Atividade Experimental 2 - Laboratório de Física II E

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UNIVERSIDADE FEDERAL DO AMAZONAS 
FACULDADE DE TECNOLOGIA 
BACHARELADO EM ENGENHARIA DE PRODUÇÃO 
 
 
 
 
 
BRUNO BANDEIRA LOPES 
BRUNO LUCAS NOGUEIRA LOPES 
DIOGISMAR JUSTINA BARAI 
GUSTAVO REGIAN FIGUEREDO FERREIRA 
JEAN SANDRO REIS DE MORAES 
 
 
 
 
 
 
ATIVIDADE EXPERIMENTAL II – LEI DE OHM E RESISTIVIDADE ELÉTRICA 
 
 
 
 
 
 
 
 
 
 
 
 
MANAUS – AM 
2021 
BRUNO BANDEIRA LOPES - 21951986 
BRUNO LUCAS NOGUEIRA LOPES - 21850605 
DIOGISMAR JUSTINA BARAI - 21954432 
GUSTAVO REGIAN FIGUEREDO FERREIRA - 21751335 
JEAN SANDRO REIS DE MORAES - 21950535 
 
 
 
 
 
 
 
 
 
 
 
ATIVIDADE EXPERIMENTAL II – LEI DE OHM E RESISTIVIDADE ELÉTRICA 
 
Trabalho solicitado para obtenção de nota parcial 
na disciplina de Laboratório de Física II – IEF039, 
ministrada pelo Prof. Dr. Octavio Daniel Rodriguez 
Salmon. 
 
 
 
 
 
 
 
 
 
 
 
MANAUS – AM 
2021 
1) (1 ponto) Baseado nos dados coletados e apresentados no vídeo monte a 
seguinte tabela (considerando as incertezas). Para isto, observe por exemplo 
a precisão da régua, da fonte e do multímetro que foram utilizados. 
 
 
 
Erro Voltagem (V) ± 0,01 
Erro i(A) ± 0,01 
Erro Comprimento (m) ± 0,005 
 
 
 
 
2) (2 pontos) Usando um programa gráfico, construa o gráfico de V = V( i ), para 
cada valor do comprimento do fio de Constantan baseado na tabela da 
questão anterior, considerando as barras de erro. 
 
 
 
(i ± 0,01) A (0,60 ± 0,005)m(0,70 ± 0,005)m (0,80 ± 0,005)m (0,90 ± 0,005)m (1,00 ± 0,005)m 2 pernas ± 0,005m 3 pernas ± 0,005m 4 pernas ± 0,005m
0,10 0,92 V 1,15 V 1,31 V 1,39 V 1,62 V 0,78 V 0,53 V 0,40 V
0,20 1,94 V 2,17 V 2,50 V 2,87 V 3,18 V 1,62 V 1,04 V 0,80 V
0,30 2,87 V 3,30 V 3,73 V 4,24 V 4,69 V 2,35 V 1,59 V 1,19 V
0,40 3,82 V 4,45 V 5,00 V 5,65 V 6,34 V 3,13 V 2,08 V 1,56 V
0,50 4,73 V 5,51 V 6,23 V 7,12 V 7,79 V 3,87 V 2,59 V 1,95 V
VOLTAGEM (V) ± 0,01 V
 
Gráfico feito no Python (Google Colab/Spider), código: 
 
 
 
Gráfico feito no Python (Google Colab/Spider), código: 
 
 
 
Gráfico feito no Python (Google Colab/Spider), código: 
 
 
 
Gráfico feito no Python (Google Colab/Spider), código: 
 
 
 
 
Gráfico feito no Python (Google Colab/Spider), código: 
 
 
 
 
 
Gráfico feito no Python (Google Colab/Spider), código: 
 
 
 
 
 
Gráfico feito no Python (Google Colab/Spider), código: 
 
 
 
 
Gráfico feito no Python (Google Colab/Spider), código: 
 
 
3) (1.0 pontos) Construa uma tabela onde a primeira coluna seja o comprimento 
L do fio, e a segunda coluna seja o valor da resistência R obtida para cada 
uma das figuras obtidas na questão anterior. A partir desta tabela, construa o 
gráfico R versus L com as respectivas barras de erro em cada ponto. 
 
