TEMA: Implementación y medición de corriente y tensión de un circuito de malla con 30 resistencias.

OBJETIVO:

- Determinar de manera óptima y eficiente las medidas de corriente y tensión en un circuito de malla con 30 resistencias.

CIRCUITO:

R2 R3 R4

R1 R9 R6

R10 R7 R5

I1 I2 I3

R11 R8

R12 R13 R14 R15 R16

R20 R17

R23 R30

I4 R21 I5 R18 I6

R22 R19

R24 R25 R26 R27 R28 R29

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

RTz= R1+R2 = 680+330 = 1010 Ω RTf = R20+R21+R22 = 33+1000+ 100 = 1133 Ω

RTa= R9+R10+R11 = 33+47+220 = 300 Ω RTe = R23+R24+R25 = 1+220+330 = 551 Ω

RTb= R6+R7+R8 = 33+4.7+250 = 287.7 Ω RTh = R26+R27 = 220+22 = 242 Ω

RTc= R14+R15 = 51+68 = 125 Ω RTi = R17+R18+R19 = 470+220+330= 1020 Ω

RTd= R12+R13 = 470 + 82 = 552 Ω RTk= R28+R29+R30 = 220+47+39 = 306 Ω

RTx = R4+R5 = 47 + 3.3 = 50.3 Ω

ANALISÍS

Malla 1

V z+V Ta+V Td = 15V

RTz (I1)+RTa (I 1+ I 2)+RTd (I 1+ I 4) = 15

1010I 1 + 300I 1 + 300I 2 + 552I 1 + 552I 4 = 15

1862I 1 + 300I 2 + 552I 4 = 15 (1)

Malla 2

V 3+V Ta+V Tc +V Tb = 0

R3(I 2)+RTa (I 2+ I 1)+RTc (I 2+ I 5) + RTb (I 2+ I 3) = 0

10I 2 + 300I 2 + 300I 1 + 125I 2 + 125I 5 + 287.7I 2 + 287.7I 3 = 0

722.7I 2 + 300I 1 + 125I 5 + 287.7I 3 = 0 (2)

Malla 3

V Tx+V 16 +V Tb = 0

RTx(I 3)+R16(I 3+ I 6)+RTb (I3+ I 2) = 0

50.3I 3 + 820I 3 + 820I 6 + 287.7I 3 +287.7I 2 = 0

1158I 3 + 820I 6 + 287.7I 2 = 0 (3)

Malla 4

V Te+ V Tf + V Td = 0

RTe(I 4)+RTf (I 4+ I 5) + RTd (I 4+ I 1) = 0

551I 4 + 1133I 4 + 1133I 5 + 552I 4 + 552I 1 = 0

2236I 4 + 1133I 5 + 552I 1 = 0 (4)

Malla 5

V Tc + V Ti + V Th + V Tf = 0

RTc( I 5+ I 2) + RTi (I 5+ I 6) + RTh(I 5) + RTf (I 5+ I 4) = 0

125I 5 + 125I 2 + 1020I 5 + 1020I 6 + 242I 5 + 1133I 5 + 1133I 4 = 0

2520I 5 + 125I 2 + 1020I 6 + 1133I 4 = 0 (5)

Malla 6

V Tk + V 16 + V Ti = 0

RTk(I 6) + R16(I 6+ I3) + RTi(I 6+ I 5) = 0

306I 6 + 820I 6 + 820I 3 + 1020I 6 + 1020I 5 = 0

2146I 6 + 820I 3 + 1020I 5 = 0 (6)

