EGR 101 LABORATORY 1 APPLICATION OF ALGEBRA IN ENGINEERING Wright State University

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1 EGR 101 LABORATORY 1 APPLCATON OF ALGEBRA N ENGNEERNG Wright State University OBJECTVE: The objective of this laboratory is to illustrate applications of algebra (lines and quadratics) in engineering. t also provides an introduction to basic MATLAB functions. EDUCATONAL OBJECTVES: 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: Source R V R 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., V R = * R (1) where V R is the voltage across the resistor in volt (V), is the current flowing through the resistor in ampere (A), and R is the resistance in ohm (Ω). From equation (1), we can write

2 VR R = 2. Kirchoff s 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 = V R = * 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.interactionivrea.it/ inflatedego/breadboard] nside 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.

3 Figure 3: Breadboard Connections ( 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.

4 Source Ammeter Voltmeter V The voltmeter is reading the R 1 R 2 voltage across R 2. Ammeter measures the current through the circuit. Current through R 1 and R 2. c) Wattmeter: Figure 4: Placement of the ammeter and voltmeter in the circuit Wattmeter is used to measure power. The power delivered or absorbed is given by the basic equation P=V. 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. Connection Current Connection Range dial Figure 5: Connection for wattmeter. 5. COLOR CODE OF A RESSTOR: 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:

5 Table 1: Resistor Color code. Number Color Black Brown Red Orange Yellow Green Blue Violet Grey White The tolerance given in Table 2 indicates the percentage accuracy of the resistor value. Table 2: Tolerance values. Tolerance ±1% ±2% ±5% ±10% Color Brown Red Gold Silver Consider the resistor shown in Figure 6 Figure 6: Resistor with four color bands. First band 1 st Digit (yellow = 4) Second band 2 nd Digit (violet = 7) Third band Multiplier (red = * 10 2 ) Last/ Fourth band Tolerance (gold = ±5% ) Hence the resistor in figure 6 has resistance value of 47 * 10 2 Ω.

6 PROCEDURE:. To calculate the resistance value of the resistor shown in Figure 7, measure the current and record the value in Table 3. Ammeter Source (V s ) 1000 Ω 25 V power supply output 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 in volt (V S ) 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: V s = * R where R is the resistance in ohm, V s is the applied voltage in volt. 3. Plot the voltage on the Yaxis and current on the Xaxis 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.

7 . An additional voltage source is added in the circuit of part as shown in the Figure 8. V R Ammeter Source (V s ) 25 V power supply output 1000 Ω Additional voltage source (V) 6V power supply Figure 8. Circuit for procedure Vary the voltage source (V s ) keeping V constant, as shown in Table 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 V s where R is the resistance in ohm, the current in ampere. = * R V V s is the applied voltage in volt, and is Table 4: To calculate the resistance of the circuit shown in Figure 8. Sr. No in volt (V S ) Additional source in volt (V) Measured Current in ampere Calculated Resistance in ohm 4. Plot the data obtained in Table 4 (using Matlab) with voltage on the Y axis and current on the Xaxis. Using the axis properties (under the Edit tab of the Figure window), change the Xaxis limit from to and the Yaxis from 9 to Extend the plotted line to cut the Yaxis. 6. Find both the slope and yintercept of the plotted line. 7. Explain the reason of the yintercept.. 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.

8 V R Ammeter 10 Ω Source (V s ) 25 V power supply output 20 Ω Wattmeter Figure 9: Circuit to measure the power dissipation across the load (resistive). 1. Vary the voltage of the voltage source (V s ). 2. Measure the current through ammeter. Convert it to amperes and note it down in Table 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: 2 P = * Vs * R where P is the power dissipated across the resistive load in watt (W), V s is the applied voltage in volt (V), is the current in ampere, R is the resistance in ohm (Ω). 5. Compare the calculated current to the current measured by the ammeter. Sr. No Table 5: To compare the current in the circuit shown in Figure 9. in volt Measured (V S ) Power in watt Measured Current in ampere Calculated Current in ampere 6. Using MATLAB, plot the power on the Yaxis and measured current on the Xaxis. LAB NOTEBOOK: Your lab notebook should contain: 1. Completed tables and all the calculations. 2. Plots for parts, and. 3. Answers to the questions on each plot.

9 APPENDX 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 = [ ]: 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. = V/R; Calculates value of the variable. 7. plot(v, ): Plots the graph of V on xaxis and on yaxis. The Command window will look as shown below: