Obliczenie węzłowych napięć metodą wyznaczników (Cramera)
Δ = y11⋅y22⋅y33 - G1⋅G4⋅G3 - G3⋅G1⋅G4 - G3⋅y22⋅G3 - y11⋅G4⋅G4 - G1⋅G1⋅y33
3
2
1
G5
G1
J1
J6
J5
G4
G3
R2
E2
|
|
1 |
2 |
3 |
|
1 |
y11 |
-G1 |
-G3 |
Y= |
2 |
-G1 |
y22 |
-G4 |
|
3 |
-G3 |
-G4 |
y33 |
|
1 |
2 |
3 |
1 |
J11 |
-G1 |
-G3 |
2 |
J22 |
y22 |
-G4 |
3 |
J33 |
-G4 |
y33 |
V1
|
1 |
2 |
3 |
1 |
y11 |
J11 |
-G3 |
2 |
-G1 |
J22 |
-G4 |
3 |
-G3 |
J33 |
y33 |
|
1 |
2 |
3 |
1 |
y11 |
-G1 |
J11 |
2 |
-G1 |
y22 |
J22 |
3 |
-G3 |
-G4 |
J33 |
Δ1 = J11⋅y22⋅y33 - G1⋅G4⋅J33 - G3⋅J22⋅G4 - G3⋅y22⋅J33 - J11⋅G4⋅G4 - G1⋅J22⋅y33
|
J11 |
|
J1+J5 |
J = |
J22 |
= |
E2/R2 - J1 |
|
J33 |
|
-J6 |
Δ2 = y11⋅J22⋅y33 - J11⋅G4⋅G3 - G3⋅G1⋅J33 - G3⋅J22⋅G3 - y11⋅G4⋅J33 - J11⋅G1⋅y33
Δ3 = y11⋅y22⋅J33 - G1⋅J22⋅G3 - J11⋅G1⋅G4 - J11⋅y22⋅G3 - y11⋅J22⋅G4 - G1⋅G1⋅J33
V3
V2
gdzie:
y11 = G1+G3+G5,
y22 = G1+G2+G4,
G2 = 1/R2,
y33 = G3+G4.
V1 = Δ1 / Δ, V2 = Δ2 / Δ, V3 = Δ3 / Δ
Obliczenia numeryczne:
y11=9 S, y22=0.5 S, y33 = 7 S,
J11 = 6 A, J22 = 0, J33 = −6 A.
Δ = 122, Δ1 = 12, Δ2 = -120, Δ3 = -168,
V1 = 0.098 V, V2 = −0.984 V, V3 = −1.377 V
Liczba operacji:
[±] = 27, [*] = 48, [ / ] = 4.
Razem 79 o.a.