Thevenin Lab

The purpose of this lab was to create a complicated circuit experimentally and to confirm that the simpler equivalent Thevenin circuit is equivalent to this circuit.

Figure 6a

Figure 6b

Given values of Rc1=100 ohms, Rc2=Rc3=39 ohms, Rl1=680 ohms, Vs1=Vs2=9V, and Vload2,min=8V, we were asked to determine the smallest possible value of Rl2, and to determine the open circuit voltage and short circuit current for Vload2.

Before beginning the lab, we were asked to compute the open-circuit voltage for Figure 6a. Using nodal analysis, we came up with a value of 8.64 ohms. Next we were asked to compute Vy and the short circuit current for Figure 6b. After using nodal analysis and setting up a system of equations we came up with values of 5.11 V and 0.1311 A for Vy and the short-circuit current, respectively. We were asked to verify our results by computing Rth, which was determined to be 65.95 ohms. 

Figure 3

Next we were asked to compute the minimum resistance for Rl,2 using a number of methos such as through a voltage divider, the short-current using Ohm's law, and through the open circuit voltage through inspection. Using all three methods, we came with a value of Rl,2min= 5.28 ohms each time. 

Next, we were asked to devise the experiment into two phases as listed in the above photo. Notice that in Stage 1 we were asked to model the simplified Thevenin equivalent, whereas in Stage 2 we were required to construct the original complex circuit. Before setting up the breadboard for the Thevenin equivalent, we were required to make measurements of the resistors using a multimeter and to compare these values with their nominal values. The following photo shows these values.

The values were indeed close enough to their nominal values. Next, we were required to set up the breadboard for the Thevenin equivalents. After receiving verification from our instructor, we went ahead and performed this part of the experiment. This was the power supply this we used for this experiment. It was rated at 1W.

As you can see, our measured values for Rl2,min, and Rl2=inf came very close to their theoretical values. Hence, we were satisfied with how successful we were with the Phase 1 of this experiment. Notice the low percent errors in each case.

We were now required to begin preparing for Phase 2 of the experiment, which we mentioned earlier was the complicated original circuit. Again, we were asked to measure the values of our components and to compare them to their nominal values. And once again the measured values were measured to be very close to their nominal values. A power supply rated at 1W was used.

Then we were required to set up the breadboard for this phase of the experiment. After getting verification from our instructor, we went ahead and performed the experiment. Here were our results for the measured voltages for Rl2,min and Rl2,inf as compared to their theoretical values. Our percent errors with slightly higher than those for the Thevenin equivalent circuit, but we were satisfied with our results because 6.43% is still a low percent error.

Now we were required to answer some analysis questions. Before disassembling the circuit, we were asked to compute the value of the maximum  power delivered to the load resistance Rl2. We did so by using the formula Pmax=(Vl2^2)/4Rth= 0.287W.

Now we were required to establish this maximum power in the laboratory by setting Rl2 equal to 0.5Rth, Rth, and 2Rth, measuring the voltage across each of these loads and calculating the corresponding power delivered to each of these loads. Our instructor wanted us to show our work for the power delivered to the first load, which is shown above the table in the photo below. Also notice how close the experimental value of 0.279W is to the theoretical value of 0.287W. This low percent error indeed confirmed our results.

This lab assignment was now over and we were asked to disassemble the lab setup. This lab assignment really helped me to reinforce the concept of Thevenin equivalents. More importantly, I felt accomplished for the low percent errors that we measured for all phases of this lab assignment. Hopefully this will carry into future lab assignments.