(L ± 0,005)m Ω (R) 
0,60 9,5 ± 0,4 
0,70 11,0 ± 0,5 
0,80 12,5 ± 0,5 
0,90 14,3 ± 0,6 
1,00 15,6 ± 0,7 
2 pernas 7,7 ± 0,3 
3 pernas 5,19 ± 0,24 
4 pernas 3,91 ± 0,19 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Gráfico de 0,60m – 1,00m 
4) (3.0 pontos) Calcule a resistividade ρ ± Δρ do fio de Constantan pelo método 
gráfico (baseado na figura da questão anterior). Compare com o valor 
tabelado (pode procurar em alguma fonte bibliográfica). 
 
Resistividade do fio de Constantan calculo pelo método gráfico no Python (baseado 
no gráfico de 0,6m-1,0m da questão anterior): 
 
 
O valor da resistividade do Constantan ρ ± Δρ deu aproximadamente: 
(4,9 X 10-7 ± 0,8 X 10-7) Ω · m 
 
Comparando com o valor tabelado de fontes bibliográficas, a resistividade é 
semelhante com a encontrada pelo método gráfico nesse experimento. 
5) (3.0 pontos) Construa, baseado na tabela da primeira questão, o gráfico R 
versus 1/A, onde se manteve constante o valor de L, tal que A é a área da 
secção transversal do fio de Constantan. Considere neste caso a incerteza na 
área A igual a zero. Assim, as barras de erro só serão verticais. Calcule 
usando o método gráfico a resistividade ρ ± Δρ. Compare com o valor obtido 
na questão anterior. 
1
𝐴
 Ω (R) 
31830988,618 15,6 ± 0,7 
15915494,309 7,7 ± 0,3 
10610329,539 5,19 ± 0,24 
7957747,154 3,91 ± 0,19 
 
Erro do comprimento (L) ± 0,005 
Erro da área (A) ± 0,000 
 
 
 
 
Código do gráfico feito no Python: 
 
Cálculo da resistividade ρ ± Δρ pelo método gráfico: 
 
Logo o valor da resistividade deu aproximadamente: 
(4,9 X 10-7 ± 2,1 X 10-7) Ω · m 
 
 
Contudo, esse valor obtido é similar com o da questão anterior. 
 
 
 
 
 
 
 
 
 
 
 
 
 
5/5/2021 Untitled4.ipynb - Colaboratory
https://colab.research.google.com/drive/1F3yY-7SQs92NTqaQj6REx6hWI5gz-8Rp#scrollTo=SdKVi7w6jrCt&printMode=true 1/5
import numpy as np
x = [0.0,0.10,0.20,0.30,0.40,0.50]
y = [0.0,0.92,1.94,2.87,3.82,4.73]
deltax = [0.01,0.01,0.01,0.01,0.01,0.01]
deltay = [0.01,0.01,0.01,0.01,0.01,0.01]
xi=x[0]
xf=x[-1]
yi=y[0]
yf=y[-1]
sigma_y=0.01
sigma_x=0.01
a_max=(yf-yi+2*sigma_y)/(xf-xi-2*sigma_x)
a_min=(yf-yi-2*sigma_y)/(xf-xi+2*sigma_x)
a0=(a_max+a_min)/2
sigma_a=(a_max-a_min)/2
x = np.array(x).reshape((-1, 1))
y = np.array(y)
print("Resistência: ",round(a0,3))
 
 
 
 
 
