EGR 101
LABORATORY 1
APPLICATION OF ALGEBRA IN ENGINEERING
Wright State University
OBJECTIVE: The objective of this laboratory is to illustrate applications of algebra
(lines and quadratics) in engineering. It also provides an introduction to basic
MATLAB functions.
EDUCATIONAL OBJECTIVES:
After performing this experiment, students should be able to:
1. Perform basic algebraic manipulation with linear equations..
2. Perform basic algebraic manipulations with quadratic equations.
3. Measure and understand the relationship between voltage, current and
resistance.
4. Apply basic functions in MATLAB toward the solution of engineering
equations using the command window.
5. Use MATLAB for plotting data.
BACKGROUND:
1. Ohm’s Law:
I
Voltage
Source
+
-
+
R
VR
-
Figure 1: Electrical circuit with a resistive element.
The voltage across a resistor shown in Figure 1 is equal to the product of the
current and the resistance; i.e.,
VR = I * R
(1)
where VR is the voltage across the resistor in volt (V), I is the current flowing
through the resistor in ampere (A), and R is the resistance in ohm (Ω). From
equation (1), we can write
R=
VR
I
2. Kirchoff’s Voltage Law:
The Kirchoff’s voltage law states that the sum of the voltage drops in a
circuit is equal to the sum of the voltage rises, i.e.,
∑(voltage rise)= ∑(voltage drop)
(2)
Therefore, for the circuit shown in Figure 1
V = VR = I * R
3.
BREADBOARD:
A breadboard shown in Figure 2 is a medium to prototype a circuit. Since the
components are not soldered in place, the circuit can be easily changed.
Figure 2: Picture of a breadboard. [zope.interaction-ivrea.it/ inflatedego/BreadBoard]
Inside the breadboard are metal contacts that connect the holes. The
breadboard is used by sticking components into the holes and hence building
the circuit. The internal connections of the breadboard are as shown in Figure
3.
Figure 3: Breadboard Connections
(http://fluffah.phy.uncwil.edu/phy/gan/fizix102labs/breadboard.jpg)
4. PALCEMENT OF METERS:
a) Ammeter:
Ammeter is always connected in series to measure the current flowing
through the circuit as shown in Figure 4.
b) Voltmeter:
Voltmeter is connected in parallel with the element to measure the voltage
across the element as shown in Figure 4.
Voltmeter
The voltmeter is reading the
voltage across R2.
V
Ammeter
Voltage
Source
R1
R2
Ammeter measures the
current through the circuit.
Current through R1 and R2.
+
-
Figure 4: Placement of the ammeter and voltmeter in the circuit
c) Wattmeter:
Wattmeter is used to measure power. The power delivered or absorbed is
given by the basic equation P=VI. Therefore, to measure power, the
voltage and the current across the element needs to be known. This is the
principle that wattmeter uses. Hence, we have four connections to make.
Two connections are used to measure current and two for voltage as shown
in Figure 5. The wattmeter provided has two voltage ranges: 75 V and 150
V. We will use the 75 V range in our experiment.
Voltage
Connection
Voltage
Range dial
Current
Connection
Figure 5: Connection for wattmeter.
5. COLOR CODE OF A RESISTOR:
The color code is used to determine the resistance value of the resistor. There
are 4 bands on the resistor as shown in the Figure 6. The color code for the first
three bands gives the value of the resistance and the fourth band gives the value
of the tolerance. Each color represents a number according to the scheme
shown in Table 1:
Table 1: Resistor Color code.
1
2
3
4
5
6
7
8
9
Number 0
Black Brown Red Orange Yellow Green Blue Violet Grey White
Color
The tolerance given in Table 2 indicates the percentage accuracy of the resistor
value.
Tolerance
Color
±1%
Brown
Table 2: Tolerance values.
±2%
±5%
Red
Gold
Consider the resistor shown in Figure 6
Figure 6: Resistor with four color bands.
First band
Second band
Third band
Last/ Fourth band
– 1st Digit (yellow = 4)
-- 2nd Digit (violet = 7)
– Multiplier (red = * 102)
– Tolerance (gold = ±5% )
Hence the resistor in figure 6 has resistance value of 47 * 102 Ω.
±10%
Silver
PROCEDURE:
I. To calculate the resistance value of the resistor shown in Figure 7, measure
the current and record the value in Table 3.
