Lab 3

pdf

School

Texas A&M University *

*We aren’t endorsed by this school

Course

217

Subject

Electrical Engineering

Date

Feb 20, 2024

Type

pdf

Pages

Uploaded by jjulianmurilloc

LAB 3: RESISTIVITY Drew Curlin, J Julian Murillo, Louise Reisner Texas A&M University College Station, TX 77843, US. Abstract This report covers the general theory behind resistivity. Using the DAQ system and the power supply the voltage and current of three wires is measured, these values are computed, and the resistance is calculated, the length and diameter of the wires are also measured, and all are used to calculate the resistivity and consequentially determine the composition of each of these wires. This exercise provides a physical representation of resistivity, resistance and Ohm’s law concepts. Keywords: resistivity, resistance, Ohm’s Law, voltage, current 1. Introduction Resistivity measures how strongly a material resist electric current, and resistance is a measure of the opposition to current flow on an electrical circuit. Ohm’s Law analysis the relation between current, resistance, and voltage, expressed as: ࠵? = ࠵?࠵? Equation 1 Where V is voltage, I current, and R is resistance. This relationship just translates to “the current through a conductor between two points is directly proportional to the voltage across the two points”, which means that in a graph of Voltage vs. Current, the Resistance would be the slope. Resistivity is an intrinsic property of an object, and it depends only on its composition, while resistance is an extrinsic property which depends on its dimensions. Comparing these two properties result in: ࠵? = ࠵? ! " Equation 2 Where ࠵? is resistivity, l is length, and A is the cross-sectional area, since the cross-sectional area of a wire is a circle where d is the diameter of the wire. ࠵? = ࠵? ( # $ ) $ Equation 3 To calculate the uncertainty of the resistivity, the partial derivative approach should be used, where s symbolizes the uncertainty and d the derivative: ࠵?࠵? $ = ( %& %’ ࠵?࠵?) $ + ( %& %! ࠵?࠵?) $ + ( %& %" ࠵?࠵?) $ Equation 4 2. Experimental Procedures Four different data sets were taken in this procedure. The first required measurements of a constant Voltage against varying distance. To do so, a DC power supply was set to a constant voltage of 1.5V, though this is an arbitrary number. A maximum amperage was also set for safety reasons, but the power supply hit a constant amperage below this maximum while maintaining the set voltage. The power supply was set up across a wire of unknown resistivity. Then, beginning at the negative or ground side of the wire, voltage measurements were taken at increasing distance integrals using a voltage probe to DAQ machine. This data was used to extrapolate a line of best fit showing the relationship between voltage and distance. The second, third, and fourth data sets were taken in the same manner. These data sets represented Voltage against changing Current for a constant distance. Three different wires were tested using these measurements, the idea being to calculate the resistivity of each wire using the data harvested. This time around the power supply was set to multiple constant Current measurements. The power supply was again set up over each wire. To measure, the Voltage probe was set at an arbitrary but constant distance from the positive node of each wire. Then, a new current was set on the power supply, and the voltage resulting measured. Ten currents were tested for resulting voltage for each wire. This data was used to create a line of best fit for the relationships between current and voltage respective to each wire, and these lines used to calculate the resistivity of each wire using Equation 1, Equation 2, and Equation 3.

3. Results and Analysis Figure 1. Voltage drop across a segment of wire Figure 2. Voltage drop across wire 1. ( D V vs. I) Figure 3. Voltage drop across wire 2. ( D V vs. I)

Figure 4. Voltage drop across wire 3. ( D V vs. I) Table 1 : Properties for each wire Property Wire 1 Wire 2 Wire 3 R [ W ] 15.9605 ± 0.07867 9.66631 ± 0.05026 6.11369 ± 0.03947 d [m] 0.00025 ± 5x10 -6 0.00032 ± 5x10 -6 0.0004 ± 5x10 -6 l [m] 0.7 ± 5x10 -4 0.7 ± 5x10 -4 0.7 ± 5x10 -4 r [ W *m] 111.922x10 -8 ± 4.51x10 -8 111.06x10 -8 ± 3.52x10 -8 109.75x10 -8 ± 2.83x10 -8 The three wires are Nichrome (NiCr or nickel-chromium) an alloy of nickel, chromium and often iron. 4. Conclusions There are two different relationships examined in this lab, and two sets of conclusions to be made. In the first part of the procedure voltage (V) was measured against distance. The data clearly shows a linear relationship between the two. As the distance increased from the negative node (decreased from the positive node), the voltage measured increased. It can be concluded that the greater the distance between where Voltage is measured and the positive node of its voltage source, the greater the loss of voltage. In other words, the smaller the distance, the more voltage conserved. From the calculated average resistivity of each data point, it was determined that the material of the wire was Nichrome for all three wires. Nichrome is a non-magnetic alloy that is commonly composed of 80% nickel and 20% chromium and has a resistivity of approximately 110 x 10 -8 [ W *m]. Although the length of the wire varied throughout the experiment, it was concluded that the resistance of the material stayed the same, thus proving that resistivity is a constant. The data collected demonstrates that current and potential difference or voltage must be proportional to each other. Although not all the resistances equaled out to be the exact same, it can be concluded that error when calculating the diameter, length, or perhaps the interval between the data points weren’t always collected with complete accuracy. Regardless of the errors that may have been made during data collection, all three wires were shown to follow Ohm’s Law.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version