XLIX Engineering Design Firm 9201 University City Blvd Charlotte, NC 28223
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James Kelly Electrical Project Laboratory Report - Final
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Electrical Project Laboratory Report
ENGR 1201 - Section 013
James Kelly
Electrical Project Laboratory Report Submitted: October 2, 2015
I have neither given nor received any unauthorized help on this assignment, nor witnessed any violation of the UNC Charlotte Code of Academic Integrity.
James Kelly October 2, 2015
Abstract The Electrical Circuit project was designed for interns to demonstrate their knowledge of the mathematics behind an electrical circuit problem, and to construct a circuit that involves calculated solutions. After the project is complete, interns should be able to use and understand Ohm’s Law and Kirchhoff’s Kirchhoff’s Voltage Laws. Interns are given a breadboard and resistors of various resistance. They must construct a circuit using the provided breadboard and resistors. In order to do so, they must first calculate the total resistance between each node in their circuit. After calculating each equivalent resistance between each node, the interns will calculate a combination of resistors that will give them a value within five percent error of the equivalent resistance. After completing completing testing testing of the project, project, interns interns are able to verify Ohm’s Law Ohm’s Law (V = IR) within their given five percent error. The reason as to why this error percentage is occurring is due to individual resistance within the resistors themselves, resistance in the wires, and resistance in the breadboard. Introduction Problem Statement In order to complete the electrical circuit project, interns were provided a breadboard, which contained five 220 Ω resistors, five 330 Ω resistors, five 2200 Ω resistors, five 3300 Ω resistors, and five 10000 Ω resistors. The interns had to use t hese resistors as a means to complete the electrical circuit. Before beginning the project, interns learned the basics of series and parallel circuits, and how to calculate the total resistance, voltage, and current of a circuit. Interns had to apply their knowledge of Kirchhoff’s Rule and Ohm’s Law to complete a self -constructed self -constructed circuit. Design Requirements, Constraints, and Assumptions The circuit had to meet specific demands set forth by XLIX Engineering Design Firm. The circuit would have a total voltage of 18 volts, and a total current of 0.0009 Amperes. The given voltages across each node included: 18 Volts, 11.646 Volts, 4.8776 Volts, 2.1892 Volts, 0.3092 Volts, and 0 Volts. Interns had to find the voltage drop across various nodes in order to calculate the equivalent resistance across each node. Once interns found the required equivalent resistance across a node, they would then have to find a combination of resistors that would equal the given equivalent resistance. When the interns have completed their project, the project will be tested using a multimeter. In order for the project to be deemed successful, each voltage drop and equivalent resistance across each node must be within the parameters of a five percent error. If the readings measured by the multimeter are outside of this five percent error range, the project will be declared unsuccessful, and the intern’s grade will be reduced. Interns are only allowed to use the materials provided to them. In addition, interns must assume that the voltage supplied to the circuit is a consistent 18 Volts. Background Information and Research In order to successfully complete this project, interns had to obtain an understanding of basic electrical theory, which involves Ohm’s Law and Kirch hoff’s Laws. Ohm’s Law (V = IR) is key to successfully calculating the equivalent resistance across each node in the circuit. The interns then had to understand the difference between Kirchhoff ’s Kirchhoff ’s Voltage Voltage and Current Laws.
