FUNDAMENTAL OF ELECTRICAL ENGINEERING LABORATORY

DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLAGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING FUNDAMENTAL OF ELECTRICAL ENGINEERING LABORATORY 1 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING LAB REPORT GUIDELINES Welcome to Fundamental of Electrical Engineering Labs here at the University of Bahir Dar . As your Teaching Assistant for labs, I want to help you understand Fundamental of Electrical Engineering. Why? Because, not only do I love Electrical Engineering, but I also love teaching it to others. Regarding the labs; they are wonderful from the standpoint of being able to provide accurate and reproducible experiments that demonstrate fundamental properties of Electrical Engineering. If you follow the instructions in the lab book precisely, you’re almost assured of highly accurate results. However, sometimes the MEANING of what the experiments represent is lost on students, precisely BECAUSE the experiments, in an attempt to make the labs so precise, have become somewhat convoluted. This is why I usually take a few minutes to explain what the underlying Electrical Engineering principles are, as well as how they are being shown in a particular experiment. If I write comments on your paper, think about what those comments mean; if you’re not sure, ask. I want you to be a better writer, and have a better understanding of the material. Part the process of helping you understand what’s going on is writing the lab reports. This is because one of the best ways to learn something is to have to explain it to someone else. Below are some guidelines for the process of writing up your lab reports. I discuss the labs report section by section you should break your lab report up into the same sections I have used below. In general, lab reports should be typed (an optional exception is the calculations section), neat, and easy to read  PURPOSE AND METHOD: This is the most important portion of the lab report, and consequently has the most points assigned to it. In this section you should show me that you understood what the purpose of the lab was, and what the underlying Electrical Engineering principles were. As a hint, the purpose of the lab experiment is usually to verify a particular law or relationship Electrical Engineering. The purpose of a lab report is almost NEVER the purpose stated in the lab manual. On a related note, do not copy from the lab manual or any other sources. I consider this plagiarism, and if I am feeling benevolent, I will merely assign a grade of zero for the purpose and method section. If I am not feeling benevolent, or you’ve made a habit of copying from other sources, I’ll make the entire grade zero. Using your own words is important, because it is the process of restructuring and rephrasing the material covered in the lectures and manual that helps you understand the material. If you need help understanding what was happening, feel free to email me, come by my office or lab, or get help in the tutoring center, but do NOT copy material wholesale. The lab report, in addition to explaining the major goal of the experiment, should discuss any potential errors and how you accommodated for them. Most people find they can discuss these concepts adequately in 1 or at most 2 pages. Occasionally, someone will be able to convey the information succinctly enough to adequately demonstrate their understanding of the material in a few paragraphs, but this isn’t common, and I recommend you take the approach of explaining the basic concepts and procedure as though you were explaining them to a friend. This means that you should discuss WHAT the law in question was, WHAT you expected to see, and HOW you checked for that result. This does NOT mean that you should explain every 2 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING nuance of the lab such as what information was typed into Excel. Remember you’re trying to show me that you understand the fundamental concepts , not that you know what numbers to enter. If you don’t know the meaning of a word or concept, look it up. There are numerous online references that can help you with definitions, concepts, and writing skills. Remember, success in any endeavor is partly based upon you ability to communicate your ideas to other people. While I do not require you to include diagrams of your experimental setup, you are welcome to if you like. However, they should be follow conventions where appropriate (especially for any sort of circuit diagram). They should also be (like the writing) your own work, not something you copied, photocopied, or scanned out of the lab manual.  