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GSCI 164 Learn Through Teach James Madison University Laboratory #5 Ohm’s Law Spring 2006, Section 0405 Objectives Learn to use basic electronic instrumentation. Verify Ohm’s law for a resistor. Review spreadsheet skills. Learn how to use linear regression analysis to test and model experimental data. Theory According to Ohm’s law, V = IR, the voltage across a resistor is proportional to the current through the resistor. The constant of proportionality, R, is called the resistance. For example, Ohm’s law applies to a piece of metal (e.g., a wire) as long as the voltage and current are not so large that the metal heats appreciably. The resistance of a wire or other sample is given by R = L/A, where L is the sample length, A is its cross-sectional area, and is a property of the material, called the resistivity (see Figure 1). Figure 1. Electric resistance of a wire If is in ohm-meters, L is in meters and A is in meters2, then R is in ohms. Copper and aluminum have very low resistivities (~2108 -m) and are used to fabricate wire having negligible resistance. Other materials, like carbon and “nichrome”, a nickel- chromium alloy, have resistivities 100 to 2000 times as large and are used to make heating elements and resistors for electronic circuits. Many devices do not obey Ohm’s law. For example, as the current through a light bulb increases, it gets hotter and its characteristics change – its “effective resistance” increases. This happens largely because the filament is so fine, i.e., A in Figure 1, is very small. Other devices, such as diodes, have complex current flow mechanisms that result in behavior that violates Ohm’s law. Such devices are said to be “non-ohmic”. Materials Power supply (PS) Digital multimeters (DMM) Resistors (R) Deliverables A laboratory report is required. The report should contain the items and information requested in the Data Analysis and Report section. You will be graded on completeness, neatness, organization, and the reasonableness of your answers to questions. You will be working in teams of four or five. Each team will turn in a single report. Procedure 1. Team up with three or four other people. This will speed up the data collection and recording. 2. Set up your experiment as show in the diagram in Figure 2, with all the instruments off. Note: To measure the current flow (I) through the resistor, you should use the “mA” input of DMM #1, which is connected between the power supply and the resistor, i.e., “in series with the resistor.” To measure the voltage (V) across the resistor, you should use the “V” input of DMM #2, which is connected across the resistor, i.e., “in parallel with the resistor”. If you are at all uncertain about your set up, please ask your instructor for assistance before proceeding. 3. Turn on the DMM that is to be used to measure current (DMM #1) and set it to the 40mA DC scale. 4. Turn on the DMM that is to be used to measure voltage (DMM #2) and set it to the 40V DC scale. 5. Make sure that the power supply output control is set at its minimum (counterclockwise) and turn on the power supply. 6. Increase the power supply output so that the voltage across the resistor increases in approximately 2V increments and record the voltage across the resistor and the corresponding current through it at each step, generating a table of values of V and I up to 20V. 7. Reduce the PS output to zero and reverse the wires connected to the PS. In other words, remove the wire from the + terminal and connect it to the – terminal and vice versa. 8. Repeat step 6, noting the polarities of the measured V and I. 9. Make sure that your data vary in a smooth and consistent fashion. For each pair of corresponding V and I data, if you divide V by I, you will get a value of resistance, R. If V is in volts and I is in amperes then R is in ohms. Check several data pairs. How consistent are they? You will be analyzing these data in more detail later. 10. Note: Examine the diagram in Figure 2. In this experiment, we assume that all of the current that goes through the DMM used to measure current (#1) then goes through the resistor. In other words, we assume that no current goes through the DMM used to measure voltage (#2). This assumption is very good for a “good” DMM and for a “reasonable” (i.e., not too high) value of R. Figure 2. Resistor Characterization 11. Make sure that the PS is off. Leave DMM #2 connected to the resistor and remove the other connections from the resistor. Use the or R input of DMM #2 and set the DMM to a scale that allows you to read the resistance directly. Record this value. Data Analysis and Report Your report should include the following items and answers to the following questions. You should generate your tables and graphs using an Excel spreadsheet. 1. Prepare a table of your V and I data for the resistor. Columns should be labeled and units should be specified for each column. 2. Prepare a graph of V versus I for the resistor. V should be plotted on the vertical axis and I should be plotted on the horizontal axis. Plot your data as points only, with no connecting lines, and plot your data for both polarities on the same set of axes. Both axes should have labels and the appropriate units should also be specified. 3. The data that you acquired from the resistor will be used to introduce linear regression analysis. When you perform an experiment and plot your data, the results of a linear regression analysis tell you how well your graph of y versus x can be modeled by a straight line, y = mx + b. Moreover, the analysis will give you the values of the slope, m, and the y-intercept, b, for the straight line that describes your data best. When your tables and graphs are prepared in an Excel spreadsheet, this analysis can be done easily. The quantities that tell you how well the straight line, y = mx + b describes or “fits” your data are the correlation coefficient, r and the coefficient of determination, R2. If the slope, m, is positive, then r is positive. If m is negative, than r is negative. Obviously R2 is always positive. The closer that |r| and R2 are to 1, the better the straight line fits your data. Perform a linear regression analysis (least squares fit) of the resistor data and plot the linear regression line on the same graph axes as you used for Step 2 of this section. Plot the regression line as a line only, with no data points. There are several ways to do this. The easiest is as follows, using Microsoft Excel. Go to your graph of V versus I that you created in Step 2. Double-click on the graph and right- click on one of the data points. Choose “Insert Trendline…” and from the “Type” menu, choose “Linear”. From the “Options” menu, choose to “Display Equation on Chart” and choose to “Display R-squared Value on Chart”. You can also “Forecast” the line forward and backward to see where it intersects the axes. 4. The results of your analysis will tell you how well your graph of voltage versus current can be modeled by a straight line, y = mx + b (i.e., voltage = slopecurrent + b). You should give the values of slope, y-intercept, and the coefficient of determination, R2. Also give the units of slope and y-intercept. 5. Compare m with your results in steps 9 and 11 of the (resistor characteristic) measurement procedure. 6. Prepare a table of your V and I data for the diode. Remember labels and units. Laboratory #5 Data Sheet Ohm’s Law Date: ________________ The numbers of the questions below correspond to the numbers in the Data Analysis and Report section of the lab procedure. 4. Fill in the values in the table below: Quantity Value Units slope _________ _____ y-intercept _________ _____ coefficient of determination, R2 _________ ******** 5. Compare m with your results in steps 9 and 11 of the Resistor Characteristics measurement procedure using the table below: Quantity Value Units m from linear regression _________ _____ Typical result from step 9 _________ _____ Result from step 11 _________ _____ Comments: GSCI 164: Learn Through Teach James Madison University Laboratory #5 Ohm’s Law Spring 2006, Section 0405 Instructor: Dr. Tony D. Chen Group Members: ________________________ _________________________ ________________________ _________________________ ________________________ _________________________ Cover Sheet _____/10 Introduction _____/10 Data Sheet _____/20 Table and Graph _____/50 Conclusions _____/10 Total _____/100