Practica 5 Lf.docx

Resultados Parte 1. Resisitividad de un conductor Tabla 1. Datos experimentales de la resistencia de un alambre de metal. Diámetro del alambre D [m] 7.8𝑥10−4 Área del alambre A [m] 4.778𝑥10−7

R[Ω] L[m]

L/A [m-1]

1

0.097 0.157 0.227 0.297 0.397 0.487 0.557 0.677 0.867 0.957

202998.415 328564.445 475058.147 621551.849 830828.566 1019177.61 1165671.31 1416803.37 1814429.13 2002778.18 L[m] L/A [m-1] promedio promedio 0.472 987786.103

2

0.6 0.8 0.8 0.9 1 1.1 1.3 1.5 1.6 2.4

R[Ω] promedio

3

0.6 0.7 0.8 0.9 1 1.2 1.3 1.4 1.7 2.4

0.6 0.7 0.9 0.9 1 1.1 1.3 1.4 1.6 2.3

0.6 0.73333333 0.83333333 0.9 1 1.13333333 1.3 1.43333333 1.63333333 2.36666667 R[Ω] promedio 1.19333333

Tabla 2. Resistividad de un alambre por ajuste de mínimos cuadrados X= L/A [m-1]

202998.415 328564.445 475058.147 621551.849 830828.566 1019177.61 1165671.31 1416803.37 1814429.13 2002778.18 ∑X [m-1] 9877861.03

Y= R[Ω] promedio 0.6 0.73333333 0.83333333 0.9 1 1.13333333 1.3 1.43333333 1.63333333 2.36666667 ∑ Y [Ω] 11.9333333

X2 [m-2] 4.1208E+10 1.0795E+11 2.2568E+11 3.8633E+11 6.9028E+11 1.0387E+12 1.3588E+12 2.0073E+12 3.2922E+12 4.0111E+12 ∑ X2 [m-2] 1.316E+13

Y2 [Ω2]

XY [Ωm-1] a1[m Ω] a0[Ω] r 121799.049 8.1295E-07 0.39031259 0.95614781 240947.26 395881.789 559396.664 830828.566 1155067.96 1515372.71 2030751.5 2963567.59 4739908.36

0.36 0.53777778 0.69444444 0.81 1 1.28444444 1.69 2.05444444 2.66777778 5.60111111 ∑ Y2 [Ω2] ∑ XY [Ωm-1] 16.7 14553521.4

Tabla 3. Incertidumbres -1

X= L/A [m ]

202998.415 328564.445 475058.147 621551.849 830828.566 1019177.61 1165671.31 1416803.37 1814429.13 2002778.18

Y= R[Ω] promedio 0.6 0.73333333 0.83333333 0.9 1 1.13333333 1.3 1.43333333 1.63333333 2.36666667

Δa0[Ω]

(yi-a1x-a0) ∑(yi-a1-a0) σ Δa1[m Ω] 0.0019945 0.21098405 0.16239768 8.80421E-08 0.00576298 0.00322876 1.9332E-05 0.00432105 0.00731362 0.00143983 0.01183083 0.05383304 0.1212401 2

2

0.275013

Resistencia de un alambre 2.5

Resistencia[Ω]

2 1.5 1 0.5 0 0

500000

1000000

1500000

2000000

2500000

longitud/area del alambre [1/m]

𝑅[𝛀] = 𝟖. 𝟏𝟐𝟗𝐱𝟏𝟎−𝟕 ± 𝟖. 𝟖𝟎𝟒𝒙𝟏𝟎−𝟖 [𝒎𝛀] ∗

𝐋 [𝒎−𝟏 ] + 𝟎. 𝟑𝟗 ± 𝟎. 𝟐𝟕[𝛀] 𝟒. 𝟕𝟕𝟖𝐱𝟏𝟎−𝟕

Resistividad: 𝜌 = 8.129𝑥10−7 ± 8.804𝑥10−8 [𝐦 𝛀]

Medida indirecta Tabla 4. Ley de la propagación de la incertidumbre

s [m] ua [m] ub [m] Uc[m]

L [m] 0.293796982 0.029379698 0.0005 0.029383953

𝝏𝝆 [Ω] 𝝏𝑳

-2.5595E-06

Ucombinada [Ω*m]

s[Ω] ua[Ω] ub[Ω] Uc[Ω] 𝝏𝝆 𝝏𝑹

[m]

