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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