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.