UNC CHARLOTTE
Electrical Circuit Design Package
Seth Preston Locklear
1201 Introduction to Engineering
Terrence Jordan
11/19/2012
I have neither given nor received any unauthorized help on this assignment, nor witnessed any violation of the
UNC Charlotte Code of Academic Integrity.
11/19/2012
1.0 Problem Statement
XLIX Engineering Firm has requested the design and constructed of a simple voltage divider. Using power source,
the circuit must reduce the voltage for five separate nodes. The power source used is an 18 volt direct current with
a flow of 0.0012 amps. The required voltages for the five nodes are the following: 15.36 volts, 13.644 volts, 7.248
volts, 1.968 volts, and 0 volts.
The circuit board must be constructed using a variety of resistors to decrease the voltage to satisfy the required
voltage for each node. There are twenty-five resistors provided for the project. The values of these resistors are
the following: 220 ohms, 330 ohms, 2200 ohms, 3300 ohms, and 10k ohms. Each resistor has a tolerance ±5%. No
other resistors may be used for the project’s completion. There must be at least one combination of parallel
resistors in the circuit design.
Research must be conducted for the successful completion of this project. This research must cover the concepts
used in basic electrical theory. Only one reliable online may be used. The project must be ready to be tested
November 19, 2012.
2.0 Research Findings
2.1 Circuit Design.
Electrical circuits are made up of a variety of electronic parts such as capacitors, transistors, and resistors. These
elements are required in order to achieve the required flow of electrical current (Whitaker 2001, 6.1). Two
essential variables involved in the flow of electricity are voltage, and current. Voltage is best described as a small
electrical force. When a voltage is applied to a conductive material, a flow of electrons occurs, this is called
current. These two variables are dependent on the conductivity of the metallic material being used. Conductivity is
how tightly the atoms in a substance hold onto their electrons (Whitaker 2001, 1.2.1).
2.2 Direct Current.
Direct current is described as the steady flow of electrical current in a constant direction. Direct current was first
used to supply power for household and industrial reasons. For the public’s safety, the voltage output was 110
volts. Because of the loss of voltage due to distribution, power plants could only supply a small area with
electricity. Because of this loss of voltage, power lines could no stretch out for long distances. In order to supply
power to meet our society’s consumption of energy, we would have to have power plants in almost every city and
neighborhood. Luckily, the United States uses alternating current instead of direct current to give us power
(Whitaker 2001, 1.2.2).
2.3 Ohm’s Law.
In an electrical circuit, there is a direct relationship between the current and the voltage. The relationship is known
as Ohm’s Law. Ohm’s Law states that the voltage of a circuit varies according to the electrical current. Another
variable that is used in Ohm’s Law is resistance (Whitaker 2001, 6.1). The ratio between voltage, current, and
resistance is shown here:
V  I R
In this equation represented,
resistance.
V
(2.1)
represents the voltage, I represents the current, and R represents the
Power can also be calculated using Ohm’s Law. Using voltage and current, we can calculate how many watts a
circuit puts out:
P V I
(2.2)
P is the variable used to represent power in watts.
This equation can be rewritten as:
P  I2 R
(2.3)
2.4 Resistors.
Resistors are electrical devices whose sole function is to reduce the flow of electrical current in a circuit (Dorf 2000,
1.1). The opposition applied by the resistor to the current flow is called the resistance. The unit of measurement
for resistance is called an ohm, and the symbol is characterized with the Greek letter Omega (Ω). Resistance is
directly related to the material and the length of the resistor. In order to find the amount of resistance of the
resistor, four colored bands are placed on the resistor to indicate resistance value (Whitaker 2001, 7.2). These
values are shown in Figure 2.1 (Whitaker 2001, 7.2.1).
Figure 1. Color code for fixed resistors in accordance with IEC publication 62.
Resistors can be placed in a combination to create the desired voltage drop in the circuit. These combinations are
referred to as networks. If the resistors are placed in series, the equivalent resistance is equal to the sum of the
individual resistors (Dorf 2000, 1.1). The equation is shown here:
n
RT   Ri
(2.4)
i 1
The variable RT represents the sum of the individual resistances in the circuit (Dorf 2000, 1.1).
If the resistors are placed in parallel, then the equivalent resistance is the reciprocal of the sum of the reciprocals
of the individual resistors. This equation is shown here:
n
1
1

RT i 1 Ri
(2.5)
2.5 Kirchhoff’s Laws.
The first of Kirchhoff’s laws is the Current Law. This law states that the sum of the currents entering in the node
must equal the sum of current leaving the node (Dorf 2000, 3.1). This principle looks like this in an equation:
i
km
The variable
(t )  0
(2.6)
ikm (t ) represents the current in branch k across node m (Dorf 2000, 3.1). A branch is a portion of
circuit between two terminals, and a node is where these branches meet on the circuit (Whitaker 2001, 6.1).
The second of Kirchhoff’s laws is the Voltage Law. This law states that the sum of the voltage drop in a closed
circuit must equal zero. This equation is shown as:
v
km
The variable
(t )  0
(2.7)
vkm (t ) is the instantaneous voltage drop in the branch k of the path m (Dorf 2000, 3.1).
3.0 Calculations
The circuit constructed has an initial voltage of 18 volts, and a current of 0.0012 amps. In order to find the correct
resistor combination, the voltage drop is calculated at each node. Using Ohms Law (eq. 2.1), we can calculate the
equivalent resistance. Using trial-and-error, the correct combination of resistors can be calculated. There is a ±5%
tolerance taken into account the calculation for each resistor.
These are the calculations for Node 1:
V  18V 15.36V  2.64V
2.64V  0.0012 A  R
2.64V
 2200
0.0012 A
According to the calculations, the best resistor combination for Node 1is one 2200Ω resistor in series.
These are the calculations for Node2:
V  15.36V  13.644V  1.716V
1.716V  0.0012 A  R
1.716V
 1430
0.0012 A
According to the calculations, the best resistor combination for Node 2 is one 330Ω resistor in series with two
2200Ω resistors in parallel.
Req  330  (
1
1

) 1
2200 2200
These are the calculations for Node 3:
V  13.644V  7.248V  6.396V
6.396V  0.0012 A  R
6.396V
 5330
0.0012 A
According to the calculations, the best resistor combination for Node 3 is one 3300Ω resistor in series with two
10kΩ resistors.
1
1 1
Req  330  (

)
10k  10k 
These are the calculations for Node 4:
V  7.248V  1.968V  5.28V
5.28V  0.0012 A  R
5.28V
 4400
0.0012 A
According to the calculations, the best resistor combination for Node 4 is one 3300Ω resistors in series with two
2200Ω resistors in parallel.
Req  3300  (
1
1

) 1
2200 2200
These are the calculations for Node 5:
V  1.968V  0V  1.968V
1.968V  0.0012 A  R
1.968V
 1640
0.0012 A
According to the calculations, the best resistor combination for Node 5 is one 220Ω resistor in series with one
330Ω resistor, and three3300Ω resistors in series.
Req  220  330  (
1
1
1


) 1
3300 3300 3300
4.0 Circuit Diagram
R1=2200Ω
Node 1:
15.36V
R2=330Ω
18V
R5=220Ω
Node 5:
0V
R4=220Ω
Node 2:
13.644V
R6=330Ω
R15=3300Ω
R14=3300Ω
R8=10kΩ
R16=3300Ω
R7=10kΩ
Node 3:
7.248V
R13=330Ω
R9=3300Ω
R12=220Ω
R11=2200Ω
Node 4:
1.968V
Figure 2. Circuit Board Diagram.
R10=2200Ω
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.