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Dave Shattuck University of Houston © Brooks/Cole Publishing Co. Problems With Assistance Module 2 – Problem 2 Filename: PWA_Mod02_Prob02.ppt Go straight to the First Step Go straight to the Problem Statement Next slide Dave Shattuck University of Houston © Brooks/Cole Publishing Co. Overview of this Problem In this problem, we will use the following concepts: • Equivalent Circuits • Series and Parallel Combinations of Resistors Go straight to the First Step Go straight to the Problem Statement Next slide Dave Shattuck University of Houston © Brooks/Cole Publishing Co. Textbook Coverage The material for this problem is covered in your textbook in the following chapters: • Circuits by Carlson: Chapter 2 • Electric Circuits 6th Ed. by Nilsson and Riedel: Chapter 3 • Basic Engineering Circuit Analysis 6th Ed. by Irwin and Wu: Chapter 2 • Fundamentals of Electric Circuits by Alexander and Sadiku: Chapter 2 • Introduction to Electric Circuits 2nd Ed. by Dorf: Chapter 3 Next slide Dave Shattuck University of Houston © Brooks/Cole Publishing Co. Coverage in this Module The material for this problem is covered in this module in the following presentations: • DPKC_Mod02_Part01. Next slide Dave Shattuck University of Houston Problem Statement © Brooks/Cole Publishing Co. Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] R3= 150[W] A R2= 300[W] R4= 100[W] B Next slide Dave Shattuck University of Houston Solution – First Step – Where to Start? © Brooks/Cole Publishing Co. Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] R3= 150[W] A R2= 300[W] R4= 100[W] B How should we start this problem? What is the first step? Next slide Dave Shattuck University of Houston Problem Solution – First Step © Brooks/Cole Publishing Co. Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] R3= 150[W] A R2= 300[W] R4= 100[W] B Problems such as this one ask us to analyze a part of a circuit, one that is probably going to be connected to sources in some way in the future. We are asked to find the ratio of voltage to current at the terminals; this is the same thing as the resistance. How should we start this problem? What is the first step? 1. Attach a source to the terminals. 2. Define currents and voltages for each of the elements in the circuit. 3. Write a series of KVL and KCL equations. 4. Combine resistors in series and in parallel to simplify the circuit. Dave Shattuck University of Houston © Brooks/Cole Publishing Co. Your Choice for First Step – Attach a Source to the Terminals Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] R3= 150[W] A R2= 300[W] R4= 100[W] B This is not the best choice for the first step. We could indeed apply a source, with the intention of then finding the ratio of the voltage at the terminals to the current through the terminals. This ratio would be the resistance. However, this would require solving the circuit, and we can do the problem more easily. Go back and try again. Dave Shattuck University of Houston Your choice for First Step was – © Brooks/Cole Publishing Co. Define Currents and Voltages for each of the Elements in the Circuit Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] R3= 150[W] A R2= 300[W] R4= 100[W] B This is not the best choice for the first step. In general, we do like to define currents and voltages. However, if it is clear that we are not going to be using the variables we define, then this is not a good use of our time. In this problem, there is a better approach. At some point we will need to define variables, but it is best to wait until you have a good idea of which ones you need. Go back and try again. Dave Shattuck University of Houston Your Choice for First Step – Write a Series of KVL and KCL Equations © Brooks/Cole Publishing Co. Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] R3= 150[W] A R2= 300[W] R4= 100[W] B This is not the best choice for the first step. We could indeed write a set of KVL and KCL equations, once we had defined voltages and currents. However, without sources all voltages and currents would be zero. The only way to meaningfully do this would be to apply a source, and then solve for the ratio of voltage to current at the terminals. There is a better approach. Go back and try again. Dave Shattuck University of Houston Your Choice for First Step Was – Combine Resistors in Series and in Parallel to Simplify the Circuit © Brooks/Cole Publishing Co. Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] R3= 150[W] A R2= 300[W] R4= 100[W] B This is the best choice for the first step. The goal is to simplify the circuit, to make the solution easier and faster. Since all we really need in this problem is the current through the voltage source, we can get this by converting the circuit connected to the source to a single resistor. We can do with using equivalent circuits, specifically by repeatedly combining resistors in series and parallel. Let’s begin that process. Dave Shattuck University of Houston © Brooks/Cole Publishing Co. Combining Resistors in Series and in Parallel Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] R3= 150[W] A R2= 300[W] R4= 100[W] B We have decided to simplify this circuit by combining resistors in series and in parallel. Where should