Risoluzione di un circuito

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qui x=j1   ;   y=  j2  ;  z=j3

correnti di maglia

V1 = j1*r1 +r2(j1+j2)+r4(j1+j3)                     ---> 10=x*10+10(x+y)+30(x+z)
V2 = r2(j1+j2)+r6(j2-j3)+r3*j2                          --> 20 = 10(x+y)+100(y-z)+30y
V3 = -r4(j1+j3)+r6(j2-j3)-r5*j3                         --> 30 = -30(x+z)+100(y-z)-50z

j1=x = 53/139 A , j2=y = -45/556 A , j3= z = -153/556 A

j1= x≈0.38129 A , j2= y≈-0.080935 A , j3= z≈-0.27518 A

i1=j1;i2=j1+j2; i3 = j2 ; i4 = j1+j3 ; i5 = j3 ; i6 = j3-j2

i2 = 167/556 A =167/556 ≈0.30036 A

Pr1 = r1*i1² = r1*j1²= 10*0.38129^2 = 1.453820641 W

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mentre qui...

x=i1; y=i2 ; z=i3; t=i4 ; u=i5 ; v=i6

Kirchhoff...

nodoA
i1+i3=i2              --> x+z=y
nodoB
i2+i6=i4               --> y+v=t
nodoC
i4+i5=i1               ---> t+u=x
m1
V1 = r1*i1 +r2*i2+r4*i4           --> 10=10*x+10y+30t
m2
V2=r2*i2 - r6*i6 +r3*i3            --> 20 = 10y -100v + 30z
m3
V3 = -r4*i4 -r6*i6 +r5*i5             --> 30 = -30t -100v+50u

t = 59/556, u = 153/556, v = -27/139, x = 53/139, y = 167/556, z = -45/556

t≈0.10612, u≈0.27518, v≈-0.19424, x≈0.38129, y≈0.30036, z≈-0.080935

i2 = 167/556 A = ≈0.30036 A

Pr1 = r1*i1² = 10*0.38129^2 = 1.453820641 W

...controlla!!!