Réseau électrique - différents exemples

s_2

Cas 1

Cas 2

Cas 3

cas1

cas2

cas3

F = (-5.946675070956309, 0.5197506989164417)
C = (-4.241062158252773, -0.44282292508457133)
B = (-4.241062158252773, 0.5197506989164417)
a(x) = x < -0.7
R_1 = 0.05 (slider from 0.01 to 0.2, step 0.01)
R_2 = 0.25 (slider from 0.01 to 0.25, step 0.01)
I1_{max} = 4.5 (slider from 1 to 5)
I2_{max} = 5 (slider from 1 to 5)
I_3 = 4 (slider from 1 to 5)
I_4 = 2 (slider from 1 to 5)
R_3 = 0.25 (slider from 0.1 to 1, step 0.05)
R_4 = 0.25 (slider from 0.1 to 1, step 0.05)
K: I_3 + I_4
E(x) = (R_1 * x^(2)) + (R_2 * (K - x)^(2)) + (R_3 * I_3^(2)) + (R_4 * I_4^(2))
A = Extremum(E)
g = Expand(E)
h = CompleteSquare(E)
D = (-5.946675070956309, -0.44282292508457133)
t1, i, j, k, l = Polygon(B, C, D, F)
f(x) = If[Max[K - I2_{max}, 0] ≤ x ≤ I1_{max}, E(x)]
F_1 = (-8.033611523028368, 0.5197506989164421)
C_1 = (-6.327998610324835, -0.44282292508457144)
B_1 = (-6.327998610324835, 0.5197506989164421)
D_1 = (-8.033611523028368, -0.44282292508457144)
t1_1, i_1, j_1, k_1, l_1 = Polygon(B_1, C_1, D_1, F_1)
F_2 = (-10.100547975100442, 0.5366379554778636)
C_2 = (-8.394935062396899, -0.42593566852315023)
B_2 = (-8.394935062396899, 0.5366379554778636)
D_2 = (-10.100547975100442, -0.42593566852315023)
t1_2, i_2, j_2, k_2, l_2 = Polygon(B_2, C_2, D_2, F_2)
Somtest: R_1 + R_2 + R_3 + R_4 + I1_{max} + I2_{max} + I_3 + I_4
Prodtest: ((((((((R_1 * R_2) * R_3) * R_4) * I1_{max}) * I2_{max}) * I_3) * I_4) * 1000)
b = If(Somtest ≟ 16.5 ∧ Prodtest ≟ 45, true, false)
c = If(Somtest ≟ 15.65 ∧ Prodtest ≟ 64, true, false)
d = If(Somtest ≟ 16.3 ∧ Prodtest ≟ 140.625, true, false)
K_1: I_3 + I_4
E_1(x) = (R_1 * x^(2)) + (R_2 * (K_1 - x)^(2)) + (R_3 * I_3^(2)) + (R_4 * I_4^(2))
A_1 = Extremum(E_1)
g_1 = Expand(E_1)
h_1 = CompleteSquare(E_1)
K_3: I_3 + I_4
K_2: I_3 + I_4
E_2(x) = (R_1 * x^(2)) + (R_2 * (K_2 - x)^(2)) + (R_3 * I_3^(2)) + (R_4 * I_4^(2))
A_2 = Extremum(E_2)
g_2 = Expand(E_2)
h_2 = CompleteSquare(E_2)
texte1: "P=R_1\cdot I_1^2+R_2(I_3+I_4 -I_1)^2+R_3\cdot I_3^2+R_4\cdot I_4^2\\
P(x)= " + (LaTeX[E]) + ""
texte1_1: "Forme\ développée :\\
P(x)=" + (LaTeX[g_1]) + ""
texte1_2: "Forme\ canonique :\\
P(x)=" + (LaTeX[h_2]) + ""