ELECTRICAL RESISTANCE AND RESISTIVITY



Give Up! Resistance is Futile!Chris Peoples, Physics Teacher Sunny Hills High School, Fullerton California 1.0 Introduction Aim/Objective In this laboratory you will investigate how the transmission of electrical energy is affected by the properties of the material that conducts it. Background information The transmission of electrons through a conductor is a complicated process to understand at the atomic level. However, we can investigate how different types of conductors affect the transmission of electrical energy. Different metals transmit electricity with different levels of effectiveness. Silver, copper and aluminum are the best electrical conductors, while chromium, iron and nickel are significantly less effective. In this laboratory exercise, we will use different grades of pencil lead to serve as our conductors. The pencil leads used are 2 mm diameter drafting leads of varying hardness. The lead hardness depends on the corresponding mixture of graphite and clay used; note that pencil leads do not contain any lead metal in their composition. Drafting leads are rated on a hardness scale ranging from 9B for the softest lead to 9H for the hardest. Harder leads are used because they will maintain a finer point longer for use while drawing. The intermediate lead grade of HB is equivalent to the No. 2 grade of lead used in common wood pencils and mechanical pencils. 3591128532028The electrical conductivity of a substance is the inverse of its resistance, and we will compute and use the resistance values instead since this is more common and intuitive. A conductor’s resistance (R; units are Ω) depends on three factors: the length (l), the cross sectional area (A), and the resistivity (ρ; units are Ωm). The last of these parameters is material specific, while the first two are affected by the geometry of the conductor. R= ll AThe relationship between these parameters is given by the following equation: A pencil lead is a long cylinder, and the cross sectional area is given by A=πr2. 2.0 Equipment and Materials DC Power Supply, Knife Switch, Alligator clip leads, Voltmeter, Ammeter, 2 mm diameter graphite drafting pencil leads (2B, 1H, 3H, and 9H grades recommended) 3.0 Experiment Equipment Set-up 3.1) prepare a data table for collecting the following information: Voltage, Current, and Clip Separation Distance for the four different grades of pencil lead. Plan for at least 10 measurements for each type of pencil lead. (Data and Observations section of Report) 3.2) Assemble the basic electric circuit shown in the diagram, leaving the knife switch in the OPEN POSITION (BLADE UP). Do not plug in or turn on the power supply until your instructor has checked your circuit. Black alligator clips Low Voltage Power Supply Ammeter Voltmeter Pencil lead Red alligator clips Low Voltage Power Supply Ammeter Voltmeter Pencil lead Red alligator clips 4.0 Experiment Process / Data Acquisition 4.1) Connect the clip leads from the ammeter and knife switch to the ends of the pencil lead under investigation. Measure and record the separation distance between the clip leads. 4.2) Plug in or turn on the power supply. Close the knife switch to the circuit and then record the voltage and current values after the volt meter and ammeter displays have stabilized. DO NOT LEAVE THE SWITCH CLOSED FOR MORE THAN 20 SECONDS. Note in your Data and Observations any physical changes that occur with the pencil lead. 4.3) Open the Knife switch, move the two clip leads together so that they are now approximately 1 cm closer to each other. Measure and record the separation distance between the clip leads. 4.4) Close the knife switch, and again measure and record the voltage and current values as you did in step 4.2. 4.5) Repeat steps 4.3 and 4.4 until the clip leads are approximately 1 cm apart. You should have at least 10 measurements. 4.6) Replace the pencil lead with another lead of different grade and repeat the above data acquisition process. Collect data for 3 other different grades of pencil lead. 5.0 Preliminary Data Analysis: 5.1) Determine if the pencil leads follow Ohmic behavior by preparing a graph of Voltage (V) versus Current (I). Plot the data for each of the different grades of pencil lead (using different symbols for each lead type) on the same graph. 5.2) Using the plotted data, determine which grades of pencil lead exhibit a linear relationship between the voltage and the current. Draw or “computer-fit” the best straight line that fits the observed data. If you are using a graphing calculator or spreadsheet to fit your data, please include the equation of the line fit and its correlation coefficient (R2). 5.3) For each of the different pencil leads, compute and record in a new data table (Results) the resistance (R, using Ohm’s law) and the separation distance between the clip leads. 5.4) Using this data prepare of graph of Resistance versus Separation Distance for each of the different grades of pencil lead. Again, use different symbols for each pencil lead type. 5.5) Again using the above plotted data, determine the nature of the relationship that exists between resistance and the length of the pencil lead for each of the pencil lead types. 6.0 Secondary Data Analysis 6.1) Using the your newly computed resistance and separation data, compute the resistivity (ρ) for each measurement for each pencil lead type. Record this information in an appropriate data table. Recall the diameter of the pencil lead is 2 mm, check your units in the calculations for internal consistency. 6.2) Compute a mean resistivity value (ρmean) for each pencil lead type, using the results from the above step. Record this information in an appropriate table. 6.3) Next compute the slope for each of the lines plotted in steps 5.4 and 5.5 (i.e., the resistance per unit length). And then multiply this slope by the pencil lead’s crosssectional area to obtain the slope resistivity (ρslope). Record these results next to those from the previous step. 7.0 Analysis and Conclusions Interpretation and Analysis Discuss the significance of the following items in this laboratory exercise: the voltage versus current graphs (ohmic versus non-ohmic behavior), the resistance versus separation distance graphs, and the comparative resistivities of the different grades of pencil lead. the difference between the mean resistivity value (ρmean) and the value (ρslope) determined using the slope of the lines plotted on the resistance versus separation distance graph. Limitations and Weaknesses Evaluate you procedure and data to determine what limitations and weaknesses are present. What factor(s) could have negatively affected the outcome of this experiment? (Hint: why is the switch closed for only a short duration? Your observations should provide a clue.) Suggestions for Improvement Discuss how you would change or alter this procedure so as to improve the data quality. Also discuss how you might change or alter this laboratory exercise to expand upon our understanding of the variables under investigation. ................
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