SISTEMA DE ECUACIONES

1862I 1 + 300I 2 + 552I 4 = 15

722.7I 2 + 300I 1 + 125I 5 + 287.7I 3 = 0

1158I 3 + 820I 6 + 287.7I 2 = 0

2236I 4 + 1133I 5 + 552I 1 = 0

2520I 5 + 125I 2 + 1020I 6 + 1133I 4 = 0

2146I 6 + 820I 3 + 1020I 5 = 0

Valor de las corrientes de la malla

Corrientes ValorI 1 10.39 mA

I 2 -6.46 mA

I 3 3.848 mA

I 4 -4.37 mA

I 5 3.56 mA

I 6 -3.1673 mA

I1 I2 I3

I5

I4 I6

Calculo de la corriente y tensión en cada resistencia

Corrientes

i1 = i2 = I1 = 10.39 mA i3 = I2 = 6.46 mA

i4 = i5 = I3 = 3.848 mA i6 = i7 = i8 = I2 - I3 = 2.6155 mA

i9 = i10 = i11= I1 - I2 = 3.93 mA i16 = I3 - I6 = 0.681 mA

i12 = i13 = I1 – I4 = 6.02 mA i14 = i15 = I2 - I5 = 2.894 mA

i17 = i18 = i19 = I6 – I5 = 0.402 mA i20 = i21 = i22 = I4 – I5 = 0.805 mA

i23 = i24 = i25 = I4 = 4.374 mA i26 = i27 = I5 = 3.56 mA

i28 = i29 = i30 = I6 = 3.1673 mA

Tensiones

V1 = R1*i1 = 7.067 V V17 = R17*i17 = 186.03 mV

V2 = R2*i2 = 3.43 V V18 = R18*i18 = 87.48 mV

V3 = R3*i3 = 64.64 V V19 = R19*i19 = 131.72 mV

V4 = R4*i4 = 180.85 mV V20 = R20*i20 = 27.57 mV

V5 = R5*i5 = 12.69 mV V21 = R21*i21 = 0.808 V

V6 = R6*i6 = 86.31 mV V22 = R22*i22 = 80.52 mV

V7 = R7*i7 = 12.292 mV V23 = R23*i23 = 4.374 mV

V8 = R8*i8 = 0.65 V V24 = R24*i24 = 0.962 V

V9 = R9*i9 = 129.69 mV V25 = R25*i25 = 1.442 V

V10 = R10*i10 = 184.71 mV V26 = R26*i26 = 0.784 V

V11 = R11*i11 = 0.86 V V27 = R27*i27 = 75.32 mV

V12 = R12*i12 = 2.83 V V28 = R28*i28 = 0.696 V

V13 = R13*i13 = 0.49 V V29 = R29*i29 = 149.84 mV

V14 = R14*i14 = 148.63 mV V30 = R30*i30 = 123.51 mV

V15 = R15*i15 = 198.85 mV

V16 = R16*i16 = 0.56 V

VOLTAJES

Ω TEORICO SIMULADO MEDIDO

R1 7.067 V 7.07 V 7.05 V

R2 3.43 V 3.43 V 3.42 V

R3 64.64 V 64.9 mV 64.6 mV

R4 180.85 mV 181.1 mV 183.5 mV

R5 12.69 mV 12.72 mV 12.9 mV

R6 86.31 mV 87.01 mV 88.4 mV

R7 12.292 mV 12.39 mV 12.5 mV

R8 0.65 V 0.65 V 0.661 mV

R9 129.69 mV 128.92 mV 131 mV

R10 184.71 mV 183.61 mV 187.6 mV

R11 0.86 V 0.85 V 0.857 V

R12 2.83 V 2.83 mV 2.81 V

R13 0.49 V 0.49 V 0.498 V

R14 148.63 mV 149.38 mV 150.8 mV

R15 198.85 mV 199.17 mV 198.8 mV

R16 0.56 V 0.564 V 0.565 V

R17 186.03 mV 186.19 mV 188.1 mV

R18 87.48 mV 87.15 mV 87.3 mV

R19 131.72 mV 131.72 mV 131.9 mV

R20 27.57 mV 27.72 mV 27.1 mV

R21 0.808 V 0.809 V 0.812 mV

R22 80.52 mV 80.98 mV 81.2 mV

R23 4.374 mV 4.37 mV 4.3 mV

R24 0.962 V 0.961 V 0.969 V

R25 1.442 V 1.44 V 1.425 V

R26 0.784 V 0.783 V 0.789 V

R27 75.32 mV 75.36 mV 74.9 mV

R28 0.696 V 0.696 mV 0.690 V

R29 149.84 mV 149.79 mV 150.7 mV

R30 123.51 mV 123.47 mV 123 mV

CORRIENTES

Ω TEORICO SIMULADO MEDIDO

R1 10.39 mA 10.40 mA 10.48 mA

R2 10.39 mA 10.40 mA 10.48 mA

R3 6.46 mA 6.49 mA 6.51 mA

R4 3.848 mA 3.85 mA 3.84 mA

R5 3.848 mA 3.85 mA 3.84 mA

R6 2.6155 mA 2.64 mA 2.67 mA

R7 2.6155 mA 2.64 mA 2.67 mA

R8 2.6155 mA 2.64 mA 2.67 mA

R9 3.93 mA 3.91 mA 3.95 mA

R10 3.93 mA 3.91 mA 3.95 mA

R11 3.93 mA 3.91 mA 3.95 mA

R12 6.02 mA 6.03 mA 6.12 mA

R13 6.02 mA 6.03 mA 6.12 mA

R14 2.894 mA 2.93 mA 2.97 mA

R15 2.894 mA 2.93 mA 2.97 mA

R16 0.681 mA 0.688 mA 0.69 mA

R17 0.402 mA 0.396 mA 0.4 mA

R18 0.402 mA 0.396 mA 0.4 mA

R19 0.402 mA 0.396 mA 0.4 mA

R20 0.805 mA 0.809 mA 0.82 mA

R21 0.805 mA 0.809 mA 0.82 mA

R22 0.805 mA 0.809 mA 0.82 mA

R23 4.374 mA 4.37 mA 4.39 mA

R24 4.374 mA 4.37 mA 4.39 mA

R25 4.374 mA 4.37 mA 4.39 mA

R26 3.56 mA 3.56 mA 3.56 mA

R27 3.56 mA 3.56 mA 3.56 mA

R28 3.1673 mA 3.17 mA 3.15 mA

R29 3.1673 mA 3.17 mA 3.15 mA

R30 3.1673 mA 3.17 mA 3.15 mA

POTENCIAS

Ω TEORICO SIMULADO MEDIDO

R1

R2

R3

R4

R5

R6

R7

R8

R9

R10

R11

R12

R13

R14

R15

R16

R17

R18

R19

R20

R21

R22

R23

R24

R25

R26

R27

R28

R29

R30

SIMULACIÓN

Voltajes

Corrientes