EXP3-PHYS_182B_196L_Resistivity_screenshots (1).docx (1)

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PHYS 182B/196L Exp 3: Resistivity Page 1 of 14 Lab 3: Resistivity San Diego State University Department of Physics Physics 182B/196L Name: Partners: Introduction In the previous lab, you saw how charges could build on surfaces simply by rubbing two objects together. Those charges present on the Faraday Ice Pail caused a measurable voltage on the electrometer. What happened when you touched your finger to both the inner and outer pails at the same time? Those charges moved, so that they may balance out, back to net-neutrality. As those charges were moving, albeit extremely briefly, they produced a current. Current is simply defined as the flow of charges. Imagine water flowing through pipes. That water doesn’t flow without some sort of pressure. Similar to how water flows in pipes, Voltage is the ‘pressure’ that makes charges flow. When you rubbed the two wands together, creating an imbalance of charge, you were also creating a potential difference, like building up pressure between the opposite charges. However, when these charges flowed back to net-neutrality (zero overall charge), the amount of current created was very tiny. For example, the amount of built-up charge if the electrometer originally reads 50 Volts, is about 7 nano-Coulombs, or converting from moles, about 45 billion electrons. That may sound like a lot of electrons, but they drain nearly instantaneously. Consider a small lightbulb lit by a 1.5 Volt ‘AA’ battery. To stay lit, the bulb requires about 0.37 milli-Amps of current, or 0.37 milli-Coulombs every second. That’s more than 200 quadrillion electrons flowing through a single point, every single second. The roughly 45 billion charges you produced by rubbing wands together would be nowhere near enough to light a bulb continuously. Now, as charges flow through a material, they bump into the atoms of the material. This causes friction and can impede the flow of charge. The amount a material impedes the flow of charge is called ‘resistivity’ and is a property of the material. The resistivity of different metals is determined by finding the resistance of wires of a known diameter as a function of their length. It is also shown that the resistance of a wire of fixed length is inversely proportional to its cross-sectional area. Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

PHYS 182B/196L Exp 3: Resistivity Page 2 of 14 Theory If a current (I) is flowing through a wire, the voltage drop (V) across a certain length of wire with resistance R is given by Ohm's Law: V=IR or solving for R gives: R = V/I (1) In this experiment, you will measure V and I to determine R for various lengths of wire. You will then make a graph of R versus length (L). The resistance of a wire depends on the length of the wire, the cross-sectional area (A), and the resistivity ( ρ ) of the material: R = ρ L/A (2) A plot of R vs. L will result in a straight line that has a slope equal to ρ /A. Thus the resistivity is given by ρ = (slope)A = (slope) π (d/2) 2 (3) where d is the diameter of the wire. Setup Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

PHYS 182B/196L Exp 3: Resistivity Page 3 of 14 Figure 1: Setup 1. Press the power button on the 850 Universal Interface to turn it on. Open PASCO Capstone. 2. Make the connections as shown above in Figure 1. Click on “Hardware Setup”, then click on the yellow circle around “Output 1” and select the Output Voltage Current Sensor. Set the sample rate of all the sensors to 100 Hz. See below for some screenshots describing how to do this step. Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

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PHYS 182B/196L Exp 3: Resistivity Page 4 of 14 The image on the top left shows how to connect the Output Voltage-Current Sensor. The image on the bottom left shows where to change the sample rate. Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

PHYS 182B/196L Exp 3: Resistivity Page 5 of 14 3. Open Data Summary and click on the gear icon for the Voltage Sensor. Set the gain to 10x. 4. You should have a wire installed in your apparatus already. If you do, proceed to step 4. If not, follow these steps: a. Select one type of wire. The different wires are either copper, brass, aluminum, steel, or nichrome. You will be determining which wire type you have later. b. On the Resistivity apparatus, move the Reference Probe and the Slider Probe to the Park position. The probes should be as far left and right respectively as possible, so the probe lifts up to allow installation of the sample wire. They will click into position. c. Turn the two black handles counterclockwise to open the clamps to allow the sample wire to slide into position. d. Install the wire in the apparatus. Slide from left or right using the white line-up hash marks. Figure 2 shows the right-hand side as the wire slides in. Note that on the right-hand side, the wire is on the far side of the silver clamp (with black handle), but on the left-hand side the wire will be on the near side of the clamp as shown in Figure 3. This prevents the wire from bowing as you tighten the clamps. e. Tighten the clamps by turning the black handles clockwise. Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

PHYS 182B/196L Exp 3: Resistivity Page 6 of 14 5. Position the reference probe at the 0 cm mark and the slider probe at the 5 cm mark. Figure 2: Right Hand Clamp Figure 3: Left Hand Clamp 6. In Capstone, create a table with a user-entered data set called “Wire Length” with units of ‘cm’. Then, in the second column, create a user-entered data set called “Resistance” with units of ‘m Ω ’. For capital Greek Omega ( Ω ), right-click where you are typing and go to ‘Insert’ and choose either ‘Symbol’ or ‘Upper-case Greek.’ Below are screenshots showing how to do this step and an example of the table. The figure at left shows how to create a new User-Entered data set. Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

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PHYS 182B/196L Exp 3: Resistivity Page 7 of 14 The figure at left shows how to insert a special character. The figure at left shows how your table should look. Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

