Lab Report 4 (DOCX) - Resistivity and Ohms Law - 2024

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Columbus State University *

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Electrical Engineering

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Feb 20, 2024

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Resistance, Resistivity, and Ohm’s Law Lab Assignment OBJECTIVES  Determine the mathematical relationship between current, potential difference, and resistance in a simple circuit.  Determine the mathematical relationship between resistance and resistivity. MATERIALS Computer Vernier computer interface Logger Pro Vernier Current Probe Vernier Differential Voltage Probe Wires Clips to hold wires Two resistors (approx. 10 Ω and 47 Ω) Adjustable 5 Volt DC power supply Part 1 In this part of the lab, we are going to be looking at the current, voltage and resistance in a circuit with a single resistor. (Next week, we’ll build on this and do parallel and series resistor circuits.) First, we’re going to wire a resistor to a power supply, and set up the current probe and voltage probe so that they can get accurate measurements. 1. Connect the Current Probe to Channel 1 and the Differential Voltage Probe to Channel 2 of the computer interface. 2. After opening LoggerPro from the desktop, use the File > Open pulldown menu to open the file “22 Ohms Law” in the Physics with Vernier folder. A graph of potential vs . current will be displayed. The meter displays potential and current readings. 3. With the power supply turned off, connect the power supply, 10  resistor, wires, and clips as shown in Figure 1. Take care that the positive lead from the power supply and the red terminals of the Current & Voltage Probes are connected as shown in Figure 1. Note : Attach the red connectors electrically closer to the positive side of the power supply. + - I R e s i s t o r B l a c k R e d C u r r e n t p r o b e V o l t a g e p r o b e 1

Resistance, Resistivity, and Ohm’s Law Lab Assignment Figure 1 4. Click . A dialog box will appear. Click to zero both sensors. This sets the zero for both probes with no current flowing and with no voltage applied. 5. Have your lab instructor check the arrangement of the wires before proceeding. This will count as part of your grade for this lab. 6. Turn the control on the DC power supply to 0 Volts, and then turn on the power supply. In 0.5 Volt steps, increase the voltage. For each of these steps, record the voltage, and the current, in the table below. Voltage (Volts) Current (A) 7. Looking at the trends in the data you just took, what happens to the current when you double the voltage? In this experiment, resistance is the control variable; we don’t change its value throughout. Voltage is the independent variable; we change its value in a controlled way to see how it affects the value of the dependent variable. In this case, current is the dependent variable. We will follow the common strategy of graphing the dependent variable on the y-axis, and the independent variable on the x-axis. 8. Create this graph in Excel, using the data from your table above. Be sure to add a trendline, including the equation of the line, on your graph. Include a screen shot of the graph you create. Excel has found the slope of your dataset for you, but it’s up to us to consider what that slope means . We have voltage on the x-axis and current on the y-axis, so a rise-over-run calculation would give: 2

Resistance, Resistivity, and Ohm’s Law Lab Assignment m = ∆ y ∆ x = I V Remember, Ohm’s law looks like: V = IR We need to rearrange the physics equation into the same format as the slope equation above: 1 = IR V 1 R = I V So now we can put the two together: m = ∆ y ∆ x = I V = 1 R 9. Plug in the known value of this resistor into the final slope equation above. How does this result compare to the slope value from your trendline? Calculate the percent difference between the two values. Should this be a small percent difference? 10. Is this graph linear? Does the equation for Ohm’s Law predict a linear graph? For both questions, explain why or why not. Now, we are going to repeat our measurements for a 47  resistor, instead of the previous one. 11. Turn the control on the DC power supply to 0 Volts, and then turn on the power supply. In 0.5 Volt steps, increase the voltage. For each of these steps, record the voltage, and the current, in the table below. Voltage (Volts) Current (A) 3

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Resistance, Resistivity, and Ohm’s Law Lab Assignment 4

