Maximum Power Lab

The purpose of this lab was to verify the Maximum Power Transfer Theorem and to use this theorem to determine the Thevenin resistance. There were two parts for this lab assignment. To begin Part A, we were told to obtain a 5.6 kohm resistor as well as a 10kohm potentiometer. As usual, we were instructed to measure and record the value of the resistor with a potentiometer. We measured an astonishingly close value of 5.62kohm.

Next, we had to construct our circuit on the breadboard as specified in Figure 1. We measured our power supply to be 4.54 V. It should be noted that this value and that of the 5.6 kohm resistor were to be used for our theoretical calculations later. We used a multimeter to guide us into obtaining an accurate measurement. Now our job was to vary the potentiometer's resistance in small increments from it's minimum resistance value to its maximum resistance value and then measure it's voltage and resistance at each increment. The table is listed in the photo below. The power at each increment was computed manually with a calculator.

We were now instructed to answer the analysis questions for Part A. Setting the potentiometer's resistance equal to the Rth=5.6kohm, with the help of the voltage divider rule, we computed the theoretical value of the potentiometer to be 2.25 V. It's corresponding measurement for power, which is the theoretical maximum power delivered to the load was computed to be 0.226 W. Next we were instructed to create two graphs, one depicting potentiometer voltage vs. power and potentiometer vs. resistance . They are listed in the photos below.

Although not perfect, both graphs can be approximated to be linear. Since we determined that Vth= 2.25 V, a quick glance at the potentiometer voltage vs. resistor graph shows that the value of the potentiometer resistance occurs during a maximum power transfer at approximately 11.0 ohms. The theoretical resistance during maximum power transfer should be about R=(12.08+10.77)/2= 11.42 ohms. 

Now we were to begin Part B of this experiment. 

We were instructed to clear the breadboard from Part A and to construct the circuit pictured in Figure 2.  As usual, we used a digital multimeter to make sure that the resistance of these 10 kohm resistors were indeed close enough to their rated values. We recorded values of 9.85 kohm, 9.66 kohm, 9.76 kohm, 9.86 kohm, and 9.79 kohm, for resistors R1, R2, R3, R4, and R5, respectively. We adjusted the two voltage sources to values of 4.5 V and 9 V as close as possible. Using a multimeter we recorded values of 4.54 V and 9.05 V, respectively. We then placed all the resistors into their appropriate positions.

We were instructed to create an analysis using LabPro, but the entire class experienced an unfortunate technical difficulty with the software. So we were unable to do the Part 3 analysis questions. 

To wraps things up, the was perhaps the most frustrating lab assignment so far this semester, due to the LabPro software not working correctly. However, one benefit from this lab assignment is that it helped me to better understand the Maximum Power Transfer Theorem much better.