Kirchhoff ’s Kirchhoff ’s Voltage Law “states “ states that the algebraic sum of the voltages in a closed loop is always equal to zero” ("Basic Electrical Theory | Ohms Law, Current, Circuits & More"). Kirchhoff ’s Kirchhoff ’s Current Law “states “ states that current into a node will equal the current out of the node. In other words, the net current in a node is zero” ("Basic Electrical Theory | Ohms Law, Current, Circuits & More"). In addition, interns had to understand the basics behind calculating the resistance of series and parallel circuits. Further description of calculating the resistance of series and parallel circuits is provided within the Theoretical Analysis section below. Theoretical Analysis In order to successfully complete this project, interns had to obtain an understanding of basic electrical theory, which involves Ohm’s Law and Kirchhoff ’s Kirchhoff ’s Laws. Ohm’s Law (V = IR) is key to successfully calculating the equivalent resistance across each no de in the circuit. “The “ The V is for voltage, which means the potential difference between two charges. In other words, it is a measurement of the work required to move a unit charge between two points” ("Basic Electrical Theory | Ohms Law, Current, Circuits & More"). The change in voltage can be calculated by subtracting the voltage of a node from the voltage of the previous node. Once the change in voltage has been calculated, interns can then solve for the value R, resistance, since they have already been provided with the value I, current. After calculating calculating the resistance between between each node, node, the interns interns can use the rules governing governing series and parallel circuits to find a combination of resistors that will equal the equivalent resistance between each node. Before discussing series and parallel circuits, and how to calculate the resistance, it is essential that the interns understood the basic concepts behind Kirchhoff ’s Kirchhoff ’s Laws. The first thing that the interns had to understand was that “ in series circuits, current is constant and voltage varies but in parallel circuits voltage is constant and current varies” ("Basic Electrical Theory | Ohms Law, Current, Circuits & More"). The interns then had to understand the difference between Kirchhoff ’s Kirchhoff ’s Voltage and Current Curren t Laws. Kirchhoff ’s ’s Voltage Law “states “ states that the algebraic sum of the voltages in a closed loop is always equal to zero” ("Basic Electrical Theory | Ohms Law, Current, Circuits & More"). Kirchhoff ’s Kirchhoff ’s Current Law “states “ states that current into a node will equal the current out of the node. In other words, the net current in a node is zero” ("Basic Electrical Theory | Ohms Law, Current, Circuits & More"). “In a series circuit, all components are connected end -to-end, forming a single path for electrons to flow. In a parallel circuit, all components are connected across each other, forming exactly two sets of electrically common points” ("What are “Series” and “Parallel” Circuits?").
Figure 1: Series Connection.
= 1 + 2 + 3 + 4..
The equivalent resistance of a series circuit equals the sum of all the resistors.
Figure 2: Parallel Connection.
− 1 1 1 1 = (1 + 2 + 3 + 4 . . ) The equivalent resistance of a parallel circuit is equal to the inverse of each resistor added to the next inverse of the following resistor, all to the power of negative one. With this knowledge in mind, the interns were able to apply Ohm’s Law (V = IR) in order to solve for the equivalent resistance between each node. After solving for this equivalent resistance, the interns could solve for a combination of resistors that would equal the equivalent resistance. Methods and Procedures The materials provided to the interns to complete the Electrical Circuit Project included:
One breadboard. Five of each of the following resistors: 220Ω, 330Ω, 2200Ω, 3300Ω, and 10 ,000Ω. Five wires, which which would act as the nodes where the tester would test the change in voltage across each node. One plastic bag to contain all of the materials provided.
