Mathc matrices/a219
En étudiant le circuit dans le sens des aiguilles d'une montre, nous pouvons écrire :
Au noeud A :
Entrées = Sortie
I1 = I2 + I3
Au noeud B :
Entrées = Sortie
I3 = I4 + I5
Au noeud C :
Entrées = Sortie
I2 + I5 = I6
Au noeud D :
Entrées = Sortie
I6 + I4 = I1
Soit :
a) +I1 -I2 -I3 = 0
+I3 -I4 -I5 = 0
+I2 +I5 -I6 = 0
-I1 +I4 +I6 = 0
Partie gauche du circuit : 90 -I2 R2 - I6 R61 = 0
b) -I2 R2 - I6 R6 = -90
Partie droite haute du circuit : I2 R2 - I3 R3 - I5 R5 = 0
c) I2 R2 - I3 R3 - I5 R5 = 0
Partie droite basse du circuit :
I6 R6 + I5 R5 - I4 R4 = 0
d) - I4 R4 + I5 R5 + I6 R6 = 0
Partie extérieure du circuit : 90 - I3 R3 - I4 R4 = 0
e) - I3 R3 - I4 R4 = -90
Donc:
a) +I1 -I2 -I3 = 0
+I3 -I4 -I5 = 0
+I2 +I5 -I6 = 0
-I1 +I4 +I6 = 0
b) -I2 R2 -I6 R6 = -90
c) +I2 R2 -I3 R3 -I5 R5 = 0
d) -I4 R4 +I5 R5 +I6 R6 = 0
e) -I3 R3 -I4 R4 = -90
Avec R2 = 50, R3 = 20, R4 = 50,
R5 = 10, R6 = 20
a) +I1 -I2 -I3 = 0
+I3 -I4 -I5 = 0
+I2 +I5 -I6 = 0
-I1 +I4 +I6 = 0
b) -I2 50 -I6 20 = -90
c) +I2 50 -I3 20 -I5 10 = 0
d) -I4 50 +I5 10 +I6 20 = 0
e) -I3 20 -I4 50 = -90
Arrangeons le système
I1 I2 I3 I4 I5 I6
+1 -1 -1 +0 +0 +0 0 0 0
+0 +0 +1 -1 -1 +0 0 0 0
+0 +1 +0 +0 +1 -1 0 0 0
-1 +0 +0 +1 +0 +1 0 0 0
+0 -50 +0 +0 +0 -20 0 0 -90
+0 +50 -20 +0 -10 +0 0 0 0
+0 +0 +0 -50 +10 +20 0 0 0
+0 +0 -20 -50 +0 +0 0 0 -90
Le code en langage C :
double ab[RA*(CA+Cb)]={
// I1 I2 I3 I4 I5 I6
+1, -1, -1, +0, +0, +0, 0, 0, 0,
+0, +0, +1, -1, -1, +0, 0, 0, 0,
+0, +1, +0, +0, +1, -1, 0, 0, 0,
-1, +0, +0, +1, +0, +1, 0, 0, 0,
+0, -50, +0, +0, +0, -20, 0, 0, -90,
+0, +50, -20, +0, -10, +0, 0, 0, 0,
+0, +0, +0, -50, +10, +20, 0, 0, 0,
+0, +0, -20, -50, +0, +0, 0, 0, -90,
};
La solution est donné par la résolution du système :
I1 I2 I3 I4 I5 I6 +1.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +3.00 +0.00 +1.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +0.00 +0.00 +2.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +2.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 I1 = 3, I2 = 1, I3 = 2, I4 = 1, I5 = 1, I6 = 2,