Electrical Circuit Lab Report 41h5q

XLIX Engineering Design Firm 9201 University City Blvd Charlotte, NC 28223

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1201 – 009 Chris McDaniel Madison Siler Delanie Knight Electrical Circuit Lab Report Final

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Electrical Circuit Project Electrical Circuit Lab Report Draft

Prepared by: Delanie Knight Course: Intro to Engineering Practices and Principles 1 Section: 009

Date Submitted: 10/02/2015

10/02/2015 Abstract

The purpose of the electrical project was to better understand the concepts of electrical circuits, learn how they work, and connect real-life circuitry to theory. Creating a working circuit that had similarly correct currents at each node illustrated how the common physics equations are used in the real world. This project teaches how breadboards work, how to place resistors on a breadboard in series and parallel, and how power flows through the circuit. In order to start the project, the change in voltage and resistance at each had to be calculated using simple subtraction and Ohm’s Law. Once all the numbers were calculated, the organization of resistors began. Finding combinations of resistors took a few tries, since only the resistors given in the packet were allowed to be used. The combinations were checked for correctness mathematically, and the resistors were placed on the breadboard, according to how they were drawn out. The circuit was tested with a power source of 18 volts (V). Since the calculations and placement on the breadboard were correct, the actual voltage drop across each node was within

± 5% of the theoretical voltage drop.

Based on the results of the project, it can be concluded that a circuit can have many different resistor combinations, as long as the combinations are within the 5% of the actual resistance. Resistance can be calculated given the total current and voltage between each node. If the calculations and resistors are placed correctly, the experimental voltage drops will closely resemble the theoretical voltages. Introduction Problem Statement Each individual was given a specific electrical circuit to design, build, and test. The given circuit gave the total voltage, the total current, and the voltage for each node. The individual had to determine the change in voltage, and the resistance between the nodes. The resistance then determines how the resistors may be placed on the breadboard. The materials given were a small breadboard, 25 resistors, and jumper wires. Design and Performance Requirements A power source of 18V DC will be provided to the individual on test day. The total current for the circuit will be 0.0009A. The circuit will have a total of five resistor combinations. To create a voltage drop, the individual must create a resistance within

± 5% of the resistance calculated. The resistor combinations can be in

series, parallel, or both, but at least one parallel configuration must be present. The individual may only use the resistors given in the packet. In order to replicate this design, the individual must be given the following:  Five 10000Ω resistors  Five 3300Ω resistors  Five 2200Ω resistors  Five 330Ω resistors

 Five 220Ω resistors *Note that not all resistors will be used Constraints The largest constraint of deg the electrical circuit is using only the resistors given. The individual may have four of the five combinations designed, and the fifth one not work out because they need a different combination of resistors. Time and patience is needed. Other smaller constraints include the accuracy of the resistors, whether the resistors are labeled correctly, the placement of the resistors, and whether the resistors even work. Assumptions Assuming the resistors are completely accurate, and positioned correctly, the ideal total resistance and actual total resistance will be exactly the same. Another assumption would be that if the resistances between the nodes are within the actual resistances, then the voltage will be within

± 5% of

± 5%, too.

Background This project, overall, relies on the electrical theory. Electricity is the flow of electrons. How tightly the atoms of the material hold the electrons determines the conductivity. So, low conductivity is when an atom holds the electrons tightly, and vice versa for high conductivity. Naturally, electrons flow from a negative to positive charge. The flow can be drawn with a circuit schematic. The common components of a circuit include, but are not limited to, resistors, batteries, motors, generators, and inductors. This project only deals with resistors and batteries (Pre Class readings, ENGR 1201 Moodle Site, UNC Charlotte, Charlotte, NC, accessed October 1, 2015). The term “voltage” and the unit “volt” are named after the physicist, Alessandro Volta, who created the battery. Voltage, the “difference in electrical potential between two points,” is a very important factor in a circuit since it drives the electron flow. A common voltage source is a battery (Pre Class readings, ENGR 1201 Moodle Site, UNC Charlotte, Charlotte, NC, accessed October 1, 2015). Current is the movement of electrons. It is measured by area per unit of time. The two most common types of current are direct current and alternating current. For this project, only direct current is used, which move in one direction and often comes from a battery. In equations, current is symbolized by a capital I. Andre Ampere ed for the first person to describe the current of flow, so, the current unit, ampere, is fitting named after this scientist (Pre Class readings, ENGR 1201 Moodle Site, UNC Charlotte, Charlotte, NC, accessed October 1, 2015). Resistance is the restriction of flow through a current, and is measured in Ohms symbolized by the Greek letter, Ω. George Ohm related the theories of voltage, current, and resistance, creating Ohm’s Law. Similarly, the resistance unit is named

after this scientist (Pre Class readings, ENGR 1201 Moodle Site, UNC Charlotte, Charlotte, NC, accessed October 1, 2015). Theory The theory used in this project is the electrical theory, as defined above. In the context of this project, electrical theory deals with voltage, current, and resistance. The law that ties all of the measurements together is Ohm’s Law, which is defined as:

