Electrical Circuit Lab Report - Weebly



MemoTO: XLIX Engineering FirmFROM: Seth LocklearDATE: December 1, 2012RE: Electrical Lab ReportAs you requested, I created a design package for an electrical circuit board. The research was gathered through two books: The Electrical Engineering Handbook by Richard C. Dorf, and The Resource Handbook of Electronics by Jerry C. Whitaker. All the information about basic electrical theory was explained in these two sources. I calculated that the circuit board would need 15 resistors in order to achieve the theoretical voltage drop at each node. This document was submitted to on November 19th of this year.After the design package was completed, I proceeded to construct the circuit board for actual testing. The resistors’ wires were cut to fit into the breadboard. The completed circuit board was taken to class on November 19th for testing. Professor Jordan ran an 18 voltage source through the circuit, and checked the voltage drop at each node with a multi meter. The actual values were recorded on the test data sheet, and the data sheet was uploaded onto .The actual values collected from test day were extremely close to the theoretical values calculated in the design package. According to the values received during testing, I would consider the electrical circuit to be successfully designed.I have neither given nor received any unauthorized help on this assignment, nor witnessed any violation of the UNC Charlotte Code of Academic Integrity. 12/1/2012UNC CharlotteElectrical Circuit Lab ReportSeth Preston Locklear1201 Introduction to EngineeringTerrence Jordan12/1/2012I have neither given nor received any unauthorized help on this assignment, nor witnessed any violation of the UNC Charlotte Code of Academic Integrity. 12/1/20121.0 Summary.XLIX Engineering Design Firm requested the construction of a circuit board that was designed to decrease voltage at separate nodes. During class periods, the professor discussed basic electrical theory. In order to construct this circuit board, a design package had to be written and submitted to the firm. Research was conducted to enhance the understanding of the project. Calculations were made in order to discover the required resistance at each node. Using the values from the calculations, potential combinations of resistors were designed and implemented on the circuit board design. This document was submitted to the firm on November 19th of this year.The circuit board was constructed after the design package was submitted. The excess wires on the resistors were cut in order to fit them into the bread board more properly. Each resistor was placed into the bread board according to the calculated combinations. Jumper wires were placed into the bread board to indicate each node.On November 19th, the circuit board was tested. An 18V source was run through the circuit board using a portable power source. At each node, a multi meter was used to test the actual voltage drop. The theoretical values were compared to the actual values to ensure that the project functioned according to the requirements. Because the compared results were close in magnitude, the project was a success.2.0 Introduction.The XLIX Engineering Design Firm has requested the construction of an electrical circuit board. The purpose of this circuit board is to decrease the voltage of a given power source to satisfy the required voltages at five nodes. The given power source has a voltage of 18 DC volts, and a current of 0.0012 amps. The required voltages at the five consecutive nodes are: 15.36V, 13.644V, 7.248V, 1.968V, and 0V. In order to achieve the required voltage drops, resistor combinations must be implemented. There must be at least one resistor combination containing a parallel resistor configuration. These combinations must be calculated using five sets of given resistors: 220?, 330?, 2200?, 3300?, and 10,000?. Each of these resistors has a tolerance of ±5%. No other resistors outside of the ones given by the XLIX Engineering Design Firm may be used.3.0 Background Information.Electrical circuits are made up of components to allow an electrical to flow through the circuit (Whitaker 2001, 6.1). The two variables used involved are voltage and current. The relationship between these two variables can be seen through Ohm’s Law (Whitaker 2001, 6.1).(3.1)The variables used here are: V is voltage, I is current, and R is resistance.Resistance is the opposition of electrical current in a circuit. Resistance can be achieved by inserting devices called resistors into a circuit (Dorf 2000, 1.1).The measuring unit for resistance is the ohm, and it is represented by the Greek letter omega (?). In order to find the equivalent resistance in a circuit, the resistance given off by each resistor must be calculated. This value is interpreted into four colored bands on the device itself (Whitaker 2001, 7.2).If a set of resistors are connected end-to-end, there are considered to be in series configuration. The equivalent resistance in this configuration is equal to the sum of the individual resistors (Dorf 2000, 1.1). Equation 3.2 shows this relationship.(3.2)Resistors placed side-by-side are considered to be in parallel configuration. The equivalent resistance in this configuration is the reciprocal of the sum of the reciprocals of the individual resistors. This relationship is shown in equation 3.3.(3.3)Two other laws governing the voltage and current of an electrical circuit are called Kirchhoff’s Laws. The first law is the Current Law, which states that the sum of current entering a node must be equal to the current leaving a node (Dorf 2000, 3.1). This relationship can be represented by equation 3.4.The variables shown here are: is the current, is the branch, and is the node (Dorf 2000, 3.1).The second law is Kirchhoff’s Law of Voltage, which states that the sum of the voltage drop in an electrical circuit must equal zero. This law is represented by equation 3.4.(3.4)The variables in this equation are: is the instantaneous voltage drop, is the branch, and is the path (Dorf 2000, 3.1).4.0 Methods and Procedures.In order to begin the construction of the electrical circuit, knowledge concerning electrical circuits was researched. Two reliable sources were The Electrical Engineering Handbook by Richard C. Dorf, and The Resource Handbook of Electronics by Jerry C. Whitaker. All the background information listed in section 3.0 was gathered from those sources.After ample research was gathered, calculations were performed to find the equivalent resistance needed to achieve the necessary voltage drop. At each node, the voltage from the node was subtracted from the initial voltage to determine the drop in voltage. This relation can be shown by equation 4.1.