Lab 4 v5 -D-Y Conversion Theorem

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Lab 4: Delta-Wye Conversion Theorem Electric Circuits I Lab EECE 21052 Electric Circuits Laboratory LAB 4: Delta-Wye Conversion Theorem Student Name: Cessar Lechuga ____________________ Jerry Gamez Moreno 1

Lab 4: Delta-Wye Conversion Theorem Electric Circuits I Lab LAB 4: Delta-Wye Conversion Lab A. OBJECTIVES  Apply a ∆-Y conversion to a Wheatstone bridge to test the ∆-Y conversion equations  Compare measurements and calculation. Practice pSpice DC simulation  Practice resistance color code B. EQUIPMENT  HP-3631A DC Power Supply  Digital Multimeter (DMM)  Prototype Board  Device Test Leads and Cables C. PARTS  ¼ Watt Resistors: 3-110 Ω, 180 Ω, 220 Ω, 3-330 Ω  Hook-up Wires (#20 or #22 gauge solid conductor) D. BEFORE THE LAB 1) Measuring Nodal Voltages and Potential Differences At this point, you might need to realize that there are a couple of ways to properly represent DC voltages in a given electric circuit. It depends on whether you are in need of knowing an individual voltage value at a specific node in your circuit, or you need to find the potential difference between two different nodes. Individual voltages at nodes are what we call nodal voltages . Nodal voltage values are with respect to a reference point (ground) . In practice, to be able to measure nodal voltages, you will need the negative (common) probe of the voltmeter to be connected to the reference point of the circuit, and the positive probe to attach to the node from which you want to measure the nodal voltage. See Figure 1 as an example, where a nodal voltage V e is being measured at node e . It is also possible to measure the voltage potential difference across two points or nodes in a circuit. To achieve this in practice, the voltmeter’s positive terminal needs connection to the node being assumed having a higher potential, and the negative terminal needs connection to the node being assumed having a lower potential. It is also important to properly connect the meter’s probes according to how a circuit diagram is labeled. See Figure 1 below as an example. A resistor voltage V 1 is measured with the positive probe of the meter attached to the positive side label of the resistor, while the negative probe is attached to the negative side label of the same 2

Lab 4: Delta-Wye Conversion Theorem Electric Circuits I Lab resistor. Additionally, a voltage potential difference V bf is shown to be measured. Looking at the suffix “ bf ”, the first letter is “ b ”, which refers to node b in the diagram, and the second letter is “ f ”, which refers to node f in the diagram. The positive probe of the meter must connect to the first node being referenced in the suffix, in this case node b , while the negative probe of the meter must connect to the second node being referenced in this same suffix, in this case node f . Figure 1: Measurement of Nodal Voltage V e , Resistor Voltage V 1 , and Voltage Potential V bf 2) Delta-Wye (∆-Y) Conversion There are certain network configurations in which the resistors do not appear to be in either series or parallel. Under these conditions, it is necessary to convert the network in question from one form to another. The two networks to be investigated in this experiment are the delta (∆) and the wye (Y) configurations, which are presented in Figure 2, along with their respective conversion equations. What does it mean the equivalency of delta star circuits? It means that measurements made from the power source will not be able to distinguish the circuits’s differences. It is like being enclosed inside a box with three external terminals 3

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Lab 4: Delta-Wye Conversion Theorem Electric Circuits I Lab Figure 2: The ∆-Y Configurations and Conversion Equations Special Cases: 1. If R A = R B = R C , then we have a balanced Delta connection, and therefore: R Y = R ∆ 3 2. If R 1 = R 2 = R 3 , then we have a balanced Wye connection, and therefore: R ∆ = 3 R Y E. IN THE LAB 4

Lab 4: Delta-Wye Conversion Theorem Electric Circuits I Lab 1) Delta-Wye Conversion (a) First measure the resistors. Fill out next paragraph (b). Build the circuit shown in Figure 3. Figure 3: Dual Delta Circuit (b) Measure each one of the resistors’ resistances used in the circuit. R 1 = 217.2 ohms color code Red Red Brown R 2 = 177.45 ohms color code Brown Grey Brown R A = 326.2 ohms color code Orange Orange Brown R B = 321.5 ohms color code Orange Orange Brown R C = 324.3 ohms color code Orange Orange Brown (c) Measure the source current I and the voltage V ab using the multimeter. Remember to choose the lowest range possible for best accuracy. For current measurement, recall that after breaking the branch circuit, you should attach the positive probe at the point from which current is flowing, and the negative probe at the point to which the current is being released; see the labeled arrow for current I to know its assumed direction MEASUREMENTS: I = 38.4mA V ab = 283mV After LAB simulate Figure 3 in pSpice and obtain the value of current I 37.83mA Compare the MEASURED and CALCULATE current. Error = 1.5% 5

Lab 4: Delta-Wye Conversion Theorem Electric Circuits I Lab (d) Next, perform a Δ-Y conversion on the LOWER delta configuration (the one formed by the three 330 Ω resistors). Use the equations from Figure 2. In your calculation, assume that all resistors are exactly 330 Ω . Fill out the blanks in Figure 4. R calculated is the calculated resistance value. R measured is the measured value of the available resistor you picked from the lab’s stock. Figure 4: Delta-Wye Converted Circuit (e) Now build the circuit from Figure 4 using the resistors you just picked and measured (you are basically just replacing the lower delta with the derived wye circuit). (f) Measure the source current I and the voltage V ab using the multimeter. MEASUREMENTS: CALCULATIONS I = 38.185 mA I = 37.83 mA V ab = -258.87mV V ab = 269mV (g) Calculate the percent difference between the measurements from step (c) and those from step (f). I %Difference = 0.94% V ab %Difference = -3.75% Are your measurements approximately the same? So, has the conversion process been applied and verified successfully? Try to account for any major differences. 6 110 109.10 ohms 108.22 ohms 109.05 ohms 110 110 1 1

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Lab 4: Delta-Wye Conversion Theorem Electric Circuits I Lab Answer: Y es, we received similar readings before the conversion and after it. So, the conversion was applied and verified successfully. (h) Calculate the input total resistance of the circuit in Figure 4 using measured resistor values. CALCULATIONS: R T (calculated) = 275ohms (i) Disconnect the power supply and measure the input resistance of the circuit using the ohmmeter. Then calculate the percent difference between the calculated and measured values of this total resistance. R T (measured) = 261.33 ohms R T %Difference = 4.97% ** Show your results to your instructor to obtain a signature. Instructor’s Signature: Jaime Ramos **When done with the laboratory, please return every component to its respective storage. Thank you! F. AFTER THE LAB 1) Perform a Δ-Y conversion on the UPPER delta configuration as shown in Figure 4 and calculate the current I with a 10 V voltage source connected at the input. Show calculations and redrawn circuit below! You don’t need to use pSpice. For the new Y circuit, calculate the three resistors on top (see formulas in the next page). Apply series/parallel reduction to find the equivalent resistance, and finally, obtain the current I I = 37.7mA Rewrite the current I from page 6. I = 37.83 mA Percent Error = 0.34% 7

Lab 4: Delta-Wye Conversion Theorem Electric Circuits I Lab Figure 4- Transforming the upper delta Using the formulas from page 4 R 1 = 220 ∗ 330 220 + 180 + 330 R 2 = 180 ∗ 330 220 + 180 + 330 R 3 = 180 ∗ 220 220 + 180 + 330 c 8