Hector Martinez UFT

1. UNIVERSIDAD “FERMIN TORO”
VICERRECTORADO ACADEMICO
FACULTAD DE INGENIERIA
CABUDARE EDO. LARA
PRACTICA No 7
Teorema de Superposición
Alumno:
Hector Martinez
Ci: 23.836.320
Cabudare, 25 de julio de 2015

2. Pre laboratorio
1.- Para el siguiente circuito, calcular todas las tensiones y
corrientes por mallas. Indiciar el sentido correcto de las corrientes
y tensiones.
Malla I₁
(910+560+390)I₁ -390I₂ - 910I₃ = 15
1860 I₁ -390I₂ -910I₃ = 15 I
Malla I₂
(820+390+220)I₂ - 390I₁ -820I₃ = 0
-390I₁ + 1430I₂ - 820I₃ = 0 II
Malla 3
(910+820+620)I₃ -820I₂ -910I₁ = 9
-910I₁ -820I₂ + 2350I₃ = 9 III

3. 1860I₁ - 390I₂ - 910I₃ = 15 I₁= 19,091x10¯³ A
-390I₁ + 1430I₂ - 820I₃ = 0 I₂= 14,554x10¯³ A
-910I₁ - 820I₂ + 2350I₃ = 9 I₃= 16,301x10¯³ A
Voltaje:
VR(620)= 16,301x10¯³x 620Ω = 10,10V
VR(910)= (I₁ - I₃) x 910Ω = (19,091x10¯³ -16,301x10¯³) x 910 = 2.538V
VR(820)= (I₃ - I₂) x 820Ω = (16,301x10¯³- 14,554x10¯³) x 820 = 1.432V
VR(390)= (I₁ - I₂) x 390Ω = (19,091x10¯³- 14,554x10¯³) x 390 = 3.720V
VR(560)= I₁ x 560Ω = 19,091x10¯³ x 560 = 10,69V
VR(220)= !₂ x 220Ω = 14,554x10¯³ x 220 = 3,20V
Corrientes
IR(620)= I₃ = 16,301x10¯³ A
IR(910)= I₁ - I₃ = 19,091x10¯³ - 16,301x10¯³ = 2,79x10¯³ A
IR(820)= I₃ - I₂ = 16,301x10¯³ - 14,554x10¯³ = 1,74x10¯³ A
IR(390)= I₁ - I₂ = 19,091x10¯³ - 14,554x10¯³ = 4,53x10¯³ A
IR(560)= I₁ = 19,091x10¯³ A
IR(220)= I₂ = 14,554x10¯³ A

4. 2. Con los datos del punto 1, llene la siguiente tabla.
620 910 820 390 560 220
Voltaje 10,10V 2.538V 1.432V 3.720V 10,69V 3,20V
Corrien
te
16,301x10
¯³ A
2,79x10
¯³ A
1,74x10
¯³ A
4,53x10
¯³ A
19,091x10
¯³ A
14,554x10
¯³ A
3. Aplicando superposición. Calcular las tensiones y corriente con
el sentido correcto para F₂= 0 y F₁ = 15V
Malla 1
1860I₁ - 390I₂ - 910I₃ = 15 I
Malla 2
-390I₁ + 1430I₂ -820I₃ = 0 II
Malla 3
-910I₁ - 820I₂ + 2350I₃ = 0
1860I₁ - 390I₂ - 910I₃ = 15 I₁ = 14.018 x10¯³ A
-390I₁ + 1430I₂ - 820I₃ = 0 I₂ = 8.671x10¯³ A
-910I₁ - 820I₂ + 2350I₃ = 0 I₃ = 8.454 x10¯³ A