DATA AND GRAPHS: This section is just the printout and/or photocopies of your lab data and results. This is supposed to be any easy few points, the only way you can get marked off here is if you didn’t come to lab, or your printout is so difficult to read that I quit trying, or if you results were so far outside the acceptable error that the results don’t even indicate the basic premise of the experiment. Do not ever submit original material; in the unlikely event that I lose your lab report, this provides proof that you actually did conduct the lab. All of the data, axis, etc. should be labeled clearly, with units as appropriate. A given set of data or graph should NOT hang over multiple pages. You may have to do some manipulating on the computer to get this to print out correctly. Any graphs should also have the data taking up most of the space on the graph; you may have to alter the default maximum and minimum scale values in order to do this.  CALCULATIONS: In this section, you should include EVERY formula you used in the process of analyzing your data. In addition, you should include one sample calculation, using YOUR data that you acquired during the experiment. The purpose of this is to make sure that you understand what the formulas were and how they were applied (rather than just taking the results from Excel for granted). Additionally, if you have made a mistake entering your formulas in Excel, you may discover it when you calculate the answer by hand. This section is just few point. It should be quick and painless.  CONCLUSIONS: This is the second most important section of the lab report. Here you should restate the basic premise of the lab, and whether or not your results were in agreement with the theory. For most labs, I’ll assign a “standard error” value, based on what I expect the standard deviation for the experiment to be (either by calculating the various experimental uncertainties or based on the error *I* got, whichever is greater). If your percent error is within the standard deviation, then your results agree with the theory within the bounds of the experimental uncertainty, and you merely need to recap the basic premise and your agreement with theory. If you results do not agree within the standard error, but are within double the standard error, then you must include an error analysis section where you explain probable sources for error. If you adequately explain your error, you still receive full credit for the experiment. Please note, however, that your 3 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING sources of error must also make sense. I’ll mark off one point from your “DATA” section, but I still expect to see an explanation. If your explanation is reasonable, you’ll still get full credit on the CONCULSIONS section. Lab # 1: RESISTORS AND THE RESISTOR COLOR CODE  Theory: An important lesson to learn in electronics is how to read the color codes for resistors. If you plan a career in electronics, it will be a big help to memorize the color code, and the technique for calculating the resistor value. This essay will teach you how to read resistor color codes. Reading the resistor color code is easy with a little practice. Most resistors have four color bands, while some have five bands. The chart below (Figure 1) shows the color codes and their respective values depending on which band they fall on. The resistor value is decoded by reading the colors from left to right. The tricky part is determining which the left side is and which the right side is. Do this by finding the gold or silver band which is always on the right side. Then start reading the resistor colors from the left. Look at a common 1K resistor. From left to right, a 1K resistor will have brown-black-red-gold Looking at Figure 1, this decodes respectively to 1 - 0 - x100 - ±5%. Take the first and second significant digits together to be 10. Then multiply by the multiplier 100. That gives you 1000 ohms as the resistor value, which is 1K. So what's with the ±5? The tolerance band tells us that the measured resistance can be off by plus or minus 5%. So the actual measured resistor value could be anywhere from 950 ohms to 1050 ohms. Now look at a 27K resistor. Again from left to right it reads red-violet-orange-gold which translates to 2-7-x1000-±5. So this would be 27 x 1000 = 27000 ohms which is 27K. The fifth band is rarely used on resistors, but is included in the color code chart so that you have a more complete reference. The fifth color band signifies the rate at which the resistor fails when operating at its full rated wattage. It is read as a percentage failure per 1000 hours. For practice, try reading color codes from resistors with unknown values. Try to figure out what the resistor value should be from the color code. Then measure the resistor with an ohmmeter or multimeter to see if you got it right. With some practice, you will be able to pick out common resistors from a box of spare parts just by glancing at the color bands. 