form.

Solution

w=10^3 rad/sec

xc1=1/(jwc1)=1/(j10^3*100*10^-9)=-j10000 ohms

xc2=-j10000 ohms

apply nodal analysis

(v-1<0)/(-j10,000)+v/(10000)+v/(100-j10,000)=0

v[1/10000]+1/(-j10,000)+1/(100-j10,000)]=1<0/(-j10,000)

solving the above equation

v=0.446<26.79 volts

vc2=[(0.446<26.79)/(100-j10,000)*(-j10,000)]=0.445<26.217 volts

repeat the same procedure for other frequencies.