In order to successfully complete the project, interns had to use background knowledge of Series and Parallel circuits, as well as apply Ohm’s Law and Kirchhoff ’s Kirchhoff ’s Laws in order to calculate the equivalent resistance across each node. Sample Calculations Sample Series Circuit Calculation (With Ohm’s Law and Kirchhoff ’s Kirchhoff ’s Laws): Laws): Δ V = 18 V – 11.646 V = 6.354 V
= = = 6.354V/0.0009A = 7060 Ω (Theoretical Value) = 1+ 1 + 2+ 2+.. = = 3300 Ω + 3300 Ω + 220 Ω + 220 Ω = 7040 Ω (Actual Value) % = −ℎ ℎ ∗100%
=
7−76 76 ∗100% = 0.283 % error
Sample Parallel Circuit Calculation (With Ohm’s Law and Kirchhoff ’s Kirchhoff ’s Laws): Laws): Δ V = 2.1892 2.1892 V – 0.3092 – 0.3092 V = 1.88 V
= = = 1.88V/0.0009A = 2088.89 Ω (Theoretical Value) − 1 1 = (1 + 2 +..) = 1+ 1 + 2+. 2+.. + + − + 330 Ω + 330 Ω = 2076.31 Ω (Actual Value) = % = −ℎ ℎ ∗100% 76.−88.89 ∗ 100% = 0.602 % error = 88.89 Inter ns ns had to use Ohm’s Law in order to calculate the equivalent resistance across each node. Once the equivalent resistance was calculated, the interns could then apply rules of series and parallel circuits to find a combination of resistors that would be within five percent error of the calculated equivalent resistance. After the interns interns have have finished finished the calculations calculations of of each node, node, and have have found found a combination combination of of resistors, the interns then had to construct the circuit using the breadboard, resistors, and wires provided to them. The final product should look similar to the following image:
Figure 3: An intern’s electrical circuit breadboard with resistors and nodes. As shown in the image, image, there are are resistors in series and parallel with with an individual individual wire between each combination of resistors, which will act as the node between the resistors. The change in voltage will be measured and recorded on each intern’s test data sheet. Interns should print the test data sheet out from Moodle prior to the testing period. If the measured voltage is not within five percent error to the theoretical voltage, the intern’s grade on the project will be reduced, and the intern must attempt to reconstruct the circuit.
After the testing period period is complete, complete, interns interns must deconstruct deconstruct their their breadboard, breadboard, and return all materials to their instructor. Following the testing period, interns must upload their test data sheet results to Moodle for grading and review. In addition to submitting the test data sheet, interns are asked to complete a design package for the project. Within the design package, interns will include a schematic of their circuit design, which must be created using Microsoft Visio software. Here is an example of one intern’s Visio schematic: Node 1 11.646 V
Node 2 4.8776 V
Node 3 2.1892 V
Δ V = 6.354 V
Δ V = 6.7684 V
Δ V = 2.6884 V
Req = 7060
Req = 7520.4 Ω
Req = 2987.1 Ω
Ω
Node 4 0.3092 V
Node 5 0V
Δ V = 0.3092 V Req = 343.56 Ω
Δ V = 1.88 V Req = 2088.89 Ω
10000 Ω
3300 Ω
220 Ω
3300 Ω
R actual = 7040
3300 Ω
220 Ω
Ω
2200 Ω
2200 Ω
R actual = 7700 Ω
2200 Ω
220 Ω
330 Ω
3300 Ω
330 Ω
220 Ω
R actual = 2970 Ω
330 Ω
330 Ω
3300 Ω
R actual = 2076.31 Ω
R actual = 330 Ω
+ 18 V
I = 0.0009 A
Figure 4: An intern’s Visio schematic of his Electrical Circuit. Results Table 1 below shows the actual and theoretical values of the resistance between each node. The table additionally displays the percent difference of the actual and theoretical values of resistance. None of the values have a percent difference greater than five percent. Therefore, the resistance of each node measured is approved by the five percent constraints of the electrical circuit project. Table 1: Actual vs. Theoretical Values of Resistance between Nodes. Node 1 2 3 4 5
Actual 7040 Ω 7700 Ω 2970 Ω 2076.31 Ω 330 Ω
Theoretical 7060 Ω Ω 7520.4 Ω Ω 2987.1 Ω Ω 2088.89 Ω Ω 343.56 Ω Ω
Percent Difference 0.28% 2.39% 0.57% 0.60% 3.95%
Table 2 below shows the actual and theoretical values of the voltage between each node. The table additionally displays the percent difference of the actual and theoretical values of voltage.