4 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING Color Digits Multiplier Tolerance Thermal Coefficient Black 0 1 Brown 1 10 1% 100ppm Red 2 100 2% 50ppm Orange 3 1k 15ppm Yellow 4 10k 25ppm Green 5 100k 0.5% Blue 6 1M 0.25% Violet 7 10M Gray 8 White 9 Gold 5% Silver 10% Figure 1: Resistor color coding To understand the numbering skims, look the example shown below: 6-band color code 5-band color code 3 digits, multiplier, tolerance, 3 digits, multiplier, tolerance thermal coefficient 4-band color code 2 digits, multiplier, tolerance Enter all the color bands. Select None for field 6. Select None for fields 3 and 6. 5 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING Finally you can see the normal designation as shown in the table below: Band designation for the Resistor Color Codes First Band Second Band Third Band Fourth Band First Significant Figure Second Significant Figure Multiplier Tolerance (%) Black Brown Red Orange Yellow Green Blue Violet 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Gray 8 8 - - - White 9 9 - - - Gold - - - ±5 Silver - - - ± 10 No Color - - - ± 20 Color x 1 = 100 x 10 = 101 x 100 = 102 x 1000 = 103 x 10000 = 104 x 100000 = 105 x 1000000 = 106 x 10000000 = 107 Fifth Band Fail Rate (% per 1000 hrs) 1.0 0.1 0.01 0.001 6 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING  Objectives:  To study various types of resistors used in electrical circuit and codes.  To study ohmmeter and their use in determining resistor.  To determine the ohmic value, tolerance, and reliability of carbon compositions resistors using color code  To study relation between wattage and resistance of a resistor and determine their resistance value.  Materials Required: 1. Ohmmeters 2. Different color-coded resistors 3. Circuit construction board 4. Probes (connecting wires) if it is needed.  Procedure: 1. Arbitrarily assign numbers for each resistor 2. Comfortably mount each resistors on the circuit construction board 3. Record the color of each band for resistor # 1 in the appropriate horizontal columns in Data table 1-1 then indicate the resistors color-coded ohmic value in vertical column labeled Res (ohms) 7 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING 4. Calculate the resistors upper and lower tolerance limit and record in the appropriate vertical columns. Show a sample calculation. 5. Measure the ohmic value of # 1 resistor using ac ohmmeters properly and record in vertical column labeled meas (ohm). 6. When applicable record the resistors reliability in the last vertical column. 7. Repeat steps 2-6 for each of the remaining resistors. Data Table 1-1: Color Code No 1st 2nd 3rd 4th Calculated 5th Res (Ω) Tol. (%) Meas. Upper Lower Res limit limit (Ω) 1 2 3 4 5 6 7 8 9 10  Review Questions: 1. Predict the color coding of .870 Ω, 9.2 Ω and 0.50 Ω resistors. 2. Differentiate the reliability and tolerance of a carbon composition resistor? 3. Compare the Res (ohm) and the Meas. (ohm) column from the Data-table and come to a conclusion. 8 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING 4. How does the physical size of a resistor relate to its wattage rating? 5. Discuss the effect of temperature on the resistance. BAHIR DAR UNIVERSITY ENGINEERING FACULTY DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING FUNDAMENTAL OF ELECTRICAL ENGINEERING LABORATORY LABORATORY #2: RESISTORS IN SERIES, IN PARALLEL AND BOTH COMBINATIONS 9 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING Lab # 2: RESISTORS IN SERIES, IN PARALLEL AND BOTH COMBINATIONS:  Theory:  Series circuits A series circuit is a circuit in which resistors are arranged in a chain, so the current has only one path to take. The current is the same through each resistor. The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors: Equivalent resistance of resistors in series: R = R1 + R2 + R3 + ...  