Electronics lab experiment in circuit, Lab Reports of Electronics

Download Electronics lab experiment in circuit and more Lab Reports Electronics in PDF only on Docsity! University of the East- Caloocan College of Engineering Department of Electronics Engineering Final Experiment: Millman’s Theorem Submitted by: Kristine Andrea B. Arcega Submitted to: Engr. Sinforoso Cimatu Jr. Subject and Section: NEE2102- 1EC Experiment No. 9 Millman’s Theorem I. Objectives ¢ 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. ll. Theory 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. Ill. — Introduction 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 V; or the combined voltages in each Vi ,V¥2 V3 V; Va ,V2 V3 Yn . . 1 Ry, Rz R3"R, trials using the formulas Rg = =—z—z7— os and V; = we =a RyRy Rs "Rn Ry TR, Rs” Rn 9. Show the computations made below the table. Vv. SCHEMATIC DIAGRAM Figure 1.1. Schematic representation of the circuit Vi. WIRING CIRCUIT Figure 1.2. Simulation of Trial 1 Figure 1.3. Trial 5 and last simulation Vil. DATA AND COMPUTATIONS Table 1.1 [TRIAL ADDED Ve Ve Ro COMPONENT | (MEASURED) | (COMPUTED) | (COMPUTED) 1 - 4.615V 4.615V 1.846Q 2 V3= 15V 9.231V 9.231V 1.8460 3 R4= 10 7.792V 7.792V 1.5580 4 V4= 20 10.909V 10.909V 1.5580 5 R5= 120 9.655V 9.655V 1.3790 Millman’s Theorem Parameters Computations for V; TRIAL 1 TRIAL 2 TRIAL 3 5, 10 5, 15, 10 5, 15, 10 m= AS v= 48 m= ASS atots8 ators ar ee) y= 25 5 5 F 0.5417 B 0.5417 F 0.6417 V_ = 4.6150 Vp = 9.230 Vp = 7.792V TRIAL 4 TRIAL 5 5,15, 10, 20 5,15, 10, 20 y,- fot et v,-41 6+ 3+ 1,1,1,1 ®“7T /1,1,1,1 4+ 6+ 8+ T0 atotetiot i 7 v 7 F 0.6417 B 0.725 Vg = 10.909V Vi = 9.655V Here, the voltage yet again increase as the source with high voltage was placed and then again slightly decrease at the 5" 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 V; but when a resistance is added, there’s not much of a decrease happens to the V;. 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. 12 10 a 6 J VE RO 2 a ——__ =_— = 0 1 2 3 4 5 TRIAL Graphic representation of data from the table As for the resistance Ro, 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 Rg 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 Ro 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. CONCLUSION As | finish through this experiment, | 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 Millman’s theorem is used in obtaining the total voltage of complex circuits that is in parallel or can be redrawn to become parallel which contains multiple sources. YiyYe4¥s, Vn Millman’s theorem uses the formula V; = 2333 Ry" RzR3 Rn in which the Vs represent 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 without using mesh or nodal analysis which are commonly used in analyzing complex circuits. 3. In this experiment, when a source is added the total voltage increases but when a resistance is added, the total voltage decreases a little like in any other circuit. 4. A circuit that uses Millman’s theorem is no different to circuits used in Thevenin and Norton. With this, the Ro for a circuit which uses Millman’s theorem is similar to that of getting the total resistance in an ordinary parallel circuit or that of the looking-back resistance of a Thevenin circuit. It also uses the formula Ro = 1 TW Ri "Ra *R3"Rn X. REFERENCES e Electrical4U (Oct. 25, 2020). Millman’s Theorem. Retrieved from https //www.electrical4u.com/millman-theorem/ e Kutraphaldt, T. (1996). Millman’s Theorem. Retrieved from https ://www.allaboutcircuits.com/textbook/direct-current/chpt-10/millmans- theorem/ e N.a (n.d) Millman’s Theorem. Retrieved from https://circuitglobe.com/what- is-millmans-theorem.html