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OHM'S LAW PURPOSE: To measure resistance by application of Ohm's law and to verify the equations for series and parallel combinations of resistors. APPARATUS: Ohm's Law Board Assorted wire leads Variable Regulated Power Supply Digital Voltmeter and Digital Ammeter METHOD: Three unknown resistances are measured by taking a series of voltage and current readings for each. Since Ohm's law states V = IR , a graph of V versus I for each resistor will have a slope R. Therefore each resistance can be determined from the graph. The resistance of the three resistors connected in series is also found by taking a sequence of voltage-current readings. The resistance from the slope of the graph may then be compared with the value calculated from the series resistance formula. Then the three resistors are connected in parallel and the resistance of that combination is measured in the same manner. The result can be compared to the value calculated from the formula for parallel resistors. Finally, a series-parallel combination of the three resistors is found by graphing V versus I and the result compared to that from formula. PROCEDURE: HAVE AN INSTRUCTOR CHECK ALL CIRCUITS BEFORE TURNING ON ANY POWER SUPPLY 1. Individual resistors a. Connect the resistor marked R1 in series with the dc power supply and ammeter as in Figure 1. Power Supply + V + + R1 Figure 1 I b. 2. Connect the voltmeter across the resistor. Turn on both digital meters. c. The current control on the power supply should be near, but not at its maximum, the voltage control should be at its minimum. Note that with no applied voltage, the current reads zero. Record these two values. Turn on the power supply and adjust it until the voltmeter reading is 2 volts. Record this voltage and its corresponding current reading. d. Take additional readings at 4, 6, 8, and 10 volts. e. Repeat steps 1a through 1d with each of the other two resistors. (R2 and R3) f. Turn off the digital meters turn the voltage to zero, then turn off the power supply. Resistors in series a. Connect the three resistors in series with each other and with the dc power supply and the ammeter as in Figure 2. Power Supply + V + + R1 R2 R 3 Figure 2 b. c. d. 3. Connect the voltmeter so that it is across all three resistors as shown. Turn on both digital meters. Turn on the power supply and take readings as before, but with voltages of 0, 3, 6, 9 and 12 volts. Turn off the digital meters turn the voltage to zero, then turn off the power supply. Resistors in parallel a. Connect the three resistors in parallel, and the combination in series with the power supply and ammeter as shown in Figure 3. I Power Supply + + + V I R2 R3 b. c. d. 4. Figure 3 Connect the voltmeter across the parallel combination of resistors. Turn on both digital meters. Turn on the power supply and take readings as before for applied voltages of 0, 2, 4, 6 and 8 volts. Turn off the digital meters turn the voltage to zero, then turn off the power supply. Series-parallel combination a. Connect R2 and R3 in parallel and that combination in series with R1, the power supply and the ammeter as shown in figure 4. + Power Supply V + + R I 2 R1 R3 b. c. d. Figure 4 Connect the voltmeter across the series-parallel combination of resistors as shown. Turn on both digital meters. Again make measurements for voltage and current with applied voltages of 0, 3, 6, 9 and 12 volts. Turn the voltage to zero, then turn off the power supply and disconnect the circuit. Make sure that all digital meters are turned off. 1. 2. 3. 4. 5. ANALYSIS: Use Graphical Analysis to produce a graph of voltage (volts) versus current (amperes) for each of the three resistors. These graphs should be done on the same sheet do this by entering your data for R1, then choose New Data Set from the Data menu and enter the data for R2 etc. From these graphs determine values for R1, R2 and R3. Use Graphical Analysis to produce graphs on the same sheet of voltage versus current for the series, parallel and series-parallel combination. From these graphs determine the equivalent resistance for each case. Using resistance values found in step 1, compute a theoretical value for the series equivalent resistance using: R = R1 + R2 + R3 Equation 1 Compare your experimental value to that computed from Equation 1. Using resistance values found in step 1, compute a theoretical value for the parallel equivalent resistance using: 1 1 1 1 = + + Equation 2 R R1 R2 R3 Compare your experimental value to that computed from Equation 2. Using resistance values found in step 1, compute a theoretical value for the series-parallel equivalent resistance using: R R R = R1 + 2 3 Equation 3 R2 + R3 Compare your experimental value to that computed from Equation 3.