Small current sources are frequently used in many electronic circuits and integrated circuits; however, they are rarely used in industrial power circuits. They are also commonly used to drive light emitting diodes (LEDs). The maximum power theorem states that the maximum power will be delivered to a load when the load resistance is equal to the Thévenin resistance. This is the basis for selecting the resistance of a speaker system for a stereo. This assures that in the design stereo systems that maximize the power will be delivered from the amplifier to the speakers. PROCEDURE Part 1 Measure the resistor values R1, R2, and R3 the myDAQ multimeter. Figure 5-2. Do not use the color code to determine the resistance value. Choose three resistors that are reasonably close in value. Do not pick, for example, 10K, 300, and 100 ohms. You should realize by now that the resistor color codes are not an accurate way to determine resistor values. Construct the circuit shown in Figure 5-2 on the protoboard. Using a multimeter, measure the voltage between points “a” and “b” with NO LOAD connected. Record your measurement in column 6. This is VThevenin by definition. Remove the 10 Vdc power source and connect a jumper between “1” and “2.” This is the same as shorting the supply voltage mathematically. Now measure the resistance between “a” and “b” using your multimeter. By definition this is RThevenin. Record this value in Table 5-1. Column 1. Calculate RThevenin by combining the series and parallel resistors with the source disabled (shorted). Record this value in Table 5-1. Column 2. Now compare your measured value and calculated values in order to perform an error analysis. Enter this value in column 3. Figure 5-2. Linear resistor network. We are now going to determine RThevenin in another way. Connect a load to the circuit as shown in Figure 5-1. For best results the load resistance should be in the same range as your estimated RThevenin. Now measure the output voltage between “a” and “b” in order to make the appropriate calculation. Divide this voltage by Rload. This will be the current going through the Thévenin equivalent circuit.
Simply apply Ohm’s Law to find rThevenin.. How does this RThevenin compare to the value determined in column 2. Calculate % difference between columns 2 and 4 then enter this value in Table 5-1, column 5. Table 5-1. Measured and calculated data. 1 2 3 4 5 6 7 8 Measured with sources removed (shorted) Calculated 1 with sources removed % between measured and Calculated 2 using Ohm’s Law and Rload % between calculated 1 and calculated 2 Vab (This is Vth) Vab % Error Thévenin voltage measured and Part 2 Now construct the network shown in Figure 5-2, but replace Rload with a potentiometer connected between “a” and “b.” The equivalent circuit is shown in Figure 5-3. We will now determine rthevenin using the potentiometer. Measure the voltage between “a” and “b” as the potentiometer is adjusted. Adjust the potentiometer wiper until the voltmeter reads VThevenin/2 (Column 6 Table 5-1) NOT Vsource/2. The potentiometer is now set at the maximum power load which is equal to rthevenin Calculate the maximum power delivered to the load using equation (5-2). Measure the value of the potentiometer and determine how close it is to the value of rthevenin determined in part 1, step 3. (5-2) Figure 5-3. Maximum power network. Now that this is the load for maximum power. Prove it by measuring the voltage Vab across the potentiometer after the potentiometer is rotated 1 turn CW. Then measure the potentiometer resistance at this position. Calculate the power delivered to the potentiometer using equation (5-3).