esercizio principio di sovrapposizione

agisce solo E1:
i1' +i2'+i4' = 0 ---> x+y+t =0
i3'= i2'+i4' ---> -z = x + t
e1 = -R1*i1' +R2*i2' +R3*i3' ---> 20=-20*x + 40*y + 80*z
Vab'= R2*i2' = R4*i4' ---> 40*y = 160*t
i1' = 5/29 A; i2' = 4/29A ; i3' = 4/29 A; i4' = 1/29 A
t'≈0.034483, x'≈-0.17241, y'≈0.13793, z'≈0.13793
agisce solo io2:
io2 = i1"+i2"+i4" ---> x+y+t = 1
i3" = i2" + i4" ---> -z = x + t
0 = -R1*i1" +R2*i2"+R3*i3" ---> 0=-20*x + 40*y + 80*z
Vab" = R2*i2" = R4*i4" ---> 40*y = 160*t
i1" = 4/29 A; i2" = 20/29A ; i3" = -9/29 A; i4" = 5/29 A

t" = 5/29, x" = 4/29, y" = 20/29, z" = -9/29
t"≈0.17241, x"≈0.13793, y≈"0.68966, z"≈-0.31034
sovrapponendo:
i1 = i1'+ i1" = 5/29 +4/29 = 9/29 A;

 i2 = i2'+i2" = 4/29 + 20/29 = 24/29 A ;

i3 =i3'+ i3" = 4/29 -9/29 = -5/29 A;
i4 = i4'+i4" = 1/29 + 5/29 = 6/29 A ;

... supponendo i conti e le equazioni corrette