Fall22 Resistance and Resistivity Lab Online EDITED 8.16.22(1)

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University of Texas, San Antonio *

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1631

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Electrical Engineering

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Dec 6, 2023

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Resistance and Resistivity Part 1 Table 1 Resistivity : 0.50 ohms cm Cross-Sectional Area: 5.00 cm^2 Trial Length (cm) Resistance (Ώ) Resistivity (Ώ cm) 1 2.00 0.200 0.50 2 4.00 0.400 0.50 3 6.00 0.600 0.50 4 8.00 0.800 0.50 5 10.00 1.00 0.50 6 12.00 1.20 0.50 7 14.00 1.40 0.50 8 16.00 1.60 0.50 9 18.00 1.80 0.50 10 20.00 2.00 0.50 Average ρ 0.50 Sample Calculation for resistivity (ρ): (10 points) Part 2 Table 2: Resistivity: 0.50 ohms cm Length: 10.00 cm Trial Area (cm 2 ) Resistance (Ώ) Resistivity (Ώ cm) 1 1.00 5.00 0.50 2 2.00 2.50 0.50 3 3.00 1.67 0.50 4 4.00 1.25 0.50 5 5.00 1.00 0.50 6 6.00 0.833 0.50 7 7.00 0.714 0.50 Copyright ©2021 Robert Hamby Resistance and Resistivity 1

8 8.00 0.625 0.50 9 9.00 0.556 0.50 10 10.00 0.500 0.50 Average ρ 0.50 Sample Calculation for resistivity (ρ): (10 points) Part 3 Length: 10.0 cm Cross-Sectional Area: 5.00 cm 2 Ratio of Length to Area (L/A): 2:1 Table 3: Trial Resistivity (Ώ cm) Resistance (Ώ) 1 0.100 0.200 2 0.200 0.400 3 0.300 0.600 4 0.400 0.800 5 0.500 1.00 6 0.600 1.20 7 0.700 1.40 8 0.800 1.60 9 0.900 1.80 10 1.00 2.00 (10 points) Analysis of Resistance and Resistivity Lab Copyright ©2021 Robert Hamby Resistance and Resistivity 2

Name: Atticus Royer Course/Section: PHY 1631-005 Instructor: John Harrison 1a) Using Excel, or some other graphing program, and the data in Table 1, make a graph of measured Resistance versus Length. Display the trendline on the graph. Using dimensional analysis, determine the units of the slope of this graph. (10 points) 1b) Use the slope of the line to calculate the Resistivity (ρ). (5 points) 2) What was the relationship between the length of the wire and the measured Resistance ? Was this the expected result? Explain. (5 points) - The length of the wire is directly proportional to the resistance. The longer the wire, the higher the resistance. This is the expected result for the relationship, and you can see given the graph there is a linear relationship since Resistance = (ρ /A)(L). 3) Calculate the percent difference between the average value of Resistivity in Table 1 and the value for Resistivity found using the slope of line (in question 1b). (3 points) Copyright ©2021 Robert Hamby Resistance and Resistivity 3

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4a) Using Excel, or some other graphing program, and the data in Table 2, make a graph of measured Resistance versus 1/Area. Display the trendline and the trendline equation on the graph. Using dimensional analysis, determine the units of the slope of this graph. (10 points) 4b) Use the slope of the line to calculate the Resistivity. (5 points) 5) What was the relationship between the Cross-sectional Area of the wire and the measured Resistance ? Was this the expected result? Explain. (5 points) Copyright ©2021 Robert Hamby Resistance and Resistivity 4

- The cross-sectional area of the wire is inversely proportional to the resistance. If the area of the wire increases, the resistance will proportionately decrease. In the above graph, the inverse of the area was plotted against the resistance. This shows that the resistance is directly proportional to 1/A. This is the expected result for the relationship, and you can see given the graph there is a linear relationship. 6) Calculate the percent difference between the average value of Resistivity in Table 2 and the value for Resistivity found using the slope of line (in question 4b). (3 points) 7a) Using Excel, or some other graphing program, and the data in Table 3, make a graph of measured Resistance versus Resistivity. Display the trendline and the trendline equation on the graph. Using dimensional analysis determine the units of the slope of this graph. (10 points) 7b) What does the slope of the line represent? (5 points) Copyright ©2021 Robert Hamby Resistance and Resistivity 5

- The slope represents the ratio of resistance to resistivity, which is equal to the ratio of the length to area, represented as 2.0 cm in the graph above. 8) What was the relationship between the Resistivity of the wire and the measured Resistance ? Was this the expected result? Explain. (5 points) - The resistivity of the wire is directly proportional to the resistance. The more resistivity of the material, the higher the resistance. This is the expected result for the relationship, and you can see given the graph there is a linear relationship. 9) Calculate the percent difference between the slope found in question 7a and the ratio of the Length to Area calculated above Table 3. (4 points) Copyright ©2021 Robert Hamby Resistance and Resistivity 6

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