Resistance, Resistivity, and Ohm’s Law Lab Assignment 12. Create this graph in Excel, using the data from your table above. Be sure to add a trendline, including the equation of the line, on your graph. Include a screen shot of the graph you create . 13. What is the value of your slope? Include units in your answer. 14. Using this slope value, what resistance value do you calculate based on your graph? How does that compare to the theoretical value of 47  ? Part 2 For the next part of this lab, you will need to open the Resistance in a Wire simulation found here: https://phet.colorado.edu/sims/html/resistance-in-a-wire/latest/resistance-in-a-wire_en.html Length Use the reset at the lower right corner of the screen to bring all values back to the initial values. 15. Use the slider for length, sliding it from its minimum value to its maximum. a. What happens to the image of the wire in the simulation when it is at a minimum length? b. What happens to the image of the wire in the simulation when it is at a maximum length? 16. Now look at the equation that is written over the wire. Leave the resistivity and the area at their initial values, and record them here: a. area = __________ cm 2 b. Resistivity = __________ ohm cm 5

Resistance, Resistivity, and Ohm’s Law Lab Assignment 17. Keeping those values of area and resistivity constant, record the length and the resistance in the table below. Do at least 5 values of length, and make the range go from approximately 1 cm to the maximum 20 cm. Length (cm) Resistance (ohms) 18. Now graph this data in Excel, with length on the x-axis, and resistance on the y-axis. Be sure to add a trendline, including the equation of the line, on your graph. Include a screen shot. Again, it’s up to us to consider the meaning of the slope value that Excel found for us. We know it should be equivalent to a rise-over-run calculation, so relating it back to the physics variables gives: m = ∆ y ∆ x = R L Remember, resistance and length are related using the physics equation: R = ρL A Next, we plug this physics equation into the slope equation: m = R L = ( ρL A ) L = ρ A 19. Is this graph linear? Does the equation for resistance (on the screen in the simulation) predict a linear graph? For both questions, explain why or why not. 6

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Resistance, Resistivity, and Ohm’s Law Lab Assignment 20. Plug in the values of resistivity and Area (from #16) into the final slope equation above. How does this compare to the slope of your graph from the trendline? Calculate the % difference between the values. Resistivity Use the reset at the lower right corner of the screen to bring all values back to the initial values. 21. Use the slider for resistivity, sliding it from its minimum value to its maximum. a. What happens to the image of the wire in the simulation when it is at a minimum resistivity? b. What happens to the image of the wire in the simulation when it is at a maximum resistivity? 22. Now look at the equation that is written over the wire. Leave the area and the length at their initial values, and record them here: a. Length = __________ cm b. area = __________ cm 2 23. Keeping those values of length and area constant, record the resistivity and the resistance in the table below. Do at least 5 values of resistivity, and make the range go from approximately 0.1 ohm cm to the maximum 1.0 ohm cm. Resistivity (ohm cm) Resistance (ohms) 7

Resistance, Resistivity, and Ohm’s Law Lab Assignment 8

Resistance, Resistivity, and Ohm’s Law Lab Assignment In this experiment, area and length are the control variables; we don’t change their values throughout. Resistivity is the independent variable; we change its value in a controlled way to see how it affects the value of the dependent variable. In this case, resistance is the dependent variable. We will follow the common strategy of graphing the dependent variable on the y-axis, and the independent variable on the x-axis. 24. Create this graph in Excel, using the data from your table above. Be sure to add a trendline, including the equation of the line, on your graph. Include a screen shot of the graph you create . 25. Following the pattern we used in the previous graph, look at what the slope ought to be equal to, using the resistance and resistivity formula, in equation form. (Follow the strategies we used earlier.) Show your calculations. 26. Is this graph linear? Does the equation for resistance (on the screen in the simulation) predict a linear graph? For both questions, explain why or why not. 27. Plug in the values of length and Area (from #22) into the final slope equation above. How does this compare to the slope of your graph from the trendline? 9

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