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Experiment about Millman's Theorem
Typology: Lab Reports
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The objective of this experiment is to be familiarize with an easier way in combining multiple sources in a parallel circuit by using Millman’s Theorem. To be able to identify how Millman’s Theorem works and how to get the values using measurement and computations.
The Millman’s Theorem states that, when a number of voltage sources are in parallel having internal resistance respectively, the component’s arrangement can be replace by a single equivalent voltage source V in series with an equivalent series resistance R. The theorem is said to only be applicable given that only one resistor is connected to each voltage or current source in the parallel circuit. The said theorem is known to be very useful when it comes to simplifying complex circuits.
The Millman’s Theorem, also known as the Parallel Generator Theorem is a DC network analysis theorem developed and proposed by the famous electrical engineer
also the values of the Ro or the looking-back resistance at each trial as well as the computed values of the or the combined voltages in each trials using the formulas and.
Figure 1.1. Schematic representation of the circuit
Table 1. TRIAL ADDED COMPONENT (MEASURED) (COMPUTED) (COMPUTED) 1 - 4.615V 4.615V 1.846Ω 2 V3= 15V 9.231V 9.231V 1.846Ω 3 R4= 10 7.792V 7.792V 1.558Ω 4 V4= 20 10.909V 10.909V 1.558Ω 5 R5= 12Ω 9.655V 9.655V 1.379Ω
MIllman’s Theorem Parameters
Computations for
Computations for
For this experiment which aims to show the use of Millman’s theorem in obtaining the voltage throughout a complex circuit that contains multiple sources, the dependent variable that is obtained were the which can be get with regards to the resistance connected to the circuit as well. For the dependent variables, the values for were taken without other components from the circuit aside from all the resistors. The computed values for the table were taken using the formulas and. For this experiment, I add components simultaneously. I add sources first befor I add another resistance and so on. The components I add to the circuit, as seen from the table and the wiring circuit is increasing in values for both the sources and the resistors.
𝑅𝑂 4 6 8 𝑅𝑂 .846Ω
𝑅𝑂 4 6 8 0 𝑅𝑂 .558Ω
𝑅𝑂 4 6 8 0 𝑅𝑂 .558Ω
𝑅𝑂 4 6 8 0 2
𝑅𝑂 .379Ω
Here, the voltage yet again increase as the source with high voltage was placed and then again slightly decrease at the 5 th^ trial in which we add another resistance parallel to the circuit. From the set of data, we can see that when the voltage is added, there is a drastic increase in the but when a resistance is added, there’s not much of a decrease happens to the. The circuit can go on more than this so long that the components that are added are placed or can be placed to the circuit in parallel. Either way, the results will be the same. If a resistance is added, the value of the combined voltages as per using Millman’s theorem will decrease and if a source is added it will increase as illustrated at the graph below.
Graphic representation of data from the table
0
2
4
6
8
10
12
1 2 3 4 5
VE RO
As for the resistance , it is noticeable that so long as another resistance has been added to the circuit, the overall resistance of the circuit decreases. In all of the trials on the table and also as based on the representation on the graph above some of the trials have the same like that of trial 1 and 2 as well as the trials 3 and 4. They are similar because for a trial that a source is added, no resistance is added together with it and so it retains. The formula used to get the is just like that of getting the total resistance in a normal parallel circuit or that of getting the looking-back resistance of a Thevenin circuit. After all, the only difference of this experiment to that of a normal parallel circuit is that it has more than one source connected and for the Thevenin, it is easier to use because it does not require any KVL.
IX. CONCLUSION As I finish through this experiment, I have learned a lot of things about the Millman’s theorem and its use in solving a complex circuit. To summarize these learning, here stated are my findings and conclusion:
the voltages connected to the circuit and the Rs are the resistances. Millman’s theorem makes it easier to obtain the total voltage of a complex parallel circuit
