PHYS .212.600 – University Physics II
University Physics II
PHYS.212.600
Fall Semester 2023
Experiment 1: Resistivity and Resistance
Done By: Abla Belmesk
Partners: rocky, Faaz
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PHYS .212.600 – University Physics II
Part A:
Current, I
(A)
1
L (cm)
V (volt)
R (ohm)
24
0.085
0.085
20
0.071
0.071
16
0.056
0.056
12
0.042
0.042
8
0.028
0.028
4
0.014
0.014
Table 1: Data Results showing the relationship between R and L
Graph 1: Data Findings illustrating the link between R and Length
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PHYS .212.600 – University Physics II
Data Analysis of Part A:
We maintained a constant current and varied the measurement points for voltage
along the wire. This allowed us to determine the wire's resistance at different
lengths. As indicated in Table 1, the voltage increases with the length of the wire.
To calculate resistance, we rearranged Ohm's Law as R = V / I.
Plotting resistance on the x-axis and length on the y-axis, we observed that
resistance is directly proportional to length, leading to the relationship R ∝ L. This
aligns with the theoretical prediction expressed as 𝑅 = 𝜌𝐿/𝐴. Consequently, our
findings are consistent with the theoretical expectations, demonstrating a linear
relationship.Furthermore, Graph 1 demonstrates that the optimal thin line roughly
originates at the zero point.
The best fit line equation is y = 0.0036 x - 0.0005
Part B:
L (cm)
24
D (cm)
R (ohm)
V (volt)
I(A)
1/D
1/D^2
0.13
0.0126316
0.012
1
7.692
59.172
0.1
0.0210526
0.02
1
10.000
100.000
0.081
0.0336842
0.032
1
12.346
152.416
0.051
0.0852632
0.081
1
19.608
384.468
Table 2: Relationship between R and D, the inversely proportional relationship
between R and D, and the inversely proportional relationship between R and D,
in addition to the square inverse relationship between R and D.
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PHYS .212.600 – University Physics II
Graph 2: A non-linear relationship between R and D.
Graph 3: Graph showing the inverse curve fit between R and D
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PHYS .212.600 – University Physics II
Graph 4: Graph exhibiting the square inverse linear connection between R and
D.
Data Analysis of Part B:
When the graphs were compared, it was clear that the relationship between R and D, as
well as the inverse of D, was not linear. This demonstrated that the theoretical equation
was correct. When the values of D are inversely squared, the line that is the best fit
reveals a linear relationship.
When compared to the numbers in Table 2, the value with a very small error number is
shown as less than 1%, which demonstrates that the calculations were carried out
correctly.
The best fit line equation is y = 0.00022401 x – 0.000823
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PHYS .212.600 – University Physics II
Part C:
L (cm)
24
ρ (Ω.cm)
Uncertainit
y%
ρTh
(Ω.cm)
0.013
7.19E-06
2.710
0.000007
0.021
0.021
6.87E-06
1.825
0.000007
0.00515039
0.033
0.033
7.09E-06
1.220
0.000007
0.00204179
0.085
0.085
7.23E-06
3.357
0.000007
D (cm)
A (cm^2)
R (ohm)
0.13
0.0132665
0.013
0.1
0.00785
0.081
0.051
V (volt)
Table 3: A tabular representation of the square-inverse linear relationship
between R and the resistivity ρ of Brass at different lengths.
Data Analysis of Part C:
By keeping the current, length and resistivity (same material) constant and varying the
diameters, we were able to calculate the resistivity across the wire at different
diameters. This was to confirm that diameter does not affect resistivity but most
importantly to calculate the resistivity of the same material across different diameters.
Resistivity can be found by rearranging the equation below;
𝑅 = 𝜌 𝐿 /𝐴 => 𝜌 = 𝑅 𝐴/ 𝐿
By referring to Table 3, The value of resistivity is roughly the same for all the diameters of
the brass wires after rounding the numbers off. Except for perhaps some rounding errors,
all the uncertainty values were less than 5%, indicating accuracy. The computed values
were extremely close to the provided values. The highest value of resistivity derived
(Table 3) was 7.19 × 10−6 Ω 𝑐𝑚 and the lowest value was 6.87 × 10−6Ω 𝑐𝑚.
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PHYS .212.600 – University Physics II
Part D:
L (cm)
24
Material
D(cm)
A(cm^2)
R(ohm)
V(volt)
ρ (Ω.cm)
I(A)
Copper
0.1
0.00785
0.005
0.005
1.64E-06
1
Aliminum
0.1
0.00785
0.016
0.015
5.24E-06
1
Nichrome
0.1
0.00785
0.325
0.309
1.06E-04
1
Stainless Steel
0.1
0.00785
0.25
0.238
8.18E-05
1
Table 4: Table showing resistivity values for different materials.
Data Analysis of Part D:
The calculated values closely approximate the figures presented in the handout's
table, indicating a high level of precision. To further substantiate this claim, the
margins of uncertainty associated with these measurements are consistently within
the acceptable error range of 5%.
Conclusion:
Based on the four experiments conducted, we can draw the following conclusions.
Firstly, we verified the validity of the resistance formula. We established that
resistance exhibits a direct proportionality to length and is inversely proportional
to the square of the diameter (1/D^2). Additionally, we successfully determined
the resistivity values for five distinct materials.
This series of experiments not only introduced us to the operation of new
equipment such as the multimeter and Resistance Apparatus but also provided
valuable lessons in scientific methodology, analytical skills, and scientific thinking.
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