ESCUELA SUPERIOR POLITÉCNICA DE CHIMBORAZO

FACULTAD DE INFORMÁTICA Y ELECTRÓNICA

INGENIERÍA EN ELECTRÓNICA TELECOMUNICACIONES Y REDES

CIRCUITOS ELECTRICOS I

PROYECTO N.- 02

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

Resistencias a Implementar

R1 R2 R3 R4 R5 R6 R7 R8 R9 R10680 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 R20220 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 R301000 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

RTa= R1+R2+ R3+R4+R5= 680+330+10+47+3.3= 1070.3 Ω

RTf = R20+R21+R22 = 33+1000+ 100 = 1133 Ω

RTb= R6+R7+R8+R9 = 33+4.7+250+33=320.7 Ω

RTg = R23+R24+R25 = 1+220+330 = 551 Ω

RTc= R10+R11+R12+R13 = 47+220+470+82= 819 Ω

RTh = R26+R27 = 220+22 = 242 Ω

RTd= R14+R15+R16 = 51+68+820= 939 Ω RTi = R28+R29+R30 = 220+47+39= 306 Ω

RTe= R17+R18+R19 = 470+220+330= 1020 Ω

ANALISÍS

Nodo 1

I Ta+I Td + I Tb+ I Tf = 0

V 1−V 4

RTa+V 1−V 3

RTb+V 1−V 2

RTd+V 1

RTf=0

3V 1

500−V 2

939−V 3

320.7−

V 4

1070.3=0(1)

Nodo 2

I Tc+I Te + I Tg+ I T d' = 0

V 2−V 4

RTc+V 2−V 3

RTe+V 2

RTg+V 2−V 1

RTd=0

−V 1

939+5.08 x10−3V 2−

V 3

1020−V 4

819=0(2)

Supernodo 3,4

I T a'+ I T c'+ I T b'+ I T e'+ ITh + I Ti= 0

V 4−V 1

RTa+V 4−V 2

RTc+V 3−V 1

RTb+V 3−V 2

RTe+V 3

RTh+V 4

RTi=0

−4.05x 10−3V 1−2.2x 10−3V 2+8.23x 10−3V 3+5.42x 10−3V 4=0(3)

Fuente

V 3−V 4=5.3(4)

SISTEMA DE ECUACIONES

3V 1

500−V 2

939−V 3

320.7−

V 4

1070.3=0

−V 1

939+5.08 x10−3V 2−

V 3

1020−V 4

819=0

−4.05 x 10−3V 1−2.2x 10−3V 2+8.23 x 10−3V 3+5.42 x 10−3V 4=0

V 3−V 4=5.3

Valor de las tensiones del supernodo

Tensiones ValorV 1 0,69691761 VV 2 -0,1358738 VV 3 2,28934754 VV 4 -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

Tensiones ValorV Ta 3,7 VV Tb 1,58 VV Tc 2,85 VV Td 0,83 VV Te 2,43 VV Tf 0,69 VV Tg 0,13 VV Th 2,28 VV Ti 3,01 V

Calculo de la corriente y tensión en cada resistencia

Corrientes

Ita =i1=i2=i3=i4=i5 =V Ta / RTa = 3.45 mA

Itb = i6=i7=i8=i9 = V Tb / RTb = 4.92 mA

Itc =i10=i11=i12=i13 = V Tc / RTc = 3.47 mA

Itd =i14=i15=i16 = V Td / RTd = 0.88 mA

Ite =i17=i18=i19 = V Te / RTe= 2.38 mA

Itf =i20=i21=i22 = V Tf / RTf = 0.61 mA

Itg =i23=i24=i25 = V Tg / RTg = 0.23 mA

Ith =i26=i27 = V Th /¿ ¿ RTh= 9.42 mA

Iti =i28=i29=i30 = V Ti/ 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

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

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

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

POTENCIAS

Ω TEORICO MEDIDO

R1 73,42613 mW 74,0412 mWR2 35,6377 mW 35,8416 mWR3 417,5744 mW 420,546 mWR4 0,69591 mW 0,69446 mWR5 48,831uW 49,536 uWR6 230,74 W 234,96 uWR7 32,15 uW 33,375 uWR8 17,001 uW 17,649 uWR9 509,68 uW 515,49 uWR10 725,91 uW 726,79 uWR11 3,3798 mW 3,3723 mWR12 17,0366 mW 17,1972 mWR13 2,9498 W 3,05878 mWR14 0,43014 mW 0,44788 mWR15 580,47 uW 590,44 uWR16 3,8136 mW 3,864 mWR17 1,26686 mW 1,29789 mWR18 595,74 uW 602,37 uWR19 527,51 uW 526,88 uWR20 222,194 uW 222,22 uWR21 6,5044 mW 6,6584 mWR22 0,00064819 W 665,84 uWR23 19,132 uW 21,07 uWR24 4,20779 mW 4,7481 mWR25 6,307308 mW 6,9825 mW

R26 2,79104 mW 2,80884 mWR27 268,14 uW 266,64 uWR28 2,20444 mW 2,1735 mWR29 474,59 uW 474,71 uWR30 389,19 uW 387,45 uWSIMULACIÓN (BRIGHT SPARK)

Voltajes

Corrientes