Equivalent Resistance Delta Wye TransformationExperiment # 4

ByJohn Phillip L. MasagcaMEE31

Basic Electrical Engineering Laboratory1st Semester 2014 - 2015Date Submitted: August 26, 2014

Abstract:As future engineers, it is crucial that we are familiar with these measurements and we also must know how to build, analyze and design systems containing electrical components. The purpose of this experiment is to make us familiar in equivalent resistance delta wye transformation. This experiment also makes us familiar in traditional Instruments and equipments such as the DMM or the Digital Multimeter. Like other types of measurements, electrical measurements are common measurements in the career of any type of engineer. Before we start we transformed the circuit into a solvable circuit using the delta wye transformation.

Introduction:In this lab, you will gain some experience using two basic electronic instruments: a DC power supply, which produces an adjustable DC voltage, and a digital multimeter, which can measure resistance and voltage. You will construct some simple & complex circuits using resistor module and make measurements to check the validity of Ohms Law and Delta Wye Transformation.

Body:Background:In many instances circuits are composed of series and parallel arrangements of resistors and loads. The procedure for solving such a circuit is to reduce the series strings and parallel branches to their equivalent resistances. The process is continued until only the final equivalent resistance remains. During this process the original circuit is reduced to an equivalent circuit. Equivalent circuits are models of actual circuits and are used to simplify circuit analysis.

For certain types of circuits, the method described above would not suffice. The delta wye and wye delta transformation technique must be used. The circuit configuration of the delta and wye circuits is shown in Figure 3.1. The delta equivalent of the wye circuit is given by the following equiations:R12 = (R1R2+R2R3+R3R1)/R3R23 = (R1R2+R2R3+R3R1)/R1R31 = (R1R2+R2R3+R3R1)/R2The wye equivalent of a delta network is given by the following equations:R1 = R12R31/(R12+R23+R31)R2 = R23R12/(R12+R23+R31)R3 = R31R23/(R12+R23+R31)

Methods (Procedures):1. Connect the circuit shown in Figure 3.2.2. Record the circuit voltage and current in the data table under circuit 1.3. Using the current and voltage, compute for the resistance of the circuit.4. Disconnect the source and measure the total resistance of the circuit with the VOM5. Using the indicated value of the resistors, calculate the total resistance.6. Connect the circuit shown in Figure 3.3. Repeat steps 2 to 5. Record these data in the table under circuit 2.Results:DATA AND RESULTSEIRt = E/IRt (VOM)Rt (calc)

Circuit 120V8.83mA2.2654k2.3k2.2654k

Circuit 220v8.36mA2.393k2.4k2.393k

Discussion:These are the following results for table 1: The voltage is 20V in table 1. We set up the resistor module and we get the Total Resistance which is Rt and we get 2.3k. Using 2.3k we get the Total Current (I) which is 8.83mA. Using what we got and using the formula V=IR we get the calculated Rt which is 2.2654k.

These are the following results for table 2: Just like table 1, we set the voltage to be 20V as well. We figured out that the electric circuit is a delta wye circuit. After getting the new electric circuit we set up the resistor module and we found out that Total resistance (Rt) is 2.4k. After which we get the total current (I) to be 8.36mA. Using what we got and using the formula V=IR we get the calculated Rt which is 2.393k.

Answers to the Problems:1. Definea.) Circuit - Anelectric circuitis a path in which electrons from a voltage or current source flow.Electriccurrent flows in a closed path called anelectric circuit. The point where those electrons enter anelectrical circuitis called the "source" of electrons.b.) Linear circuit - Alinear circuitis anelectronic circuitin which, for asinusoidalinput voltage offrequencyf, any steady-state output of the circuit (thecurrentthrough any component, or the voltagebetween any two points) is also sinusoidal with frequencyf. Note that the output need not bein phasewith the input.c.) Nonlinear circuit Acircuitinwhichthecurrentandvoltageinanyelementthatresultsfromtwosourcesofenergyactingtogetherisnotequaltothesumofthecurrentsorvoltagesthatresultfromeachofthesourcesactingalone.

d.) Bilateral circuit It is a circuit that behaves the same way if it is connected in the opposite direction. The term is typically used for components in electrical circuits. For example, a resistor behaves the same way no matter if it's connected left-to-right to right-to-left. In contrast, a diode is not a bilateral component, because it conducts current in one direction, and does not conduct in the other.

e.) Electric Network Anelectrical networkis an interconnection ofelectricalelements such as resistors, inductors, capacitors, voltage sources, current sources and switches. Anelectricalcircuit is anetworkconsisting of a closed loop, giving a return path for the current.

2. A 40 ohms resistor is in series w/ 2 resistors A and B inparallel.The resistance of A is100 ohms. The entire series-parallel circuit is connected across a 120V supply. determine (a) the resistance of the resistor B if the current drawn by this combination is 1.2 Ampere and (b) the current in resistors A and B.(a) Equivalent resistance = Re = R1+Ra*Rb/(Ra+Rb) = U/I ==>40+100*Rb/(100+Rb)=120/1.240+100*Rb/(100+Rb)=100100Rb/(100+Rb)=60Rb/(100+Rb)=0.6Rb=0.6*(100+Rb)Rb=60+0.6*Rb0.4*Rb=60Rb=150 ohms(b) Ia=Rb*I/(Ra+Rb)=150*1.2/(100+150)=0.72 AIb=I -Ia=1.2 -0.72=4.8 A3. The resistance of A, B, C are 300, 600, 1200 ohms respectively. How these resistors should be connected to get an equivalent resistance of (a) 1400 ohms (b) 700 ohms and (c) 840 ohms.a.) 1400: 1200 in series with 300 and 600 in parallelb.) 700: 300 in series with 1200 and 400 in parallelc.) 840: 600 in series with 1200 and 300 in parallelConclusions:In conclusion, engineers are viewed to be versatile and knowledgeable problem solvers who use their knowledge in problem solving and application. Therefore, as future engineers we must learn the fundamentals of every aspect and topic of every branch of engineering. In context to this, engineering students must learn the fundamentals and basics elements of electrical systems. This includes proper knowledge in measuring electrical properties and characteristics, basic analysis of circuits and basic designs of circuits.

References: 1. http://www.engineersblogsite.com/delta-to-wye-and-wye-to-delta-conversion.html