Parallel circuits A parallel circuit is a circuit in which the resistors are arranged with their heads connected together, and their tails connected together. The current in a parallel circuit breaks up, with some 10 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING flowing along each parallel branch and re-combining when the branches meet again. The voltage across each resistor in parallel is the same. The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the 1 1 1 1 total: Equivalent resistance of resistors in parallel:     ... R R1 R2 R3  Most electronic circuits consist of combination of series and parallel circuits called seriesparallel circuits. When dealing with these circuits it is necessary to reduce each combination to an equivalent resistance. These are then added to the series elements in the circuit to determine the total resistance.  Objectives :  To study series, parallel and series -parallel circuit connection of the resistors in an electrical circuit.  Determination of equivalent resistance of a series, parallel and series parallel circuit and to verify the result by theoretical calculation.  Materials Required :  Resistors different value  Circuit construction board  Digital Multimeter  Connecting wires 11 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING  Procedure (a): Construct the series circuit shown in figure a & figure b. R1=330Ω R2=470Ω R3=100Ω Figure a R1=2.2K R2=10K R3=1K R4=100K Figure b a. Calculate the circuit’s total resistance (RT) and record in a proper table. b. Measure the circuit’s resistance and record in the same table. c. Calculate the percentage difference b/n calculated and measured values of RT and record in the same table. Show your calculation. d. Remove the components for the circuit in figure a from your board and construct the series circuit shown in figure b. e. Repeat steps a-c above.  Procedure (b): 1. Construct the parallel circuit shown in figure a . 12 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING R2=100K R1=10K R1=10K R2=20K R3=30K R4=60K R5=40K RT Figure a Figure b 2. Calculate the circuit’s total resistance (RT) and record in the proper table. Show your calculation. 3. Measure the circuit’s resistance and record in the same table. 4. Calculate the percentage difference between calculated and measured values or R T and record in the same table. Show your calculation. % difference  calculated Rt  MeasuredRT Calcualted RT 5. Remove circuit figure a from your board and construct the parallel circuit shown in figure b. 6. Repeat steps 2-4 above.  Procedure (c): 1. Construct the serious parallel circuit as shown below figure a. 13 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING 300Ω D E A 100 Ω 47Ω 800Ω 400Ω RT F C B Figure a. R1 =220Ω R8=200Ω R4=1K R9=300Ω R5=22K B A C D R7=400Ω R3=47Ω E R10=400Ω R6=47K F R11=600 Ω R2= 100Ω Figure b. 2. Calculate the equivalent resistance at each junction in figure a. and record the result in the appropriate columns in data table 2.1. Calculate also the total resistance and record in the same data table. Show your calculations. 3. Measure the equivalent resistance at each junction and the total circuit resistance for figure a and record in the appropriate columns in data table 2.1. 4. Remove circuit figure a from your board and construct the circuit shown in figure b. 5. Calculate the parallel resistances (Ra-b, Rc-d and Re-f ) and the total circuit resistance and record this data in the appropriate column in data table 2.2. Show your calculation. 6. Measure the parallel resistance (Ra-b, Rc-d and Re-f ) & the total circuit resistance and record in the appropriate column in data table 2.2. 7. Calculate the difference between the measured and calculated values. 14 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING  Data Table 2.1: Series Branch Circuit Junction A-B R Calculated R measured %diff C-D E-F Parallel Branch A-B C-D E-F  Data Table 2-2: RA-B Calc: Meas: R C-D Calc: Meas: R E-F Calc: Meas: RT Calc: Meas:  Review Question: 1. What do you understand from the above experiments? 2. If you want to get the smallest resultant resistance from two or more resistances, which type of connection, do you choose? 3. If you want to get the largest resultant resistance from two or more resistances, which type of connection, do you choose? 4. Describe the advantage & disadvantage of series connection. 5. Describe the advantage & disadvantage of paralle1 connection. 