Memo
TO:
FROM:
DATE:
RE:
XLIX Engineering Firm
Seth Locklear
December 1, 2012
Electrical Lab Report
As 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 Moodle.com 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 Moodle.com.
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.
12/1/2012
UNC CHARLOTTE
Electrical Circuit Lab Report
Seth Preston Locklear
1201 Introduction to Engineering
Terrence Jordan
12/1/2012
I have neither given nor received any unauthorized help on this assignment, nor witnessed any violation of the
UNC Charlotte Code of Academic Integrity.
12/1/2012
1.0 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 19 th 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: 220Ω, 330Ω,
2200Ω, 3300Ω, and 10,000Ω. 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).
V  I R
(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 (Ω). 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.
n
RT   Ri
(3.2)
i 1
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.
n
1
1

RT i 1 Ri
(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.
i
km
The variables shown here are:
(t )  0
ikm (t ) is the current, k is the branch, and m 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.
v
km
The variables in this equation are:
(t )  0
(3.4)
vkm (t ) is the instantaneous voltage drop, k is the branch, and m 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.
V  Vi  Vnode
(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.
R1=2200Ω
Node 1:
15.36V
18V
I=0.0012 A
R2=330Ω
R5=220Ω
Node 5:
0V
R4=220Ω
Node 2:
13.644V
R6=330Ω
R15=3300Ω
R14=3300Ω
R8=10kΩ
R7=10kΩ
R16=3300Ω
Node 3:
7.248V
R13=330Ω
R9=3300Ω
R12=220Ω
R11=2200Ω
R10=2200Ω
Node 4:
1.968V
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.
2.64V  0.0012 A 2200
(3.1)
12421  220 2200 10000
(3.2)
1 
 1
1320  


 2200 3300 
1
(3.3)
2.54 A  1.26 A 1.28 A
(3.4)
0V  18V  2.64V 1.716V  6.396V  5.28 1.968V
(3.5)
2.64V  18V 15.36V
(4.1)
4.2059% 
15.26V  15.93V
100%
15.93V
(6.1)
6.0 Observations and Results.
The given values for this project are shown in Table 1.
Table 1. Given values.
Current (Amps)
Initial Voltage (Volts)
Voltage at Node 1 (Volts)
Voltage at Node 2 (Volts)
Voltage at Node 3 (Volts)
Voltage at Node 4 (Volts)
Voltage at Node 5 (Volts)
0.0012A
18V
15.36V
13.644V
7.248V
1.968V
0V
The 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)
Node 2 (V)
Node 3 (V)
Node 4 (V)
Node 5 (V)
2.64
1.716
6.396
5.28
1.968
The 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)
Node 2 (V)
Node 3 (V)
Node 4 (V)
Node 5 (V)
2.62
1.72
6.42
5.27
1.97
To calculate the percent difference in the electrical circuit, equation 6.1 is used.
% Difference 
Actual  Theoretical
Theoretical
100%
The percent difference calculated at each node is shown in Table 4. The values in Table 4 are rounded to four
significant figures.
(6.1)
Table 4. Percent difference at each node.
Node 1
Node 2
Node 3
Node 4
Node 5
0.7576%
0.2331%
0.3752%
0.1894%
0.1016%
7.0 Discussion.
Comparing 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.
Resources
Dorf, 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.