(4.1)ΔV is the voltage drop, Vi is the initial voltage, and Vnode is the voltage at the node. By using the given current and the calculated voltage drop at the given, the equivalent resistance can be found at that node using equation 3.1. Once the equivalent resistance is calculated, potential resistor combinations are configured to find the best possible configuration of resistors at that node. Figure 1 shows the electrical circuit diagram.Figure 1. Circuit board diagram.By using this diagram as the blueprint for the breadboard, the resistors were placed in accordingly. The excess wires from the resistors were cut to allow a tighter fit in breadboard. Jumper wires were inserted into the breadboard at each node. This would allow for anyone to test each node using a multi meter. Due to the fact that each breadboard was disassembled in class on testing day, no photographs of the actual breadboard were taken. On testing day, the professor connected an 18V DC power source to the first end of the breadboard, and to the last wire of the breadboard. At each node, the voltage drop was calculated to see if the theoretical values matched up with the actual values. See Appendix B for the theoretical values and the actual values. Since these two values were close in proximity, the satisfied its design requirements.5.0 Sample Calculations.(3.1)(3.2)(3.3)(3.4)(3.5)(4.1)(6.1)6.0 Observations and Results.The given values for this project are shown in Table 1.Table 1. Given values.Current (Amps)0.0012AInitial Voltage (Volts)18VVoltage at Node 1 (Volts)15.36VVoltage at Node 2 (Volts)13.644VVoltage at Node 3 (Volts)7.248VVoltage at Node 4 (Volts)1.968VVoltage at Node 5 (Volts)0VThe theoretical values calculated for the voltage drops at each node are shown in Table 2.Table 2. Theoretical values for the voltage drops at each node.Node 1 (V)2.64Node 2 (V)1.716Node 3 (V)6.396Node 4 (V)5.28Node 5 (V)1.968The actual values tested for the voltage drops at each node are shown in Table 3.Table 3. Actual values for the voltage drops at each node.Node 1 (V)2.62Node 2 (V)1.72Node 3 (V)6.42Node 4 (V)5.27Node 5 (V)1.97To calculate the percent difference in the electrical circuit, equation 6.1 is used.(6.1)The percent difference calculated at each node is shown in Table 4. The values in Table 4 are rounded to four significant figures.Table 4. Percent difference at each node.Node 10.7576%Node 20.2331%Node 30.3752%Node 40.1894%Node 50.1016%7.0 paring the data gathered during this experiment, the difference in theoretical values and actual values is incrediblely close in proximity. The values listed in Table 1 show the values given to me by the project. None of these values were calcualted. See appendix A for these given values. The values listed in Table 2 indicate the actual voltage drop needed at each given node. These calculations do not put into account the ±5% tolerence of the resistors. See Appendix A for voltage drops. The values indicated in Table 3 show the actual voltage drops that each node experienced during testing. Each of these values were found using the multi meter discussed in section 5.0. See Appendix B for actual test values. The values listed in Table 4 indicate the percent difference between the values listed in Table 2 and Table 3. The percent difference indicates how close the calculated value was to the actual value present. By examining the results gathered from Table 4, it is apparent that the calculated voltage drops were very close to the actual voltage drops in the eletrical circuit. This means that the math involved is extremely accurate. In addition to the math used, it is apparent that each resistor had a value of resistance close to the value indicate by the colored bands on the device. Since these resistors have a reasonably low tolerance, the actual resistance value is quite accurate.Taling into account of the percent difference, there was some error involved with the calculations. Firstly, the tolerance of each resistor was not taken into account. Secondly, multiple resistors in a configuration allows for a greater percent error. This is because the tolerance accumulates, causing the actual value to decrease in accuracy. Thirdly, not all equipment is 100% reliable. The multi meter may have misread the actual value, or 18V DC electrical current was not exact. All these potential errors coud account for the percent difference calculated in Table 4.8.0 Conclusions and Recommendations.For this project, the XLIX Engineering Firm requested the construction of an electrical circuit. Research and calculations were gathered to successfully construct the circuit. The circuit was constructed and tested in accordance to the requirements given in the problem statement. By comparing the theoretical values to the actual values calculated, it was determined that the circuit successfully achieved the requirements needed for the XLIX Engineering Firm. One recommendation for this project is the variety of resistors. By having a greater variety of resistance values, resistor configurations can be more accurate without using an overabudance of resistors. This would cause the actualvalues to be closer to the theoretical values.Many lessons were learned throughout this project. Firstly, there is more than one way to solve a problem. There were many different resistor configurations, but some used resistors than others. This allowed for more accurate calculations. Another lesson learned is the reliability of the math. When used correctly, the equations for solving voltage and resistance can calculate accurate findings in the electrical current.ResourcesDorf, Richard C. 2000. The Electrical Engineering Handbook. Boca Raton: CRC Press LLC.Whitaker, Jerry C. 2001. The Resource Handbook of Electronics. Boca Raton: CRC Press LLC.Appendix A: Given Electrical Circuit Values and Calculated Voltage Drops and Equivalent Resistances.Appendix B: Test Data Sheet Showing Theoretical Values and Actual Values. ................
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