6. Is the real world load purely series, parallel or series-parallel type. 15 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING BAHIR DAR UNIVERSITY ENGINEERING FACULTY DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING FUNDAMENTAL OF ELECTRICAL ENGINEERING LABORATORY LABORATORY #3: OHM’S LAW 16 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING Lab # 3: OHM’S LAW  Theory: The rate of flow of electricity in a given circuit is called current, denoted as I, the potential difference between the starting and the ending points of the circuit is known as the voltage denoted as V and the opposition to the flow of current is called resistance, denoted as R. According to Ohms law the ratio, V and I is always a constant factor for a particular conductor when the temperature, length, and conductor material is kept constant. This constant is called the Resistance that is characteristic of the conductor used. This is denoted by the formula Voltage V  cons tan t ; R Current I The unit of EMF is Volts, the unit of Current is Amperes and the unit of Resistance is Ohms. Electricity is measured in these units. Ohms law has wide applications in electrical circuits obeying Kirchhoffs Laws, heat generation, Chemical analysis deposits, and most importantly for deriving Light energy. V since the current flow is a steady one, but for AC, the I current flow is a fluctuating one with some frequency, in such case the frequency is also taken into consideration, here the Resistance of the circuit is called the Impedance represented by Z. Ohms Law applies to the conductors whose resistance is independent of voltage. When an I,V graph is drawn, it is seen the Ohms law is obeyed in the linear portion for ohmic resistors, for non-ohmic resistance substances the I,V graph is bent and curved, showing negative resistance properties like incandescent lamps where more voltage is applied, more heat is generated and the resistance rises. Ohms Law for DC circuits is  R Objectives:  To study ohm’s law and prove experimentally that current is proportional to the voltage across a dc circuit and to show that the proportionality constant is equal to the resistance of the circuit.  To study relation between current and resistance in a dc & AC circuits for various voltages across the circuit. 17 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING  Materials and Equipment: 1. Digital Voltmeters dc and Ac 2. DC Power supply 3. Resistors variable in size 4. Circuit construction board 5. Connecting wires  Procedure: 1. Adjust the power supply to deliver 1V (or as close as possible) use separate dc voltmeters for this adjustment. A A +10V dc R V AC f=1KHz R V -10V Figure a Figure b 2. Construct the dc circuit shown in diagram Figure a, and connect it to the 1V power supply. 3. Measure the voltage drop across R1 (VR1) and record in data table 3.1 in the appropriate column and record IT from the ammeter in IT (meas.) column. 4. Calculate IT and record in the appropriate column in data table 3.1. Show your calculation. 5. Repeat step 3 and 4 by increasing the power supply in steps of one volt 6. Substitute the values of R1 in data table 3.4 and calculate the corresponding circuit currents & record this information in the appropriate column in data table 3.4 7. Read the corresponding circuit current (IT meas) and record this reading in the last column in data table 3.4. 8. Repeat the steps 1-7 for the AC circuit shown in figure b.  Data Table 3.1: Source voltage VR1 IT (calc.) IT (meas.) 18 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING 1 2 3 4 5 6 7 8  Data Table 3.2: R1 IT (calc.) IT ( meas) 220 330 470 1k 1.2k 2.2k 4.7k  Review Question: 1. Draw the graph of IT Vs VRT (calc.) on a millimeter paper. 2. Draw the graph of IT Vs VRT (meas) on a millimeter paper. 3. What do you understand from your graph? 4. Does the graph linear or non linear? 5. If the graph is linear, what is the corresponding parameter in IT Vs VRT.. 6. Discuss the difference between your results when you use the dc & AC sources. 7. Conclude any other relevant points based on this experiment. 19 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING BAHIR DAR UNIVERSITY ENGINEERING FACULTY DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING FUNDAMENTAL OF ELECTRICAL ENGINEERING LABORATORY LABORATORY #4: NETWORK ANALYSIS USING KIRCHOFF’S THEOREM 20 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING Lab # 4 : NETWORK ANALYSIS USING KIRCHOFF’S THEOREM  Theory:  We will see the two basic Kirchoff’s law in the laboratory.  Kirchoff’s Voltage Law ( KVL) : This law states that the algebraic sum of the voltage in any closed loop is always zero. That means , SumVoltage drops in the loop  Sum of voltage rises in the loop  Kirchoff’s Current Law (KCL) : This law states that the algebraic sum of the current at any junction, area ,distribution is always zero. That means , Sum current entering the junction  Sum of current leaving the junction  Objectives:  To study the use of Kirchoff’s laws in analyzing current distribution in an electrical circuit.  