In the circuit shown below, let
Vs1=7;Vs2=1;R1=2000;R2=1200;R3=2200;R4=1500;R5=800;R6=500;
syms V1 V2 V3
[V1,V2,V3]=solve((V1-Vs1)/R1+(V1-V2)/R2+(V1-V3)/R3,...
(V2-V1)/R2+V2/R5+(V2-Vs1)/R4+V3/R6+(V3-V1)/R3,...
V3==V2+Vs2,V1,V2,V3);
I1=(Vs1-V1)/R1;
I2=(V1-V2)/R2;
I3=(V1-V3)/R3;
I4=(Vs1-V2)/R4;
I5=V2/R5;
I6=V3/R6;
IVs2=I2+I4-I5;
I6a=I3+IVs2;
V1=vpa(V1,7)
V2=vpa(V2,7)
V3=vpa(V3,7)
I1=vpa(I1,7)
I2=vpa(I2,7)
I3=vpa(I3,7)
I4=vpa(I4,7)
I5=vpa(I5,7)
I6=vpa(I6,7)
IVs2=vpa(IVs2,7)
I6a=vpa(I6a,7)
Answers:
V1 =
3.064234
V2 =
1.183289
V3 =
2.183289
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