None of the values have a percent difference greater than five percent. Therefore, the voltage of each node measured is approved by the five percent constraints of the electrical circuit project. Table 2: Actual vs. Theoretical Values of Voltage between Nodes. Node 1 2 3 4 5
Actual 11.62 V 4.80 V 2.15 V 0.30 V 0V
Theoretical 11.646 V 4.8776 V 2.1892 V 0.3092 V 0V
Percent Difference 0.22% 1.59% 1.79% 2.98% 0.00%
Discussion It is essential that interns realize and understand why their results will not equal the exact voltage calculated. There is resistance within the resistors, the breadboard, and the wires connecting each combination of resistors. This resistance will offset the exact amount of voltage measured at each node. In addition, the multimeter used will not have an output of exactly 18 volts. Therefore, the parameters of the project must take this information into consideration. As a result, the electrical circuit project allows for a five percent error (Percent Difference) of the voltage measured at each node. The primary purpose of the electrical circuit project is for interns to apply Ohm’s Law and Kirchhoff ’s Kirchhoff ’s Laws to series and parallel circuits in order to design and construct an electrical circuit. The circuit had to meet specific demands set forth by XLIX Engineering Design Firm. The circuit would have a total voltage of 18 volts, and a total current of 0.0009 Amperes. The given voltages across each node included: 18 Volts, 11.646 Volts, 4.8776 Volts, 2.1892 Volts, 0.3092 Volts, and 0 Volts. When measured, the results displayed that actual vs theoretical values fell within the five percent error permitted by the project’s parameters. Therefore, the interns proved successful in their completion of the electrical circuit project. The XLIX Engineering Design Firm can use the results of this report for future design and construction of electrical circuits. There are a few key issues to mention, which will aid other researchers in improving their results from a similar project. First, a more precise multimeter would be recommended if this project were to be conducted again. Additionally, resistors with a lower tolerance level is recommended for use in order to decrease the final percent error of either resistance or voltage.
References "Basic Electrical Theory | Ohms Law, Current, Circuits & More." Library.Automationdirect.com. September 15, 2014. Accessed September 28, 2015. http://library.automationdirect.com/basicelectrical-theory/.. electrical-theory/ Figure 1: Series Connection. Digital image. All About About Circuits Forum Forum RSS. RSS. Accessed September 27, 2015. . Figure 2: Parallel Connection. Digital image. All About Circuits Circuits Forum RSS. RSS. Accessed September 27, 2015. . "What Are “Series” and “Parallel” Circuits?" All About Circuits Forum RSS. Accessed September 28, 2015. http://www.allaboutcircuits.com/textbook/direct-current/chpt-5/what-are-series-andparallel-circuits/.
Appendix Figure 1: Series Connection.
Figure 2: Parallel Connection.