To analyze the current distribution to find voltage drop across the various components of an electrical circuit and to verify the results by calculation.  Materials Required: 1. Resistors variable in size 21 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING 2. Circuit construction board 3. Digital Voltmeter 4. Connecting wires  Procedure: 1. Construct the circuit as shown below in figure a on the circuit construction board. A A R1=100Ω R2=200Ω V2=24V V1=10V R3=400Ω A R4=50Ω R5=300Ω Figure a 2. Measure the voltage drops across and the current through each resistors and record in data table 4.1 3. By applying Kichoff’s voltage & current law, calculate the current distribution and the voltage drop across each circuit element. Show all steps in your calculation. 4. Put your calculated values in data table 4.1 5. Reverse the polarity of the 10V source and repeat steps 2-4 & Record your data in data table 4.2.  Data table 4.1 : VR1 IR1 VR2 IR2 IR1 VR2 IR2 VR3 IR3 VR4 IR4 VR5 IR5 IR3 VR4 IR4 VR5 IR5 Measured Calculated  Data Table 4.2: VR1 VR3 Measured Calculated  Review Question: 22 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING 1. How do the calculated values correspond to the measured values? Are there differences? If there are any, analyze the difference. 2. Check that the algebraic sum of the currents at any node is zero. 3. Check that the algebraic sum of the voltages for any closed loop is zero. 4. State important conclusions from this experiment. BAHIR DAR UNIVERSITY ENGINEERING FACULTY DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING FUNDAMENTAL OF ELECTRICAL ENGINEERING LABORATORY LABORATORY #5: 23 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING NETWORK ANALAYSIS USING SUPERPOSITION THEOREM Lab # 5: NETWORK ANALAYSIS USING SUPERPOSITION THEOREM  Theory: Superposition theorem is one of those strokes of genius that takes a complex subject and simplifies it in a way that makes perfect sense. The strategy used in the Superposition Theorem is to eliminate all but one source of power within a network at a time, using series/parallel analysis to determine voltage drops (and/or currents) within the modified network for each power source separately. Then, once voltage drops and/or currents have been determined for each power source working separately, the values are all “superimposed” on top of each other (added algebraically) to find the actual voltage drops/currents with all sources active; i.e, The current through or voltage across any element of a linear, bilateral network is the algebraic sum of the currents or voltages separately produced by each source of energy.  Objective: 24 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING  To study circuit analysis using superposition theorem  Equipment required:  Electricity & Electronics construction board  Resistors variable in size  DC power supply unit  Dc regulator if any  Digital Multimeter  Connecting wires  Procedure:  PART a:- Calculated values 1. Construct the circuit shown in figure a below. I1 I2 R1=100Ω R2=200Ω I3 V2=24V V1=10V R3=400Ω R4=50Ω R5=300Ω Figure a 2. Calculate the current I1' , I 2 ' & I 3' and the voltage V1’ ,V2’ & V3’ across each resistor using ohm's (Kirchoff’s) law for the source V1 by using the diagram shown below. R1=100Ω I2’ I1’ R2=200Ω I3’ V1=10V R3=400Ω R4=50Ω Figure a-1 R5=300Ω 25 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING 3. Calculate the currents I1" , I 2" & I 3" & the voltage V1”,V2” & V3” across each resistor using ohm's (Kirchoff’s) law for the source voltage V2 using the diagram shown below. I2” I1” R1=100Ω R2=200Ω I3’ V2=24V R3=400Ω R4=50Ω R5=300Ω Figure a-2 4. Determine I1, I2, and I3 and the voltage drops V1,V2 & V3 for the network of figure a using the calculated results of steps 2 & 3 above & show the real direction of the resultant currents on figure a. 5. Using the above result, calculate the power dissipated by each resistor. & record all results in data table shown  Table a: Calculated values I1 , I1" I1 I2 , I2 " I2 I3 , I3 " I3 V1, V1" V1 V2, V2" V2 V3, V3" V3 P1 , P1 " P1 P2 , P2 " P2 P3 , P3 " P3  PART b:- Measured values: 2. Construct the network of figure a shown below and measure the voltages V1, , V2,, and V3, compare these results with the results of part a . 