5. Voltajes
VR(620)= i₃ x 620= 8.454 x10¯³ x 620 = 5.241V
VR(910)= (I₁ - I₃) 910 = (14.018 x10¯³ - 8.454 x10¯³ ) x 910 = 5.06V
VR(820)= (I₂ - I₃) 820 = (8.671x10¯³ - 8.454 x10¯³) x 820 = 0.177V
VR(390)=(I₁ - I₂) 390 =(14.018 x10¯³ - 8.671x10¯³) x390 = 2.08V
VR(560)= I₁ x 560 = 14.018 x10¯³ x 560 = 7.85V
VR(220)= I₂ x 220 = 8.671x10¯³ x 220 = 1.90V
Tabla 2
620 910 820 390 560 220
Voltaje 5.241V 5.06V 0.177V 2.08V 7.85V 1.90V
Corriente 8.454
x10¯³
5.56
x10¯³
-2.17x10¯^5 5.34
x10¯³
14.018
x10¯³
8.671x10¯³
IR(620)= I₃ = 8.454 x10¯³
IR(910)= I₁ - I₃ = 14.018 x10¯³ - 8.454 x10¯³ = 5.56 x10¯³
IR(820)= I₂ + I₃ = -8.671x10¯³ + 8.454 x10¯³ = -2.17x10¯^5
IR(390)= I₁ - I₂ = 14.018 x10¯³ - 8.671x10¯³ = 5.34 x10¯³
IR(560)= I₁ 14.018 x10¯³ A
IR(220)= I₂ = 8.671x10¯³

6. 4. Repita 3 para F₁ = 0 y F₂ =9V
Malla I₁
1860I₁ - 390I₂ - 910I₃ = 0 I
Malla I₂
-390I₁ + 1430I₂ - 820I₃ = 0 II
Malla I₃
-910I₁ - 820I₂ + 2350I₃ = 9
1860I₁ - 390I₂ - 910I₃ = 0 I₁= 5.07 x10¯³
-390I₁ + 1430I₂ - 820I₃ = 0 I₂= 5.88 x10¯³
-910I₁ - 820I₂ + 2350I₃ = 9 I₃= 7.84 x10¯³
Voltaje
VR(620)= I₃ x 620 = 7.84 x10¯³x 620 = 4,86 V
VR(910)= (I₃ - I₁) 910 = (7.84 x10¯³- 5.07 x10¯³) 910 = 2,52V
VR(820)= (I₃ - I₂) 820 = (7.84 x10¯³- 5.88 x10¯³) 820 = 1,60V
VR(390)= (I₂ - I₁) x 390 = (5.88 x10¯³- 5.07 x10¯³) 390 = 0,31V
VR(560)= I₁ x 560 = 5.07 x10¯³x 560 = 2,83V
VR(220)= I₂ x 220 = 5.88 x10¯³x 220 = 1,29V
Corrientes
IR(620)= I₃ = 7.84 x10¯³ A
IR(910)= I₃ - I₁ = 7.84 x10¯³- 5.07 x10¯³= 2,77 x10¯³
IR(820)= I₃ - I₂ = 7.84 x10¯³- 5.88 x10¯³= 1,96 x10¯³
IR(390)= I₂ + I₁ = -5.88 x10¯³ + 5.07 x10¯³= 0,81 x10¯³

7. IR(560)= I₁ = 5.07 x10¯³
IR(220)= I₂ = 5.88 x10¯³
Tabla 3
620 910 820 390 560 220
Voltaje 4,86 V 2,52V 1,60V 0,31V 2,83V 1,29V
Corriente 7.84
x10¯³ A
-2,77
x10¯³
1,96
x10¯³
0,81
x10¯³
5.07
x10¯³
5.88
x10¯³
5. Sume las 2 y 3 y compárela con la tabla 1
620 910 820 390 560 220
Corrient
e
8.454
x10¯³
5.56
x10¯³
-
2.17x10¯
^5
5.34
x10¯³
14.018
x10¯³
8.671x10¯
³
Corrient
e
7.84 x10¯³ -2,77
x10¯³
1,96
x10¯³
0,81
x10¯³
5.07
x10¯³
5.88 x10¯³
∑Corrien
te
16,23
x10¯³
2,79x10
¯³
1.93x10¯³ 6.15x10
¯³
19,08x10
¯³
14,551x10
¯³
Corrient
e
16,301x10
¯³ A
2,79x10
¯³ A
1,74x10¯³
A
4,53x10
¯³ A
19,09x10
¯³ A
14,554x10
¯³ A
620 910 820 390 560 220
Voltaje 5.241V 5.06V 0.177V 2.08V 7.85V 1.90V
Voltaje 4,86 V 2,52V 1,60V 0,31V 2,83V 1,29V
∑Voltaje 10.10 V 7.58 V 1.77 2.39 V 10.68 V 3.19 V
Voltaje 10,10 V 2.538V 1.432V 3.720V 10,69V 3,20V