D2L-Exp7

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Mechanical Engineering

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Apr 3, 2024

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Resistance in a Wire Professor Dhiraj Maheswari March 4 th , 2024
Purpose The purpose of this lab is to investigate the relationship between resistance and resistivity. Study the relationship between the resistance of a wire and its dimensions and find resistivity of a given wire. Introduction Resistivity is a fundamental property represented by the Greek symbol “ρ.” Fundamental properties are properties that do not change based on physical factors. Resistance (R), however, depends on factors such as the type of material, length of the conductor, cross-sectional area, and the temperature of the wire. At constant temperature, resistance of a conductor is directly proportional to length and inversely proportional to its cross-sectional area A denoted in the following formula: R = ρ L A ............... ( 1 ) Procedures 1. Open the simulation using the link to PhET Interactive Simulations at the University of Colorado Boulder: PhET Interactive Simulations 2. Explore the options available in the simulator for Resistance in a wire (see screenshot below). 3. Use the three sliders (one at a time) and observe what happens with the resistance of the wire. Note the keyboard symbol at the bottom right corner for smaller steps adjustments. Data & Evaluation Part 1: Resistance versus Length
1. Adjust the resistivity pointer at the midpoint (0.50 Ω.cm) and the area pointer at 7.50 cm 2 . 2. Select the length of the wire 2 cm and take the reading of the resistance R then record the results in Table 1. 3. Repeat step 2 by increasing the length of the wire by 2 cm each time until you fill table 1. 4. Plot the graph of (R versus L) using Vernier Graphical Analysis, then find the slope. 5. From the slope of the line, find the resistivity of the wire (ρ exp ) 6. Calculate the percentage error of the resistivity Table 1 Resistivity ρ actual = .50 Ω Cross-sectional area A= 7.12 cm 2 Length L (cm) Resistance R (Ω) 1. 1.97 .131 2. 4.04 .269 3. 6.02 .401 4. 8.00 .533 5. 9.98 .665 6. 11.96 .797 7. 14.03 .935
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m=.0665 p = R (A/L) R = (p/A) L .0665 (7.12)=.4732 Ω.cm % error =[( .4732 - .50)/.50] = 5.36% Part 2: Resistance versus Area 1. Adjust the resistivity at the midpoint (0.50 Ω.cm) and the length at 10 cm. 2. Select the area of the wire around 2 cm 2 and take the reading of the resistance R. 3. Record the results in data table 2. 4. Increase the area of the wire by 2 cm 2 each time and repeat previous steps until you fill table 2. 5. Plot the graph of (R versus A), what is the expected shape of this graph? 6. Plot the graph of (R versus 1/A), then find the slope. From the slope of the line, find the resistivity of the wire (ρ exp ). 7. Calculate the percentage error of the resistivity.
Table 2 Resistivity ρ actual = .50 Ω.cm Wire length L= 9.98 cm Area A (cm 2 ) Resistance R (Ω) 1/Area (cm -2 ) 1. 1.97 2.53 .508 2. 3.99 1.25 .251 3. 6.01 .830 .166 4. 8.03 .621 .125 5. 9.98 .500 .100 6. 12.00 .416 .083 7. 14.02 .356 .071 R vs A
The expected shape of this graph is an exponential. R vs 1/A
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m= .201 2.174 Ω / 10 cm (.437 cm 2 ) = .497 Ω.cm % error = [(.497 - .50)/.50] x 100 = .50 % Results and Conclusion The factors that affect the resistance of a wire include the material, the length, the thickness, and the temperature of a wire. In this lab, it has been demonstrated that the resistance of a wire is directly proportional to the length of the same wire. Resistivity, however, will not change based on physical factors as it is a fundamental property. This is why a graph of R vs L creates a straight line. Resistance is inversely proportional to cross-sectional area. In the graph of resistance and cross-sectional area, a curve appears as it is a square of the radius. Using the slope, resistivity can be calculated.