Ph 122 July 27, 2006 Ohm's Law http://www.physics.sfsu.edu/~manuals/ph122/ I. Theory In this lab we will make detailed measurements on one resistor to see if it obeys Ohm's law. We will also verify the formulae for combining resistors in series and parallel, which indirectly tests Ohm s law. Ohm's law describes the behavior of a resistor in the thermal range where the voltage across the resistor is proportional to the current flowing through the resistor. Ohm's law is usually expressed as =IR where is the potential difference measured across the resistor in volts, I is the current through the resistor measured in amps, and R is the resistance of the resistor measured in ohms. Current flowing in a circuit divides at the junctions of wires, that is, where two or more wires connect in the circuit. oltage drops in a circuit occur only across circuit elements. We will observe how the voltage differences are different in a circuit with resistors in series compared to a circuit with resistors in parallel. Additionally, we will observe how the current is different in a circuit with resistors in series compared to a circuit with resistors in parallel. II. Experimental Procedure = IR Equation 1: Ohm s Law A. Setting up a basic circuit. Remove a resistor from the breadboard, and using the ohmmeter function of your multimeter measure its resistance; repeat this for each resistor on the board. Record your results in your lab notebook. The resistors should measure R 1 470 Ω, R 2 1,000 Ω, and R 3 3,000 Ω. The resistors are each rated by the manufacturer to have measured resistance values within 5% of the given values. Is this rating valid for each of your resistors? Draw a circuit diagram similar to figure 1a in your lab book, showing the 1 kω resistor connected to the power supply. Then connect the circuit. Turn on your power supply and set it to about 10. Draw a circuit diagram in your lab book showing how to connect the voltmeter so as to measure the voltage across the resistor. (See figure 1b.) Turn the multimeter to the " DC voltage scale, and connect the circuit. Record the voltage in your lab notebook. R R (a) (b) (c) Figure 1. (a) Resistor circuit. (b) Placement of volt-meter. (c) Placement of ammeter. A R Ohm - 1
If it doesn t seem reasonable, have your instructor check your connections. Turn the power supply off, to minimize the risk of blowing the fuse in the ammeter. We will now connect the ammeter in series with the resistor. First draw a circuit diagram in your lab book showing how to do this, based on figure 1c. Turn the multimeter to the "400 ma" setting, and connect up the circuit. Note that in order to connect the ammeter, you will need to "break" the circuit at the resistor and connect the ammeter into the circuit so that the current flows through it. Check your circuit carefully, turn on the power supply and record the current. If the result seems unreasonable, have your instructor check your connections. Use Ohm s law and your measured values of the voltage across the resistor and the current through the resistor to calculate its resistance R. Q1. Compare the calculated value of R with the measured value (% discrepancy)? What are the sources of error? Do your sources of error account for the discrepancy? B. Detailed Measurements on a Single Resistor. Let's see if the 470 Ω resistor obeys Ohm's law. You will be putting known voltages across the resistor and then measuring the current. You will then plot the results to get the value of the resistor. You will have to decide the best method to take these measurements (keep in mind the power supply display is very inaccurate, plus, you are given two multimeters). Explain the procedure you will use in your lab book and draw the appropriate circuit diagram. Setup a table in Excel to record your voltage and current measurements. Put 2.0 volts across the resistor and measure the current; record your values PRECISELY. Now take about 8 data points in the range: 2 to 16. Plot voltage (y-axis) vs. current (x-axis) on Excel. Use Excel s linest method to get the slope of this graph and the error. Use the slope to determine the resistance of your resistor (including error). For refresher about how to do this, see the first lab: Data Analysis. Write down your best experimental guess of the resistance, including error, in the standard way. Q2. Does the actual value of the resistor (as determined by the ohmmeter) fall in your range? Q3. What accounts for your error? Calculate the maximum power dissipated by your resistor (P = I 2 R = I = 2 /R). The resistor is rated for 0.5 watt of power (i.e. the resistor can dissipate up to 0.5 watt of power before it is damaged). Q4. Did you exceed the power rating, and did it do any damage? Q5. Did the resistor get hot? Why or why not? C. Resistors in Series: R R R R S = + + 1 2 3 Ohm - 2