Ammeter
1000 Ω
Voltage Source
(Vs)
25 V power
supply
output
+
-
I
Figure 7. Circuit for procedure 1.
Note: Current flows from + to –, voltage drop is designated as + to - and voltage
rise is designated as - to +.
Table 3: To calculate the resistance of the circuit shown in Figure 5.
No
Voltage in volt
(VS)
1.
2.
3.
4.
5
12
15
18
Measured
Current in
ampere
Calculated
Resistance
in ohm
1. Vary the voltage of the voltage source in Figure 7 as shown inTable 3.
Measure the value of the current, convert it to amperes and note it down.
2. Calculate the value of resistance in ohms using the following formula:
Vs = I * R
where R is the resistance in ohm, Vs is the applied voltage in volt.
3. Plot the voltage on the Y-axis and current on the X-axis using MATLAB.
(Commands to be used in command window- refer to the appendix.)
4. Find the slope of the graph and write down what the slope signifies.
II. An additional voltage source is added in the circuit of part I as shown in the
Figure 8.
+
VR
Ammeter
1000 Ω
Voltage
Source (Vs)
25 V power
supply
output
+
-
I
+
Additional
voltage
source (V)
6V power
supply
Figure 8. Circuit for procedure 2.
1. Vary the voltage source (Vs) keeping V constant, as shown in Table 4.
2. Measure the value of the current, convert it to amperes and note it down.
3. Calculate the value of resistance for the values of the voltage source
shown Table 4 using the formula
Vs = I * R − V
where R is the resistance in ohm, Vs is the applied voltage in volt, and I is
the current in ampere.
Table 4: To calculate the resistance of the circuit shown in Figure 8.
Sr.
No
Voltage in volt
(VS)
1.
2.
3.
5
7
9
Additional
Voltage source
in volt (V)
6
6
6
Measured
Current in
ampere
Calculated
Resistance in
ohm
4. Plot the data obtained in Table 4 (using Matlab) with voltage on the Yaxis and current on the X-axis. Using the axis properties (under the Edit
tab of the Figure window), change the X-axis limit from -0.015 to 0.015
and the Y-axis from -9 to 9.
5. Extend the plotted line to cut the Y-axis.
6. Find both the slope and y-intercept of the plotted line.
7. Explain the reason of the y-intercept.
III. This part covers the measurement of power dissipated across the load
(resistive load) shown in Figure 9. This part deals with a quadratic equation or
the second order equation.
+
VR
-
Ammeter
10 Ω
Voltage
Source (Vs)
25 V power
supply
output
+
-
I
20 Ω
Wattmeter
Figure 9: Circuit to measure the power dissipation across the load (resistive).
1. Vary the voltage of the voltage source (Vs).
2. Measure the current through ammeter. Convert it to amperes and note it
down in Table 5.
3. Measure the power dissipated across the load (resistive) with the help of a
wattmeter.
4. Now find the value of the current by solving the following quadratic
equation:
P = I * Vs − I 2 * R
where P is the power dissipated across the resistive load in watt (W), Vs is
the applied voltage in volt (V), I is the current in ampere, R is the resistance
in ohm (Ω).
5. Compare the calculated current to the current measured by the ammeter.
Table 5: To compare the current in the circuit shown in Figure 9.
Sr.
No
Voltage in volt
(VS)
1.
2.
3.
5
7
9
Measured
Power in watt
Measured
Current in
ampere
Calculated
Current in
ampere
6. Using MATLAB, plot the power on the Y-axis and measured current on the
X-axis.
LAB NOTEBOOK:
Your lab notebook should contain:
1. Completed tables and all the calculations.
2. Plots for parts I, II and III.
3. Answers to the questions on each plot.
APPENDIX
MATLAB Commands used:
1. clear all :
Removes all the variables from memory.
2. clc :
Clears the command window.
3. disp(‘Text to be displayed on the screen’):
Outputs the text in parenthesis on the screen.
4. V = [1 2 3 4 5]:
Assigns a set of values (example: data you have measured) to variable V.
5. R = 1000;
Assign a value of 1000 to the variable R.
6. I = V/R;
Calculates value of the variable I.
7. plot(V, I):
Plots the graph of V on x-axis and I on y-axis.
The Command window will look as shown below: