Proyecto Basico de Resistencias en Serie y en Paralelo

1. ESCUELA SUPERIOR POLITÉCNICA
DE CHIMBORAZO
FACULTAD DE INFORMÁTICA Y ELECTRÓNICA
INGENIERÍA EN ELECTRÓNICATELECOMUNICACIONES Y REDES
CIRCUITOS ELECTRICOS I
PROYECTO N.- 02

2. TEMA: Implementación y medición de corrientes y tensiones de un circuito supernodo con 30
resistencias.
OBJETIVO:
- Determinar de manera óptima y eficiente las medidas de corriente y tensión en un circuito
de supernodo con 30 resistencias.
CIRCUITO:
R1 R2 R3 R4 R5
R6 R7 R8 R9 R10 R11 R12 R13
R14 R15 R16 R17 R18 R19
R28
R20 R23 R26
R24 R27 R29
R21
R22 R25 R30

3. Resistencias a Implementar
R1 R2 R3 R4 R5 R6 R7 R8 R9 R10
680 Ω 330 Ω 10 Ω 47 Ω 3.3 Ω 33 Ω 4.7 Ω 250 Ω 33 Ω 47 Ω
R11 R12 R13 R14 R15 R16 R17 R18 R19 R20
220 Ω 470 Ω 82 Ω 51 Ω 68 Ω 820 Ω 470 Ω 220 Ω 330 Ω 33 Ω
R21 R22 R23 R24 R25 R26 R27 R28 R29 R30
1000 Ω 100 Ω 1 Ω 220 Ω 330 Ω 220 Ω 22 Ω 220 Ω 47 Ω 39 Ω
Valor de Resistencias en Serie Equivalentes
𝐑 𝐓𝐚= R1+R2+ R3+R4+R5=
680+330+10+47+3.3= 1070.3 Ω
𝐑 𝐓𝐟 = R20+R21+R22 = 33+1000+ 100 = 1133 Ω
𝐑 𝐓𝐛= R6+R7+R8+R9 =
33+4.7+250+33=320.7 Ω
𝐑 𝐓𝐠 = R23+R24+R25 = 1+220+330 = 551 Ω
𝐑 𝐓𝐜= R10+R11+R12+R13 =
47+220+470+82= 819 Ω
𝐑 𝐓𝐡 = R26+R27 = 220+22 = 242 Ω
𝐑 𝐓𝐝 = R14+R15+R16 = 51+68+820= 939 Ω 𝐑 𝐓𝐢 = R28+R29+R30 = 220+47+39= 306 Ω
𝐑 𝐓𝐞= R17+R18+R19 = 470+220+330= 1020 Ω
ANALISÍS
Nodo 1
ITa+ ITd + ITb + ITf = 0
𝑉1 − 𝑉4
RTa
+
𝑉1 − 𝑉3
RTb
+
𝑉1 − 𝑉2
RTd
+
𝑉1
RTf
= 0
3 𝑉1
500
−
𝑉2
939
−
𝑉3
320.7
−
𝑉4
1070.3
= 0 (𝟏)
Nodo 2
ITc+ ITe + ITg + IT𝑑′ = 0
𝑉2 − 𝑉4
RTc
+
𝑉2 − 𝑉3
RTe
+
𝑉2
RTg
+
𝑉2 − 𝑉1
RTd
= 0
−
𝑉1
939
+ 5.08𝑥10−3 𝑉2 −
𝑉3
1020
−
𝑉4
819
= 0 (𝟐)

4. Supernodo 3,4
IT𝑎′ + IT𝑐′ + IT𝑏′ + IT𝑒′ + ITh + ITi = 0
𝑉4 − 𝑉1
RTa
+
𝑉4 − 𝑉2
RTc
+
𝑉3 − 𝑉1
RTb
+
𝑉3 − 𝑉2
RTe
+
𝑉3
RTh
+
𝑉4
RTi
= 0
−4.05𝑥10−3 𝑉1 − 2.2𝑥10−3 𝑉2 + 8.23𝑥10−3 𝑉3 + 5.42𝑥10−3 𝑉4 = 0 (𝟑)
Fuente
𝑉3 − 𝑉4 = 5.3 (𝟒)
SISTEMA DE ECUACIONES
3 𝑉1
500
−
𝑉2
939
−
𝑉3
320.7
−
𝑉4
1070.3
= 0
−
𝑉1
939
+ 5.08𝑥10−3 𝑉2 −
𝑉3
1020
−
𝑉4
819
= 0
−4.05𝑥10−3 𝑉1 − 2.2𝑥10−3 𝑉2 + 8.23𝑥10−3 𝑉3 + 5.42𝑥10−3 𝑉4 = 0
𝑉3 − 𝑉4 = 5.3
Valor de las tensiones del supernodo
Tensiones Valor
V1 0,69691761 V
V2 -0,1358738 V
V3
2,28934754 V
V4 -3,01065246 V
Ita Rta
Itb Rtb Rtc Ita’
Itc’
Itd Itd’ Itc Itb’
Itf Rtd Rte
Itg Ite Ite’ Ith Iti
Rtf Rtg Rth Rti

5. Tensiones Valor
VTa
3,7 V
VTb
1,58 V
VTc 2,85 V
VTd
0,83 V
VTe 2,43 V
VTf 0,69 V
VTg
0,13 V
VTh 2,28 V
VTi 3,01 V
Calculo de la corriente y tensión en cada resistencia
Corrientes
Ita =i1=i2=i3=i4=i5 = VTa / RTa = 3.45 mA
Itb = i6=i7=i8=i9 = VTb / RTb = 4.92 mA
Itc =i10=i11=i12=i13 = VTc / RTc = 3.47 mA
Itd =i14=i15=i16 = VTd / RTd = 0.88 mA
Ite =i17=i18=i19 = VTe / RTe = 2.38 mA
Itf =i20=i21=i22 = VTf / RTf = 0.61 mA
Itg =i23=i24=i25 = VTg / RTg = 0.23 mA
Ith =i26=i27 = VTh/ RTh= 9.42 mA
Iti =i28=i29=i30 = VTi/ RTi = 9.83 mA
Tensiones
V1 = R1*i1 = 2.34 V V17 = R17*i17 = 1.11 V
V2 = R2*i2 = 1.138 V V18 = R18*i18 = 0.52 V
V3 = R3*i3 = 34.5 mV V19 = R19*i19 = 0.785 V
V4 = R4*i4 = 162.15 mV V20 = R20*i20 = 20.13 mV
V5 = R5*i5 = 11.385 mV V21 = R21*i21 = 0.61 V

6. V6 = R6*i6 = 162.36 mV V22 = R22*i22 = 61 mV
V7 = R7*i7 = 23.124 mV V23 = R23*i23 = 0.2 mV
V8 = R8*i8 = 1.23 V V24 = R24*i24 = 50.6 mV
V9 = R9*i9 = 162.36 mV V25 = R25*i25 = 75.9 mV
V10 = R10*i10 = 163.09 mV V26 = R26*i26 = 2.07 V
V11 = R11*i11 = 0.763 V V27 = R27*i27 = 0.207 V
V12 = R12*i12 = 1.631 V V28 = R28*i28 = 2.16 V
V13 = R13*i13 = 0.28 V V29 = R29*i29 = 0.46 V
V14 = R14*i14 = 44.88 mV V30 = R30*i30 = 0.38 V
V15 = R15*i15 = 59.84 mV
V16 = R16*i16 = 0.72 V

7. VOLTAJES
Ω TEORICO SIMULADO MEDIDO
R1 2.34 V 2.36 V 2.35 V
R2 1.138 V 1.14 V 1.14 V
R3 34.5 mV 34.64 mV 34.4 mV
R4 162.15 mV 162.8 mV 166 mV
R5 11.385 mV 11.43 mV 11.6 mV
R6 162.36 mV 163.89 mV 164.6 mV
R7 23.124 mV 23.34 mV 23.3 mV
R8 1.23 V 1.24 V 1.23 V
R9 162.36 mV 163.89 mV 165 mV
R10 163.09 mV 164.96 mV 166.5 mV
R11 0.763 V 0.77 V 0.757 V
R12 1.631 V 1.65 V 1.6 V
R13 0.28 V 0.287 V 0.289 V
R14 44.88 mV 45.23 mV 43.3 mV
R15 59.84 mV 60.30 mV 57.8 mV
R16 0.72 V 0.727 V 0.71 V
R17 1.11 V 1.12 V 1.1 V
R18 0.52 V 0.523 V 0.515 V
R19 0.785 V 0.784 V 0.79 V
R20 20.13 mV 20.32 mV 20.3 mV
R21 0.61 V 0.615 V 0.6 V
R22 61 mV 61.58 mV 60.9 mV
R23 0.2 mV 0.24 mV 0.1 mV
R24 50.6 mV 53.92 mV 50 mV
R25 75.9 mV 80.88 mV 70.6 mV
R26 2.07 V 2.08 V 2.04 V
R27 0.207 V 0.208 V 0.19 V
R28 2.16 V 2.16 V 2.10 V
R29 0.46 V 0.462 V 0.45 V
R30 0.38 V 0.383 V 0.37 V

8. CORRIENTES
Ω TEORICO SIMULADO MEDIDO
R1 3.45 mA 3.46 mA 3.4 mA
R2 3.45 mA 3.46 mA 3.4 mA
R3 3.45 mA 3.46 mA 3.4 mA
R4 3.45 mA 3.46 mA 3.4 mA
R5 3.45 mA 3.46 mA 3.4 mA
R6 4.92 mA 4.97 mA 5 mA
R7 4.92 mA 4.97 mA 5 mA
R8 4.92 mA 4.97 mA 5 mA
R9 4.92 mA 4.97 mA 5 mA
R10 3.47 mA 3.51 mA 3.5 mA
R11 3.47 mA 3.51 mA 3.5 mA
R12 3.47 mA 3.51 mA 3.5 mA
R13 3.47 mA 3.51 mA 3.5 mA
R14 0.88 mA 0.88 mA 0.8 mA
R15 0.88 mA 0.88 mA 0.8 mA
R16 0.88 mA 0.88 mA 0.8 mA
R17 2.38 mA 2.38 mA 2.4 mA
R18 2.38 mA 2.38 mA 2.4 mA
R19 2.38 mA 2.38 mA 2.4 mA
R20 0.61 mA 0.61 mA 0.6 mA
R21 0.61 mA 0.61 mA 0.6 mA
R22 0.61 mA 0.61 mA 0.6 mA
R23 0.23 mA 0.24 mA 0.22 mA
R24 0.23 mA 0.24 mA 0.22 mA
R25 0.23 mA 0.24 mA 0.22 mA
R26 9.42 mA 9.46 mA 9.3 mA
R27 9.42 mA 9.46 mA 9.3 mA
R28 9.83 mA 9.84 mA 9.6 mA
R29 9.83 mA 9.84 mA 9.6 mA
R30 9.83 mA 9.84 mA 9.6 mA

9. POTENCIAS
Ω TEORICO MEDIDO
R1 73,42613 mW 74,0412 mW
R2 35,6377 mW 35,8416 mW
R3 417,5744 mW 420,546 mW
R4 0,69591 mW 0,69446 mW
R5 48,831uW 49,536 uW
R6 230,74 W 234,96 uW
R7 32,15 uW 33,375 uW
R8 17,001 uW 17,649 uW
R9 509,68 uW 515,49 uW
R10 725,91 uW 726,79 uW
R11 3,3798 mW 3,3723 mW
R12 17,0366 mW 17,1972 mW
R13 2,9498 W 3,05878 mW
R14 0,43014 mW 0,44788 mW
R15 580,47 uW 590,44 uW
R16 3,8136 mW 3,864 mW
R17 1,26686 mW 1,29789 mW
R18 595,74 uW 602,37 uW
R19 527,51 uW 526,88 uW
R20 222,194 uW 222,22 uW
R21 6,5044 mW 6,6584 mW
R22 0,00064819 W 665,84 uW
R23 19,132 uW 21,07 uW
R24 4,20779 mW 4,7481 mW
R25 6,307308 mW 6,9825 mW
R26 2,79104 mW 2,80884 mW
R27 268,14 uW 266,64 uW
R28 2,20444 mW 2,1735 mW
R29 474,59 uW 474,71 uW
R30 389,19 uW 387,45 uW

10. SIMULACIÓN (BRIGHT SPARK)
Voltajes
Corrientes