Let's see if three resistors connected in series obey Ohm's law. Specifically, we want to test if the effective resistance, the voltage drops, and the current in our circuit agree with what we calculate using Ohm's Law. Read the following paragraph to get an understanding of what you will need to do. Then decide how you want to set up your circuit and draw a circuit diagram in your lab book before actually hooking things up. Connect R 1, R 2, and R 3 in series with the power supply as shown in circuit diagram (d). Set the power supply to give exactly 15.0. You may need to use a voltmeter to check this. Set up an ammeter on the "400 ma" setting. Connect the ammeter "upstream" from R 1 as shown in diagram (f). Use a voltmeter to measure the voltage drop separately across each of the resistors R 1, R 2, and R 3. Call these voltages 1, 2, and 3 and record them in your lab book. Record the current, I, in your lab book. Use the measured current and the voltage to calculate the total series resistance R S. Q6. Do the three separate voltage drops add up to 15? Should they? Q7. Compare R S with R 1 + R 2 + R 3 using the values you measured in part A. (i.e. is R S reasonable given your sources of error? What are the sources of error?) 1 1 1 D. Resistors in Parallel: = + RP Here, you will check the law for parallel addition of resistors by connecting the resistors in various parallel (and series-parallel) combinations, to see if prediction and measurement agree. Record all measurements and do all calculations in your lab book. 1. Two resistors in parallel. Choose two of your three resistors, and calculate a prediction for the parallel resistance that they should give. Then connect them to the ohm-meter in parallel, as shown in figure 3g, and measure their parallel resistance. Calculate the percent discrepancy between these two numbers. 2. Three resistors in parallel. Calculate the expected equivalent resistance for all three resistors connected in parallel, as shown in figure 3h. Draw the circuit, hook them up and measure the resistance. Calculate the percent discrepancy. 3. Series-parallel combination. (g) (d) (e) A (f) Figure 2. (d) Resistors in series. (e) Placement of voltmeter. (f) Placement of ammeter. Ω R 1 R 2 Ω R 1 Ω R 1 (i) Figure 3. (g) Two resistors in parallel. (h) Three resistors in parallel. (i) Series-parallel combination. (h) Ohm - 3
Now try the combination in figure 3i. As before, predict the equivalent resistance; draw the circuit; wire it up; and measure the equivalent resistance. Calculate the percent discrepancy. Q8. What are the sources of error in these measurements? Are the discrepancies you calculated reasonable given the sources of error you mentioned? Explain in detail. E. The resistor cube challenge problem. Ask your lab instructor. III. Equipment Resistors: 470 Ω, 1,000 Ω, 3,000 Ω resistors (0.5 W power) Digital multimeters (Metex M-38500) Power supply (HY30030-3) Banana-plug hookup wires: 4 short, 2 long Mini-grabbers Resistor cube for demonstration, if available (10 k on a side) I. Appendix: Resistor Color Code One of the important components in an electric circuit is the resistor. The most common kind is made from a thin carbon film. You should have some at your table. Their resistance can vary from less than one ohm to 20 million ohms or so. Each one is marked with the value of its resistance, using the resistor color code. (See Table I on the next page.) a b c d Figure 4. A color-coded resistor. Ohm - 4
There are four colored bands on a resistor. The first three colors represent numbers: a, b, and c. The value of the resistance in ohms is then given by the number: c R = abx10 Ω For example, if a=6, b=8, and c=3, R = 68 x 10 3 ohms. The fourth band indicates the precision with which the resistance is known. NOTE: you may be supplied with high-precision resistors, which have five bands, with the extra band used to give another significant figure to the resistance value. TABLE I. RESISTOR COLOR CODE color number black 0 brown 1 red 2 orange 3 yellow 4 green 5 blue 6 violet 7 gray 8 white 9 silver 10% precision gold 5% precision Ohm - 5