we start this process? a) Combine R1 and R2 in series. b) Combine R3 and R4 in series. c) Combine R1 and R3 in series. d) Combine R1 and R2 in parallel. e) Combine R2 and R4 in parallel. Dave Shattuck University of Houston © Brooks/Cole Publishing Co. You Said that We Should Combine R1 and R2 in Series Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] R3= 150[W] A R2= 300[W] R4= 100[W] B This is not possible. The problem is that R1 and R2 are not in series. To be in series, they would need to have the same current through them, and they do not. There is a current through R3 that prevents this. Do not be confused by the fact that at present, with no source, all currents are zero. Remember that we are assuming that a source will be applied later. When it is, there will be a current in R3, so R1 and R2 are not in series. This is not a correct step. Go back and try again. Dave Shattuck University of Houston © Brooks/Cole Publishing Co. You Said that We Should Combine R3 and R4 in Series Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] R3= 150[W] A R2= 300[W] R4= 100[W] B This is correct. The resistors R3 and R4 are in series. They can be combined, and replaced by a resistor with the value (R3 + R4). Let’s redraw this circuit and look for the next step. Dave Shattuck University of Houston © Brooks/Cole Publishing Co. You Said that We Should Combine R1 and R3 in Series Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] R3= 150[W] A R2= 300[W] R4= 100[W] B This is not possible. The problem is that R1 and R3 are not in series. To be in series, they would need to have the same current through them, and they do not. There is a current through R2 that prevents this. Do not be confused by the fact that at present, with no source, all currents are zero. Remember that we are assuming that a source will be applied later. When it is, there will be a current in R2, so R1 and R3 are not in series. This is not a correct step. Go back and try again. Dave Shattuck University of Houston You Said that We Should Combine R1 and R2 in Parallel © Brooks/Cole Publishing Co. Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] R3= 150[W] A R2= 300[W] R4= 100[W] B This is not possible. The problem is that R1 and R2 are not in parallel. To be in parallel, they would need to have the same voltage across them, or have their two terminals connected together. They do not, since terminal A is not connected to terminal B. Do not be confused by the fact that at present, with no source, all voltages are zero. Remember that we are assuming that a source will be applied later. When it is, there will be different voltages across R1 and R2. This is not a correct step. Go back and try again. Dave Shattuck University of Houston You Said that We Should Combine R2 and R4 in Parallel © Brooks/Cole Publishing Co. Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] R3= 150[W] A R2= 300[W] R4= 100[W] B This is not possible. The problem is that R2 and R4 are not in parallel. To be in parallel, they would need to have the same voltage across them, or have their two terminals connected together. They do not, since R3 is between two of the terminals. Do not be confused by the fact that at present, with no source, all voltages are zero. Remember that we are assuming that a source will be applied later. When it is, there will be a voltage across R3, so R2 and R4 are not in parallel. This is not a correct step. Go back and try again. Dave Shattuck University of Houston Combining Series Resistors © Brooks/Cole Publishing Co. Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] A R2= 300[W] R5= 250[W] B We have combined the series resistors, and replaced them with an equivalent resistor, which we called R5. Our next step is to combine R2 and R5 in parallel. Next slide Dave Shattuck University of Houston Combining Parallel Resistors © Brooks/Cole Publishing Co. Find the resistance seen at terminals A and B of the circuit below. R1= 200[W] A R6= 140[W] B We have combined the parallel resistors, and replaced them with an equivalent resistor, which we called R6. Remember to use the parallel combination rule for this step. At this point, it is probably clear that R1 and R6 are in series. Next we will replace R3 and R8 with their series equivalent. Next slide Dave Shattuck University of Houston © Brooks/Cole Publishing Co. Combining Resistors Yet Again Find the resistance seen at terminals A and B of the circuit below. A R7= 340[W] B We have combined the series resistors, and replaced them with an equivalent resistor, which we called R7. At this point it is clear that the resistance between the terminals A and B, which we will call REQ, is just R7, or REQ R7 340[W]. Go to Comments Slide Dave Shattuck University of Houston © Brooks/Cole Publishing Co. What if I chose another method? • If you picked another method, such as writing a set of equations using KVL and KCL, it requires that attach a source. Otherwise all currents and voltages will be zero. While this can be done, we still recommend that you learn the approach we have taken here to solving these circuits. There are many ways in which equivalent circuits can help us, and they are crucial tools. They are worth the time it take to understand them. Go back to Overview slide.