PH03_Resistivity

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Old Dominion University PHYS 112 & PHYS 227/232/262 Lab Manual 1 OLD DOMINION UNIVERSITY PHYS 112 PHYS 227/232/262 PH03 – RESISTIVITY Submitted By: 1. 2. 3. Submitted on Date Lab Instructor

2 Experiment PH03: Resistivity Resistivity Experiment PH03 Objective  Investigate factors that influence the resistivity of different materials Materials Resistivity Apparatus Resistivity Wires Digital Multimeter, x2 DC Power Supply Wire Lead, Banana-Banana (5) (3 red, 2 black) Theory Ohm’s Law describes the relationship between the resistance (R) of a wire, the voltage drop across it (V), and current through it (I): V = IR (1) However, the resistance of a wire depends on characteristics of the wire: length ( l ), the cross- sectional area ( A ), and the resistivity ( ) of the material. Some materials have more or less ρ resistivity. R = ρ l A (2) Resistance depends on and A, but is a function of the material only. Electrical resistivity, and its ρ inverse, electrical conductivity, is a fundamental property of a material that quantifies how strongly it resists or conducts electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SI unit of electrical resistivity is the ohm-meter ( Ω⋅ m) Procedure In this experiment, you will apply a known current ( I ) through a piece of wire and measure V to determine R for wires of various lengths, diameters, and materials. This will allow you to determine the fundamental property of resistivity for different materials.  Equipment Setup 1. Pick a random wire from the batch provided. Measure its diameter with the calipers and record this in Data Table 1. 2. Move the reference and slider probes to the extreme left and right positions so they are parked on the ramps that will hold them off of the wire.

Old Dominion University PHYS 112 & PHYS 227/232/262 Lab Manual 3 Figure PH03.2: Wire Installation 3. Loosen the wire clamps. Insert a wire through the clamps and under the probes, as shown in the diagram. Observe the alignment lines marked near the wire clamps and note that the wire goes through the front of the left-hand clamp and through the back of the right-hand clamp. (This configuration causes the wire to be pulled tight when the clamps are closed.) 4. Tighten both clamps enough to secure the wire in place. 5. Set the voltage of the power supply to zero. Connect the power supply to the multimeters and the apparatus as shown in the following diagram. Figure PH03.3: Equipment Setup 6. Set the top multimeter to A to measure current. Set the bottom multimeter to V– to measure voltage. (Do not use V~ as this is for alternating current. We are using direct current.)

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4 Experiment PH03: Resistivity  Data Collection 1. Turn on the power supply and adjust the voltage and current knobs to establish a current of about 1 Amp through the wire. 2. Place the reference probe on the “0 cm” mark. 3. Move the slider probe to any point on the wire. Read and record the length ( l ) in centimeters from the scale on the apparatus. This is the length of wire over which the voltage is measured. 4. Read and record the voltage ( V ) and current ( I) from the multimeters. 5. Repeat steps 3 & 4 for a total of 6 different lengths along this wire. Record all data in Data Table 1. 6. Turn off the power supply and change out the wire for another one. (Remember to measure the diameter of the new wire!) 7. Repeat steps 1-6 until you have voltage and current measurements for all materials and all sizes of wires provided. Go through this process with a plan. There are some wires of different materials and some of the same material but of different sizes!  Resistance versus Length 1. Now that you have voltage, current, and length measurements for each wire, we can delve deeper into our analysis. Create a table and calculate resistance ( R ) for each measurement using Ohm’s Law, equation (1). We recommend Excel for this as it can do batch calculations quickly. 2. Make a graph of resistance vs. length (R vs. l). All wires can be plotted on the same graph to save space. Be sure they are properly labeled to distinguish which wire is which. 3. From equation (2), we can see that the slope of a R vs. l graph is equal to ρ A . Add a trendline (set type to ‘linear’) to each data set in the graph and add the equation to the graph. Using the given slopes, calculate the resistivity of each wire. 4. Using the table below, determine the material for each wire based on its resistivity. Include a table of these determinations in your report. Material Approximate Resistivity ( ·m, x10 Ω -8 ) Copper 1.8 ±0.1 Aluminum 4.9 ±0.1 Brass 7.0 ±0.5 Nichrome 105 ±5 Stainless Steel 79 ±1

Old Dominion University PHYS 112 & PHYS 227/232/262 Lab Manual 5 Wire Your Approximate Resistivity ( ·m) Ω Guess the Material 1 2 3 4 5 6 7 8  Resistance versus Cross-Sectional Area 1. In the set of wires provided, you should have had 4 brass wires of different diameters. 2. For these 4 wires, make a graph of R vs. diameter (D). Include data for all 4 wires on the same graph.

6 Experiment PH03: Resistivity Data Table – Experiment 04 Data Table 1-8 Voltage and Current Wire 1 Wire 2 Diameter mm Diameter mm Length (m) Voltage (V) Current (A) Length (m) Voltage (V) Current (A) Resistivity Ω⋅ m Resistivity Ω⋅ m Wire 3 Wire 4 Diameter mm Diameter mm Length (m) Voltage (V) Current (A) Length (m) Voltage (V) Current (A) Resistivity Ω⋅ m Resistivity Ω⋅ m

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Old Dominion University PHYS 112 & PHYS 227/232/262 Lab Manual 7 Wire 5 Wire 6 Diameter mm Diameter mm Length (m) Voltage (V) Current (A) Length (m) Voltage (V) Current (A) Resistivity Ω⋅ m Resistivity Ω⋅ m Wire 7 Wire 8 Diameter mm Diameter mm Length (m) Voltage (V) Current (A) Length (m) Voltage (V) Current (A) Resistivity Ω⋅ m Resistivity Ω⋅ m What to Turn In  Full Lab Report o Only grading the “ Data & Data Analysis” section. This section is worth 60 points.  Data Tables 1-8  Graph of Resistance vs. Length with equations included  Graph of Resistance vs. Diameter with equations included o Introduction and Conclusion sections are worth 20 points each. These are graded strictly as 0, 10, or 20 points with notes provided for improvements.

8 Experiment PH03: Resistivity o On Canvas, in the Content section, see the file “Laboratory Report Guideline” for information on considerations when writing a lab report. o Do not turn in the questions listed below. However, these questions can be used as a guideline for the types of things to consider when writing your report. However, do NOT directly rewrite and answer them. Questions to Consider In the graph of R vs. l, is the relationship linear? Does the trendline pass (approximately) through the origin? What does this tell you about the relationship between resistance and length? Examine your data from the Length Dependence procedure. Did the resistance vary significantly with length? (Length here is the distance between the connections on the wire not the overall length of the wire.) Did the resistivity vary with length? Theoretically, should the resistance have varied with length? Theoretically, should the resistivity have varied with length? Do you get about the same resistivity value for each diameter of brass wire? Why does the resistivity approximately stay the same even though the wire’s diameter changes? In the graph of R vs D, is the relationship linear? Try an inverse curve fit. Try an inverse-square curve fit. Which fits better? What does this tell you about how resistance R is related to D? Paying close attention to the R vs. D data, does the resistance vary significantly with cross-sectional area? Did the resistivity vary with cross-sectional area? Theoretically, should the resistance have varied with cross-sectional area? Theoretically, should the resistivity have varied with cross-sectional area? As current passes through a wire it will heat up. As the wire heats, its resistivity increases (we will test this in experiment PH04 part B). How would this increase in resistivity effect the following quantities: the resistance of the wire, the voltage drop across the wire, and the current passing through the wire.