Figure 3: An intern’s electrical circuit breadboard with resistors and nodes.
Figure 4: An intern’s Visio schematic of his Electrical Circuit. Node 1 11.646 V
Node 2 4.8776 V
Node 3 2.1892 V
Δ V = 6.354 V
Δ V = 6.7684 V
Δ V = 2.6884 V
Req = 7060 Ω
Req = 7520.4 Ω
Req = 2987.1 Ω
Node 4 0.3092 V
Node 5 0V
Δ V = 0.3092 V Req = 343.56 Ω
Δ V = 1.88 V Req = 2088.89 Ω
10000 Ω
3300 Ω
220 Ω
3300 Ω
R actual = 7040
3300 Ω
220 Ω
Ω
2200 Ω
2200 Ω
R actual = 7700 Ω
2200 Ω
220 Ω
330 Ω
220 Ω
R actual = 2970 Ω
+ 18 V
3300 Ω
330 Ω
I = 0.0009 A
330 Ω
330 Ω
3300 Ω
R actual = 2076.31 Ω
R actual = 330 Ω
Table 1: Actual vs. Theoretical Values of Resistance between Nodes. Node 1 2 3 4 5
Actual 7040 Ω 7700 Ω 2970 Ω 2076.31 Ω 330 Ω
Theoretical 7060 Ω Ω 7520.4 Ω Ω 2987.1 Ω Ω 2088.89 Ω Ω 343.56 Ω Ω
Percent Difference 0.28% 2.39% 0.57% 0.60% 3.95%
Table 2: Actual vs. Theoretical Values of Voltage between Nodes. Node 1 2 3 4 5
Actual 11.62 V 4.80 V 2.15 V 0.30 V 0V
Theoretical 11.646 V 4.8776 V 2.1892 V 0.3092 V 0V
Percent Difference 0.22% 1.59% 1.79% 2.98% 0.00%
All calculations calculations needed needed in order order to complete complete the electrical electrical circuit project: Electrical Circuit Project Calculations: Node 1: Δ V = 18 V – V – 11.646 11.646 V = 6.354 V
= = = 6.354V/0.0009A = 7060 Ω (Theoretical Value) = 1+ 1 + 2+ 2+.. = = 3300 Ω + 3300 Ω + 220 Ω + 220 Ω = 7040 Ω (Actual Value) % = −ℎ ℎ ∗100% 7−76 = 76 ∗100% = 0.283 % error Node 1: Alternative Combination:
= 1+ 1 + 2+ 2+.. = 2200 Ω + 2200 Ω + 2200 Ω + 330 Ω = 6930 Ω (Actual Value) % Difference = 1.84 % error Node 2: Δ V = 11.646 11.646 V – 4.8776 – 4.8776 V = 6.7684 V
=
= = 6.7684V/0.0009A = 7520.4 Ω (Theoretical Value) = 1+ 1 + 2+. 2+.. = 3300 Ω + 2200 Ω + 2220 Ω = 7700 Ω (Actual Value) % = −ℎ ℎ ∗100% 77−75. = 75. ∗100% = 2.388 % error Node 2: Alternative Combination:
= 1+ 1 + 2+ 2+.. = 3300 Ω + 3300 Ω + 330 Ω + 330 Ω = 7260 Ω (Actual Value) % Difference = 3.46 % error Node 3: Δ V = 4.8776 4.8776 V – 2.1892 – 2.1892 V = 2.6884 V
= = = 2.6884V/0.0009A = 2987.1 Ω (Theoretical Value) = 1+ 1 + 2+ 2+.. = = 2200 Ω + 330 Ω + 220 Ω + 220 Ω = 2970 Ω (Actual Value) % = −ℎ ℎ ∗100% 987.−97 ∗ 100% = 0.572 % error = 987. Node 3: Alternative Combination:
− 1 1 = (1 + 2 +..) = 1+ 1 + 2+. 2+.. + − + 330 Ω + 220 Ω = 3031.203 Ω (Actual Value) = % Difference = 1.476 % error Node 4: Δ V = 2.1892 2.1892 V – 0.3092 – 0.3092 V = 1.88 V
= = = 1.88V/0.0009A = 2088.89 Ω (Theoretical Value) − 1 1 = (1 + 2 +..) = 1+ 1 + 2+. 2+..
+ + − + 330 Ω + 330 Ω = 2076.31 Ω (Actual Value) % = −ℎ ℎ ∗100% 76.−88.89 ∗ 100% = 0.602 % error = 88.89 =
Node 4: Alternative Combination:
− 1 1 = (1 + 2 +..) = 1+ 1 + 2+. 2+.. + − + 220 Ω + 220 Ω = 2090 Ω (Actual Value) = % Difference = 0.053 % error Node 5: Δ V = 0.3092 0.3092 V – 0 – 0 V = 0.3092 V
= = = 0.3092V/0.0009A = 343.56 Ω (Theor etical (Theor etical Value) = 1+ 1 + 2+ 2+.. = = 330Ω = 330 Ω (Actual Value) % = −ℎ ℎ ∗100% −.56 ∗ 100% = 3.947 % error = .56 Node 5: Alternative Combination:
− 1 1 = (1 + 2 +..) = 1+ 1 + 2+. 2+.. + − + 220 Ω = 352 Ω (Actual Value) = % Difference = 2.457 % error