 
 
 
print("Erro (Delta R): ", round(sigma_a,3))
Resistência: 9.477 
Erro (Delta R): 0.419 
import numpy as np
x = [0.0,0.10,0.20,0.30,0.40,0.50]
y = [0.0,1.15,2.17,3.30,4.45,5.51]
 
deltax = [0.01,0.01,0.01,0.01,0.01,0.01]
deltay = [0.01,0.01,0.01,0.01,0.01,0.01]
 
xi=x[0]
xf=x[-1]
 
yi=y[0]
yf=y[-1]
 
sigma_y=0.01
sigma_x=0.01
 
a_max=(yf-yi+2*sigma_y)/(xf-xi-2*sigma_x)
a_min=(yf-yi-2*sigma_y)/(xf-xi+2*sigma_x)
 
a0=(a_max+a_min)/2
sigma_a=(a_max-a_min)/2
 
( ) (( ))
CÁLCULO DAS RESISTÊNCIAS DA QUESTÃO 3
5/5/2021 Untitled4.ipynb - Colaboratory
https://colab.research.google.com/drive/1F3yY-7SQs92NTqaQj6REx6hWI5gz-8Rp#scrollTo=SdKVi7w6jrCt&printMode=true 2/5
x = np.array(x).reshape((-1, 1))
y = np.array(y)
 
print("Resistência: ",round(a0,3))
print("Erro (Delta R): ", round(sigma_a,3))
Resistência: 11.039 
Erro (Delta R): 0.482 
import numpy as np
x = [0.0,0.10,0.20,0.30,0.40,0.50]
y = [0.0,1.31,2.50,3.73,5.00,6.23]
 
deltax = [0.01,0.01,0.01,0.01,0.01,0.01]
deltay = [0.01,0.01,0.01,0.01,0.01,0.01]
 
xi=x[0]
xf=x[-1]
 
yi=y[0]
yf=y[-1]
 
sigma_y=0.01
sigma_x=0.01
 
a_max=(yf-yi+2*sigma_y)/(xf-xi-2*sigma_x)
a_min=(yf-yi-2*sigma_y)/(xf-xi+2*sigma_x)
 
a0=(a_max+a_min)/2
sigma_a=(a_max-a_min)/2
 
x = np.array(x).reshape((-1, 1))
y = np.array(y)
 
print("Resistência: ",round(a0,3))
print("Erro (Delta R): ", round(sigma_a,3))
Resistência: 12.482 
Erro (Delta R): 0.539 
import numpy as np
x = [0.0,0.10,0.20,0.30,0.40,0.50]
y = [0.0,1.39,2.87,4.24,5.65,7.12]
 
deltax = [0.01,0.01,0.01,0.01,0.01,0.01]
deltay = [0.01,0.01,0.01,0.01,0.01,0.01]
 
xi=x[0]
xf=x[-1]
 
yi=y[0]
yf=y[-1]
 
sigma_y=0.01
sigma x 0 01
5/5/2021 Untitled4.ipynb - Colaboratory
https://colab.research.google.com/drive/1F3yY-7SQs92NTqaQj6REx6hWI5gz-8Rp#scrollTo=SdKVi7w6jrCt&printMode=true 3/5
sigma_x=0.01
 
a_max=(yf-yi+2*sigma_y)/(xf-xi-2*sigma_x)
a_min=(yf-yi-2*sigma_y)/(xf-xi+2*sigma_x)
 
a0=(a_max+a_min)/2
sigma_a=(a_max-a_min)/2
 
x = np.array(x).reshape((-1, 1))
y = np.array(y)
 
print("Resistência: ",round(a0,3))
print("Erro (Delta R): ", round(sigma_a,3))
Resistência: 14.264 
Erro (Delta R): 0.611 
import numpy as np
x = [0.0,0.10,0.20,0.30,0.40,0.50]
y = [0.0,1.62,3.18,4.69,6.34,7.79]
 
deltax = [0.01,0.01,0.01,0.01,0.01,0.01]
deltay = [0.01,0.01,0.01,0.01,0.01,0.01]
 
xi=x[0]
xf=x[-1]
 
yi=y[0]
yf=y[-1]
 