26 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING I1 I2 R1=100Ω R2=200Ω I3 V2=24V V1=10V R3=400Ω R4=50Ω R5=300Ω Figure a 3. Construct the network of figure a-1 and measure the currents I1" , I 2" & I 3" & the voltage V1”,V2” & V3” across each resistor compare these results with the result of part a. I2’ I1’ R1=100Ω R2=200Ω I3’ V1=10V R3=400Ω R4=50Ω Figure a-1 R5=300Ω 4. Construct the network of figurea-2 and measure the currents I1" , I 2" & I 3" & the voltage V1”,V2” & V3” across each resistor compare the results with the result of part a. R1=100Ω I2” I1” R2=200Ω I3’ V2=24V R3=400Ω R4=50Ω Figure a-2 R5=300Ω 5. Determine I1, I2, and I3 and the voltage drops V1,V2 & V3 for the network of figure a using the measured results of steps 3 & 4 above & compare the results with part a.  Table b: Measured values 27 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING I1 , I1" I1 I2 , I2 " I2 I3 , I3 " I3 V1, V1" V1 V2, V2" V2 V3, V3" V3 P1 , P1 " P1 P2 , P2 " P2 P3 , P3 " P3  Conclusive Question  Compare the measured and calculated values for currents through & voltages across all elements and give a brief conclusion on Superposition theorem.  Discus the advantage of this theorem over other theorems ( such as nodal & loop analysis technique)  Where & when you chose this theorem & Why? 28 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING BAHIR DAR UNIVERSITY ENGINEERING FACULTY DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING FUNDAMENTAL OF ELECTRICAL ENGINEERING LABORATORY LABORATORY #6: NETWORK ANALYSIS USING THEVENIN’S THEOREM 29 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING Lab # 6 : NETWORK ANALYSIS USING THEVENIN’S THEOREM  Theory: Thevenin's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load. The qualification of “linear” is identical to that found in the Superposition Theorem, where all the underlying equations must be linear (no exponents or roots). If we're dealing with passive components (such as resistors, and later, inductors and capacitors), this is true. However, there are some components (especially certain gas-discharge and semiconductor components) which are nonlinear: that is, their opposition to current changes with voltage and/or current. As such, we would call circuits containing these types of components, nonlinear circuits. Thevenin's Theorem is especially useful in analyzing power systems and other circuits where one particular resistor in the circuit (called the “load” resistor) is subject to change, and re-calculation of the circuit is necessary with each trial value of load resistance, to determine voltage across it and current through it. Thevenin's Theorem makes this easy by temporarily removing the load resistance from the original circuit and reducing what's left to an equivalent circuit composed of a single voltage source and series resistance. The load resistance can then be re-connected to this “Thevenin equivalent circuit” and calculations carried out as if the whole network were nothing but a simple series circuit.  Objectives:  To study the use of Thevenin’s theorem in simple type of analyzing a dc circuit.  To determine Thevenin’s equivalent of an electric circuit.  To use Thevenin’s theorem and determine current through various branches of a circuit and to verify the results theoretically.  Material Required: 1. Resistors variable in size 2. DC power supply unit 3. Circuit construction board 4. Digital multimeter 5. Connecting wires 30 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING  Procedure: 1. Construct the circuit shown below. A A R2=50Ω R1=100Ω A RL V2=24V R3=400Ω R4= 300Ω Figure a B 2. For the figure shown above calculate the values of VTH and RTH by using Thevenin’s theorem. 3. Measure the open circuit voltage VAB and record this as VTH . 4. Replace the source with short circuit, and measure the resistance between the terminals A and B & record this as RTH. 5. Calculate the voltage across and current through a 200 load that is to be placed across the terminals A and B & record this as VRL (calc.) and as IRL (calc.) respectively. 6. Measure the voltage across and current through a 200 load that is to be placed across the terminals A and B by using a digital voltmeter & record this in the appropriate column. 7. Repeat the steps 2-6 for the rest resistor values in the data table given below. RL RTH (calc) RTH (Meas) IRL (calc.) IRL (meas) VRL (calc)VRL (meas) VRL (meas) 200Ω 1k 220 31 DEBRE MARKOS UNIVERSITY TECHNOLOGY COLLEGE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING  Conclusive questions : 1. When would you use Thevenin’s and Norton’s equivalents circuit analysis? 2. Compare this theorem with the pervious theorems. 3. Measure the value of load resistance required to transfer maximum power to the load. 32