Lab 4 v5 -D-Y Conversion Theorem
docx
keyboard_arrow_up
School
University of Texas, Rio Grande Valley *
*We aren’t endorsed by this school
Course
3301
Subject
Electrical Engineering
Date
Apr 3, 2024
Type
docx
Pages
8
Uploaded by ChiefLightning3873
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
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
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
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
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