R[Ω] 0.52276567 0.05227657 0.1 0.11283988 1.0124E-06

1.3677E-07

Resisitividad: 𝜌 = 1.20809𝑥10−6 ± 0.13677𝑥10−6 [𝛀 ∗ 𝐦] Parte 2. Conductividad Tabla. Datos experimentales Diámetro C [F] [m] d[m] A/d [m] 1 2 0.08 0.001 5.026548246 3.3E-11 Área [m2] 0.002 2.513274123 2E-11 0.00502654 0.003 1.675516082 1.7E-11 0.004 1.256637062 1.4E-11 0.005 1.005309649 1.3E-11 0.006 0.837758041 1.2E-11 0.007 0.718078321 1.1E-11 0.008 0.628318531 1.1E-11 0.009 0.558505361 1.1E-11 0.01 0.502654825 1E-10 d [m] A/d [m] promedio promedio 0.0055 1.472260024

3

3.3E-11 2.1E-11 1.6E-11 1.4E-11 1.3E-11 1.2E-11 1.1E-11 1.2E-11 1.1E-11 1E-10

3.3E-11 2E-11 1.6E-11 1.4E-11 1.3E-11 1.2E-11 1.1E-11 1.1E-11 1.1E-11 1E-10

C [F] promedio 3.3E-11 2.0333E-11 1.6333E-11 1.4E-11 1.3E-11 1.2E-11 1.1E-11 1.1333E-11 1.1E-11 1E-10 C [F] promedio 2.42E-11

Tabla. Ajuste por mínimos cuadrados X= A/d [m] 5.02654825 2.51327412 1.67551608 1.25663706 1.00530965 0.83775804 0.71807832 0.62831853 0.55850536 0.50265482 ∑ X [m] 14.2199454

Y = C [F] 3.3E-11 2.0333E-11 1.6333E-11 1.4E-11 1.3E-11 1.2E-11 1.1E-11 1.1333E-11 1.1E-11 1E-10 ∑Y [F] 1.42E-10

X2 [m2] 25.2661873 6.31654682 2.80735414 1.5791367 1.01064749 0.70183854 0.51563647 0.39478418 0.31192824 0.25266187 ∑X2 [m2] 38.9040599

Y2 [F2] 1.089E-21 4.13444E-22 2.66778E-22 1.96E-22 1.69E-22 1.44E-22 1.21E-22 1.28444E-22 1.21E-22 1E-20 2 2 ∑Y [F ] 2.64867E-21

𝒄𝟐

a1 [𝑵𝒎𝟐] XY [mF] a0 [F] r 1.65876E-10 6.26161E-12 5.58257E-12 0.999379772 5.11032E-11 2.73668E-11 1.75929E-11 1.3069E-11 1.00531E-11 7.89886E-12 7.12094E-12 6.14356E-12 5.02655E-11 ∑XY [mF] 3.06224E-10

Tabla. Incertidumbres X [m] 5.026548246 2.513274123 1.675516082 1.256637062 1.005309649 0.837758041 0.718078321 0.628318531 0.558505361

Y [F] 3.3E-11 2.0333E-11 1.6333E-11 1.4E-11 1.3E-11 1.2E-11 1.1E-11 1.1333E-11 1.1E-11

𝒄𝟐

Δa1[ 𝟐 ] (yi-a1x-a0)2 ∑(yi-a1x-a0)2 σ Δa0 [F] 𝑵𝒎 1.74948E-24 1.0789E-23 1.2415E-12 2.72487E-13 5.66529E-13 1.69638E-27 5.15569E-25 5.22902E-25 1.26827E-24 1.12687E-24 5.32407E-25 2.44637E-24 2.62599E-24

Capacitancia 3.5E-11 3E-11

C[F]

2.5E-11 2E-11 1.5E-11 1E-11 5E-12 0 0

1

2

3

4

5

6

A/d [m]

𝒄𝟐 𝟎. 𝟎𝟎𝟓𝟎[𝒎𝟐 ] 𝐶[𝐹] = 5.58257x10−12 ± 2.72487x10−13 [ ] ∗ + 6.26161𝑥10−12 𝑵𝒎𝟐 𝑳[𝒎] ± 5.66529𝑥10−13 [F] 𝜖 = 5.58257x10−12 ± 2.72487x10−13 [

𝒄𝟐 ] 𝑵𝒎𝟐

Ley de propagación

s [m] ua [m] ub [m] uc[m] 𝜕𝜀 [Fm-2] 𝜕𝑑

ucombinada

Distancia [m] 0.002738613 0.00030429 0.001 0.001045272 4.81444E-09 5.22292E-12

s ua[F] ub[F] uc[F]

Capacitancia [F] 7.15503E-12 7.95003E-13 1E-12 1.27751E-12

𝜕𝜀 [m-1] 𝜕𝐶

1.094190234

Expresión de la medida 𝜖 = 2.64794x10−11 ± [5.2229𝑥10−12 ]