PHYS 182B/196L Exp 3: Resistivity Page 8 of 14 7. Create a second table with four columns The figure at left shows how to add a new column to a table. The figure at left shows how your table should look at step 7. The first column has a user-entered data set called “Metal” with no units. The second column has a user-entered set called “Wire Diameter” with units of mm. The third column has a user-entered set called “Slope” with units of m Ω /cm. Leave the fourth column blank for now. 8. Open the calculator and create the following calculations: V = 1000*avg([Voltage, Ch A (V) ]) Units of mV I = 1000*avg([Output Current, Ch O1 (A)]) Units of mA R = 1000*[V (mV)]/[I (mA) ] Units of m Ω ρ = ( π *([Wire Diameter (mm)]/2)^2)*[Slope (m Ω /cm)]*10 Units of μ Ω -cm Note: When typing a ‘[‘ open-bracket, Capstone will pull up a list of local variables for you to choose from. Choose the variable that corresponds to the user-defined labels you made in the tables. Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

PHYS 182B/196L Exp 3: Resistivity Page 9 of 14 9. Go back to Table II and click <Select Measurement> for the fourth column. Choose ρ (μ Ω -cm). 10. Drag down three Digits displays from the far-right toolbar. Under ‘Measurement’ choose the calculations from the list: V(mV), I(mA), and R(m Ω ). These values will be averages of real-time measurements. 11. Drag a Graph from the far-right tools palette and select ‘Measurement’: ‘Resistance’ (The user-defined label in your table) on the y-axis and ‘Wire Length’ (Another user-defined label from the table) for the x-axis. Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

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PHYS 182B/196L Exp 3: Resistivity Page 10 of 14 Procedure 1. Click open the Signal Generator (left side of screen). 850 Output 1 should be set for a DC voltage of 3.0 V. Click the On button to turn the Signal Generator on. 2. Move the Slider Probe on the Resistance Apparatus so the contact is at 5.0 cm . 3. Click RECORD at the bottom left of the screen. Wait a few seconds until the numbers stop changing and then click STOP . 4. The resistance measurement (‘R’) in the lower box is calculated from R = V/I where the V and I values are averages that show in the upper two boxes. In the first row of the ‘Different Lengths’ table, enter the Wire Length (5.0 cm, which you set manually on the resistivity apparatus, but don’t type ‘cm’ in the table, as the units are already assigned) and then the resistance (‘R’ from the averaged measurement in the digits display). 5. Repeat steps 3 & 4 for Slider Probe positions of 10.0 cm, 15.0 cm, and 20.0 cm . Analysis 1. The first graph shows the resistances you measured versus the length of wire you used. 2. Click the Scale-to-fit icon at the top left of the toolbar. Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

PHYS 182B/196L Exp 3: Resistivity Page 11 of 14 3. Click the data set on the graph you wish to view. Then, click the black triangle by the Curve Fit icon on the toolbar and select Linear. Right click in the Linear box and click on Show Uncertainty if it is not already showing. 4. Record the slope, m, of the Resistance versus Wire Length graph in the Slope column of Table II. Don’t worry about typing in the 土 uncertainty value. Note that in most cases the uncertainty in the slope is less than 1%. 5. After recording the slope in the table, the ‘ ρ ’ column should automatically update with a calculation of the resistivity. If it does not, you may need to check your functions in the calculator. Conclusions 1. Paste an image here of your graph by simultaneously pressing the ‘Windows Key’ + ‘Shift’ + ‘s’ and drag the cursor (crop) over the section of the screen that only contains your graph. If this screenshot method does not work, open ‘snip & sketch’ program and click ‘new’ to drag an area to screenshot. Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

PHYS 182B/196L Exp 3: Resistivity Page 12 of 14 2. Paste a screenshot of your two data tables below. Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

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PHYS 182B/196L Exp 3: Resistivity Page 13 of 14 3. How well does the data fit a straight line? What does this show about the relationship between your data and equation 3? The data fits a straight line very well. This shows that as the length increases so does the resistance of the probes. 4. The value calculated for ρ is given in column 4 of your second table. Describe where potential sources of uncertainty for this measurement would come from. The uncertainty of the potential source of the measurement would be human errors and temperature of the environment of the experiment. Temperature has an effect on resistivity because if a temperature is higher it allows greater resistivity whereas a low temperature would allow for a lower resistivity and a higher current flow. 5. The resistivity of the different metals: 1.8 ± 0.1; 4.9 ± 0.1; 7.0 ± 0.5; 79 ± 1, and 105 ± 5; for copper, aluminum, brass, steel, and nichrome respectively. The uncertainty here Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

PHYS 182B/196L Exp 3: Resistivity Page 14 of 14 arises because the metal wires are alloys, and the actual resistivity depends on the exact composition Which metal did you have, based on the list of manufacturer resistivities above? The metal that we have based on the list given is brass which has a resistivity of 7.0 + or - 0.5. We got a resistivity of 6.81 which falls into this range. 6. Discuss how well your data agrees with the given values (is it within the given standard deviation +/-). What does this show about Equation 3? This data falls perfectly within the range of data being 0.19 below the ideal resistivity. 7. Which wire material above do you think allows the most electric current flow? Why? The wire material that allows the most electric current flow would be copper because it has the least resistivity which allows for the electric current flow to be drawn towards this path. Written by Chuck Hunt, modified by Alex Bates - Last Updated: 02/13/2023

EXP3-PHYS_182B_196L_Resistivity_screenshots (1).docx (1)

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