Proyecto Basico de Analisis de Mallas

1. 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

2. 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 𝐓𝐳= R1+R2 = 680+330 = 1010 Ω 𝐑 𝐓𝐟 = R20+R21+R22 = 33+1000+ 100 = 1133 Ω
𝐑 𝐓𝐚= R9+R10+R11 = 33+47+220 = 300 Ω 𝐑 𝐓𝐞 = R23+R24+R25 = 1+220+330 = 551 Ω
𝐑 𝐓𝐛= R6+R7+R8 = 33+4.7+250 = 287.7 Ω 𝐑 𝐓𝐡 = R26+R27 = 220+22 = 242 Ω
𝐑 𝐓𝐜 = R14+R15 = 51+68 = 125 Ω 𝐑 𝐓𝐢 = R17+R18+R19 = 470+220+330= 1020 Ω
𝐑 𝐓𝐝= R12+R13 = 470 + 82 = 552 Ω 𝐑 𝐓𝐤= R28+R29+R30 = 220+47+39 = 306 Ω
𝐑 𝐓𝐱 = R4+R5 = 47 + 3.3 = 50.3 Ω
ANALISÍS
Malla 1
Vz + VTa+ VTd = 15V
RTz( I1) + RTa ( I1 + I2)+ RTd( I1 + I4) = 15
1010 I1 + 300 I1 + 300 I2 + 552 I1 + 552 I4 = 15
1862 I1 + 300 I2 + 552 I4 = 15 (1)
Malla 2
V3 + VTa+ VTc + VTb = 0
R3( I2) + RTa ( I2 + I1)+ RTc ( I2 + I5) + RTb ( I2 + I3) = 0
10 I2 + 300 I2 + 300 I1 + 125 I2 + 125 I5 + 287.7 I2 + 287.7 I3 = 0
722.7 I2 + 300 I1 + 125 I5 + 287.7 I3 = 0 (2)

3. Malla 3
VTx + V16 + VTb = 0
RTx( I3)+ R16( I3 + I6)+ RTb( I3 + I2) = 0
50.3 I3 + 820 I3 + 820 I6 + 287.7 I3 +287.7 I2 = 0
1158 I3 + 820 I6 + 287.7 I2 = 0 (3)
Malla 4
VTe + VTf + VTd = 0
RTe( I4)+ RTf( I4 + I5) + RTd( I4 + I1) = 0
551 I4 + 1133 I4 + 1133 I5 + 552 I4 + 552 I1 = 0
2236 I4 + 1133 I5 + 552 I1 = 0 (4)
Malla 5
VTc + VTi + VTh + VTf = 0
RTc( I5 + I2) + RTi( I5 + I6) + RTh(I5) + RTf( I5 + I4) = 0
125 I5 + 125 I2 + 1020 I5 + 1020 I6 + 242 I5 + 1133 I5 + 1133 I4 = 0
2520 I5 + 125 I2 + 1020 I6 + 1133 I4 = 0 (5)
Malla 6
VTk + V16 + VTi = 0
RTk( I6) + R16( I6 + I3)+ RTi(I6 + I5) = 0
306 I6 + 820 I6 + 820 I3 + 1020 I6 + 1020 I5 = 0
2146 I6 + 820 I3 + 1020 I5 = 0 (6)

4. SISTEMA DE ECUACIONES
1862 I1 + 300 I2 + 552 I4 = 15
722.7 I2 + 300 I1 + 125 I5 + 287.7 I3 = 0
1158 I3 + 820 I6 + 287.7 I2 = 0
2236 I4 + 1133 I5 + 552 I1 = 0
2520 I5 + 125 I2 + 1020 I6 + 1133 I4 = 0
2146 I6 + 820 I3 + 1020 I5 = 0
Valor de las corrientes de la malla
Corrientes Valor
I1 10.39 mA
I2 -6.46 mA
I3 3.848 mA
I4 -4.37 mA
I5 3.56 mA
I6 -3.1673 mA
I1 I2 I3
I5
I4 I6

5. 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

6. 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

7. 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

8. 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

9. SIMULACIÓN
Voltajes

10. Corrientes