Lab Report 3

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School

Houston Community College *

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Course

217

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Electrical Engineering

Date

Dec 6, 2023

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docx

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LAB 3: RESISTIVITY Alex Vizcaya, Humzah Kashif Texas A&M University College Station, TX 77843, US. Abstract This report covers the relationship between the thickness of a wire and its resistance. It also talks about how the different parts of a wire can make its resistance value change. A current was run through one of three wires at various lengths. This was done to find out what factors, like length and current, cause resistance to change for each wire. Using the change in voltage and the amount of current coming from a power supply, one can figure out how length, resistivity, and area are related. Keywords: Resistivity, Current, Electric potential, Area 1. Introduction In this lab, the resistivity of a wire of three different materials and thickness (gauge) is being studied to examine how cross-sectional area and length affect resistance. Three identical wires are provided, and positive and negative leads are joined at various positions along the wire to represent greater and shorter lengths. The goal of this experiment is to demonstrate that length and thickness are connected to resistance and resistivity and that the difference between materials may be determined by the resistivity of certain materials. In order to achieve this the following equations were used in the process: The sample mean ( ? ) must first be calculated for graph generation, determined by: x 1 + x 2 + ¿ … + x n n ´ x = ¿ Equation 1 where ? are experimental data values and n is the total number of data values. The three graphs created from ? experimentation with each wire will prove the wires’ Ohmic behavior. From the length and voltage data collected of each wire, resistance and diameter predictions are able to be calculated. Finally, the resistivity of each wire is determined by: ρ = R ( A l ) = Rπr 2 l Equation 2 where resistivity is represented by ⍴ , R is resistance, A is the wire's cross-sectional area, and l is the wire’s length. Uncertainty and subsequent standard deviation will enhance the accuracy of experimental calculations and are discovered as follows: δ ´ x = σ √ n Equation 3 where ? ´ x is the uncertainty of the mean ´ x equal to the standard deviation (σ) divided by the square root of the total number of sample values, or ? . The standard deviation is found by: x i − ¿ ¿ ¿ 1 n − 1 ∑ i = 1 n ¿ σ = √ ¿ Equation 4 2. Experimental Procedure To begin the lab experiment, first collect the diameter of the three wires. All three are wired using lead connections at the ends. Measure the overall length of the wire from lead to lead, and then use the provided calipers to determine the diameter of the three wires by measuring the wires with a pair of dial calipers at four equally distant intervals and compute the average. The next part of the experiment requires the power supply to be connected to the DAQ and the DAQ to be connected to the MobaXterm terminal on a computer. Then, using an alligator clip, connect the terminal extender lead to the negative lead. To collect the data for this part of the lab, you will need a

Python script After taking the measurements, connect leads to the power supply with the positive lead on either side of any one of the wires, and set the current to .1 Amps. Then measure the voltage at 6 distance intervals by placing the ground wire at specific distances from the power. For each distance, run the daq_to_csv. python code this will take output a csv file which you will extract onto your device. After you have your 6 csv files, compute the average voltage at each distance and graph the results. Now for the first wire, place the leads at each end of the wire, set the current for .1A and compute the voltage using the daq_to_csv file and transfer the resulting csv file to your computer. Then increase the current to .2A and repeat process, extracting the csv to your computer. Increase the current by another .1 until you have 5 csv files for the voltage when the current is 0.1A, 0.2A, 0.3A, 0.4A, 0.5A. Now compute the average voltage at each of these currents and graph the result in Excel. Now follow these steps for the second and third Wire. Finally, after data collection, turn off the power supply and unplug all the connecting wires between the DAQ and the power supply. 3. Results and Analysis Figure 1: Drop of Voltage as compared to distance. Using a constant current and measuring the resulting drop in voltage it is evident the as wire length increases, the resistivity of the wire causes the voltage to drop, this gives credence to the claim that even the most conductive wires contain a minute amount of resistance that we must account for. 100 200 300 400 500 600 0 0.5 1 1.5 2 2.5 Length of Wire vs Voltage Wire Length (mm) Voltage (V)

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 1 2 3 4 5 6 Wire 1 Current vs Voltage Current (A) Average Voltage (V) Figure 2: Wire 1 Change in Current vs Resulting Voltage. In figure 2, The displayed graph, is the linear correlation of the average current versus the average voltage as expected, the line is linear and from the data we can extrapolate the resistance of this wire, which will be used to calculate the resistivity of this wire and subsequently it's chemical makeup. 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0 1 2 3 4 5 6 Wire 2 Current vs. Average Voltage Current (A) Average Voltage (V) Figure 3: Wire 2 Change in Current vs Resulting Voltage. As with figure 2, figure 3 displays the outputted footage that was detected once a known current was inputted into the wire, once again as expected we receive a linear correlation between the two and we once again extrapolate the resistance that we will be using to calculate resistivity in the last step.

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Figure 4: Wire 3 Change in Voltage Over Time. Figure 4 shows the final trial and pertains to the information gathered from the third wire. Table Trial Wire 1 Wire 2 Wire 3 Resistance ( Ω ) 15.7 ± .01 9.54 ± .01 6.01 ± .01 Diameter (mm) .25 ± .01 .33 ± .01 .40 ± .01 Length (m) .60 ± .01 .60 ± .01 .60 ± .01 Resistivity ( Ω/m ) 1.28*10^-8 1.36*10^-8 1.26*10^-8 Figure 5 Finally, in figure 5, for each wire the diameter and length were both converted to meters and along with the resistance that was computed from the graphs you were able to calculate the resistivity for each wire. 4. Conclusions When first learniong about fundamental forces of nature such as resistance and resistivity in class, we are given ‚“ideal“ conditions with no error to work with. While this is an incredible tool for learning, the real world is seldom as simple. This lab was a masterclass in teaching about the variability of results taken from the real world. You cannot even trust the most precise of instruments to give you an exact amount, the only thing you can trust is that their will be uncertainty, an oxymoron. In this lab after calculating the the averages of the voltages and the uncertainties therin, we were able to compute a specific resistance for each wire. After computing the physical dimensions of the wire, we were able to finally compute the resistivity of each wire. After comparing the derived values for resistance and resistivity to known values for known metals, we were able to conclude that the first and third wire are steel while the second wire is either nickel or pure iron.