sigma_y=0.01
sigma_x=0.01
 
a_max=(yf-yi+2*sigma_y)/(xf-xi-2*sigma_x)
a_min=(yf-yi-2*sigma_y)/(xf-xi+2*sigma_x)
 
a0=(a_max+a_min)/2
sigma_a=(a_max-a_min)/2
 
x = np.array(x).reshape((-1, 1))
y = np.array(y)
 
print("Resistência: ",round(a0,3))
print("Erro (Delta R): ", round(sigma_a,3))
Resistência: 15.607 
Erro (Delta R): 0.664 
import numpy as np
x = [0.0,0.10,0.20,0.30,0.40,0.50]
y = [0.0,0.78,1.62,2.35,3.13,3.87]
 
deltax = [0.01,0.01,0.01,0.01,0.01,0.01]
deltay = [0.01,0.01,0.01,0.01,0.01,0.01]5/5/2021 Untitled4.ipynb - Colaboratory
https://colab.research.google.com/drive/1F3yY-7SQs92NTqaQj6REx6hWI5gz-8Rp#scrollTo=SdKVi7w6jrCt&printMode=true 4/5
 
xi=x[0]
xf=x[-1]
 
yi=y[0]
yf=y[-1]
 
sigma_y=0.01
sigma_x=0.01
 
a_max=(yf-yi+2*sigma_y)/(xf-xi-2*sigma_x)
a_min=(yf-yi-2*sigma_y)/(xf-xi+2*sigma_x)
 
a0=(a_max+a_min)/2
sigma_a=(a_max-a_min)/2
 
x = np.array(x).reshape((-1, 1))
y = np.array(y)
 
print("Resistência: ",round(a0,3))
print("Erro (Delta R): ", round(sigma_a,3))
Resistência: 7.754 
Erro (Delta R): 0.35 
import numpy as np
x = [0.0,0.10,0.20,0.30,0.40,0.50]
y = [0.0,0.53,1.04,1,59,2.08,2.59]
 
deltax = [0.01,0.01,0.01,0.01,0.01,0.01]
deltay = [0.01,0.01,0.01,0.01,0.01,0.01]
 
xi=x[0]
xf=x[-1]
 
yi=y[0]
yf=y[-1]
 
sigma_y=0.01
sigma_x=0.01
 
a_max=(yf-yi+2*sigma_y)/(xf-xi-2*sigma_x)
a_min=(yf-yi-2*sigma_y)/(xf-xi+2*sigma_x)
 
a0=(a_max+a_min)/2
sigma_a=(a_max-a_min)/2
 
x = np.array(x).reshape((-1, 1))
y = np.array(y)
 
print("Resistência: ",round(a0,3))
print("Erro (Delta R): ", round(sigma_a,3))
Resistência: 5.19 
Erro (Delta R): 0.248 
5/5/2021 Untitled4.ipynb - Colaboratory
https://colab.research.google.com/drive/1F3yY-7SQs92NTqaQj6REx6hWI5gz-8Rp#scrollTo=SdKVi7w6jrCt&printMode=true 5/5
 0s conclusão: 23:12
import numpy as np
x = [0.0,0.10,0.20,0.30,0.40,0.50]
y = [0.0,0.40,0.80,1.19,1.56,1.95]
 
deltax = [0.01,0.01,0.01,0.01,0.01,0.01]
deltay = [0.01,0.01,0.01,0.01,0.01,0.01]
 
xi=x[0]
xf=x[-1]
 
yi=y[0]
yf=y[-1]
 
sigma_y=0.01
sigma_x=0.01
 
a_max=(yf-yi+2*sigma_y)/(xf-xi-2*sigma_x)
a_min=(yf-yi-2*sigma_y)/(xf-xi+2*sigma_x)
 
a0=(a_max+a_min)/2
sigma_a=(a_max-a_min)/2
 
x = np.array(x).reshape((-1, 1))
y = np.array(y)
 
print("Resistência: ",round(a0,3))
print("Erro (Delta R): ", round(sigma_a,3))
Resistência: 3.908 
Erro (Delta R): 0.196