V =IR In addition to Ohm’s Law, the different equations for resistors in series and parallel were used. Resistors in parallel are side-by-side. The current will through a node and will then split between the resistors. The equation for finding the resistance of a circuit in parallel can be defined as:

1 1 =Σ R eq R Resistors in series are simply connect from one end to another. The same current flows through every resistor without changing or splitting. To find the resistance for a circuit in series the following equation may be used:

Req =Σ R Kirchoff’s Current Law states that the sum of the current into any junction is zero. All current that enters the junction or node must exit. The law is shown as

I ¿ =I out Kirchoff’s Voltage Law states that the sum of voltages along a closed path is equal to zero. The equation is:

ΣV closed path =0 (Pre Class readings, ENGR 1201 Moodle Site, UNC Charlotte, Charlotte, NC, accessed October 1, 2015). Methods and Procedures The XLIX Design Firm Provided all of the necessary materials needed to complete this project, which included a small bread board and 25 common resistors. The given resistors were:  Five 10000Ω resistors  Five 3300Ω resistors  Five 2200Ω resistors

 

Five 330Ω resistors Five 220Ω resistors

Also given was a schematic of a circuit with the total voltage, total current, and voltage at each node given. First, the voltage drop between the nodes had to be determined using simple subtraction. The voltage drop was then used to find the resistance measurements between each node. Once the mathematical portion of the circuit was completed, the actual circuit had to be built. Before actually placing the resistors on the board, the set-up of each section had to be created. This process used trial and error and the equations for resistors in series. Eventually, a proper set-up had been reached. Afterwards, the technicalities of where and how to place the resistors on the bread board had to be used. Once learned, the resistors were placed on the breadboard. With the help of a multimeter, the final product was reached much quicker because the meter measured the total resistance between groups of resistors to check against the calculations. The process of trial and error was also used in this step. The final product was, eventually, reached:

Figure 1. Circuit schematic of designed circuit.

Figure 2. Image of actual designed circuit. Sample Calculations Ohm’s Law:

V =IR

1.795=0.0009 R R1+2 +3+4 =1994.44 Ω Resistors in Series:

R13+14+ 15=330+2200+330=2860 Ω

Resistors in Parallel:

R3+ 4+2=

1 1 1 + = =1650 Ω 6600 2200 1650

Kirchoff’s Current Law:

I ¿ =0.0009 A=I out =0.0009 A

Kirchoff’s Voltage Law:

18 V + [−1.7975 V + (−6.3548V )+ (−6.768 V ) + (−2.6884 ) + (−0.3938 V ) ] =0 Results Table 1 Given, Theoretical, Experimental Test Results

Volta ge Divid er Node Node 1 Node 2 Node 3 Node 4 Node 5

Theoreti cal/ Calculat ed Resista nce at Nodes (Ω)

Actual Resist ance at Nodes (Ω)

Resista nce Percen tage Differe nce (%)

1.795 6.354 8

1994.44

1980

7060.89

6.768 2.688 4 0.393 8

Volta ge Drop at Node s (V)

Theoretical/ Given Node to Ground Voltage (V)

Experim ental Node to Ground Voltage (V)

Voltage Percen tage Differe nce (%)

0.724

16.205

16.18

0.1542

7040

0.296

9.8502

9.77

0.8141

7520

7530

0.133

3.0822

2.98

2987.11

2860

4.255

0.3938

0.39

0.03315 0.00964 9

437.56

440

0.558

0

0

0

Discussion The results obtained in this project met the expectations laid out in the description. The percent difference suggest that the theoretical and experimental results may not be the same, however, they are very similar and are within the range ±5% of acceptance. All sections but one within the circuit are less than 1%, meaning that the results were similar to what was expected. There are many reasons that contribute to why the percent difference exists. First, the resistors are common, so they will not be the exact measurement of ohms needed, which s for the ±5% range. Also, the manufactured resistors’ resistance values are not always 100% accurate. Alternative resistor combinations could have been performed, but the circuit would not meet the criteria described in the project description. The results imply that the mathematical calculations throughout the project were correct, and that each theory and equation was understood. In order to complete the project successfully, an in-depth understanding of electrical theory and its applications were imperative. The project connects all theories, laws, and definitions. It is recommended that before even starting the project, to study and understand how circuits work. Beginning without understanding the processes will make the project more difficult and time consuming. At least of few hours (probably more) should be allotted for the correct completion of this project. Patience is needed because not all combinations and set-ups workout the first time. The results of this project are important because it shows how resistance, current, and voltage are calculated, within a circuit. References

1. 1202 Faculty, “Electrical Theory,” (Pre-Class readings, ENGR 1201 Moodle Site, UNC Charlotte, Charlotte, NC, accessed October 1, 2015).