Problems With Assistance Module 2 – Problem 3 Go straight to the First Step Filename: PWA_Mod02_Prob03.ppt You can see a brief introduction starting on the next slide, or go right to the problem. Go straight to the Problem Statement Next slide

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

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 This is the material in your circuit texts that you might consult to get more help on this problem. Next slide

Coverage in this Module The material for this problem is covered in this module in the following presentations: DPKC_Mod02_Part01. This is the material in this computer module that you might consult for more explanation. These are presentations of key concepts that you should find in this problem. Next slide

Problem Statement Find the resistance seen at terminals A and B of the circuit below. This is the basic problem. We will take it step by step. Next slide

Solution – First Step – Where to Start? Find the resistance seen at terminals A and B of the circuit below. Try to decide on the first step before going to the next slide. How should we start this problem? What is the first step? Next slide

Problem Solution – First Step Find the resistance seen at terminals A and B of the circuit below. Click on the step that you think should be next. We are asked to find the ratio of voltage to current at the terminals; this is the same thing as the resistance. What is the best first step? Attach a source to the terminals. Define currents and voltages for each of the elements in the circuit. Write a series of KVL and KCL equations. Combine resistors in series and in parallel to simplify the circuit. Perform a delta-to-wye transformation.

Your Choice for First Step – Attach a Source to the Terminals Find the resistance seen at terminals A and B of the circuit given. 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.

Your choice for First Step was – Define Currents and Voltages for each of the Elements in the Circuit Find the resistance seen at terminals A and B of the circuit given. 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.

Your Choice for First Step – Write a Series of KVL and KCL Equations Find the resistance seen at terminals A and B of the circuit given. 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.

Your Choice for First Step Was – Combine Resistors in Series and in Parallel to Simplify the Circuit Find the resistance seen at terminals A and B of the circuit given. 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.

Your Choice for First Step – Perform a Delta-to-Wye Transformation Find the resistance seen at terminals A and B of the circuit given. This is not the best choice for the first step. We could indeed perform a delta-to-wye transformation here. One possible delta configuration is marked in red in the circuit here. However, this transformation is complicated; generally we are best served by avoiding this unless there is no other choice. There is another choice here, combining R4 and R5 in parallel. As we will see, there will be other simplifications to make after that. We recommend that you go back and try again.

Combining Resistors in Series and in Parallel Find the resistance seen at terminals A and B of the circuit given. We have decided to simplify this circuit by combining resistors in series and in parallel. Where should we start this process? Combine R1 and R2 in series. Combine R3 and R4 in series. Combine R1 and R2 in parallel. Combine R4 and R5 in parallel.

You Said that We Should Combine R1 and R2 in Series Find the resistance seen at terminals A and B of the circuit given. 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 are currents through R4 and R5 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 R4 and R5, so R1 and R2 are not in series. This is not a correct step. Go back and try again.

You Said that We Should Combine R3 and R4 in Series Find the resistance seen at terminals A and B of the circuit given. This is not possible. The problem is that R3 and R4 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 R5 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 R5, so R3 and R4 are not in series. This is not a correct step. Go back and try again.

You Said that We Should Combine R1 and R2 in Parallel Find the resistance seen at terminals A and B of the circuit given. 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.

You Said that We Should Combine R4 and R5 in Parallel Find the resistance seen at terminals A and B of the circuit given. This is correct. The resistors R4 and R5 are in parallel. We can see this, since their two terminals are the same. The terminals in this circuit are marked in red. Thus, we find the equivalent circuit, and replace these two resistors with that parallel equivalent. Let’s do this now.

Combining Series Resistors Find the resistance seen at terminals A and B of the circuit given. We have combined the parallel resistors, and replaced them with an equivalent resistor, which we called R6. We assume at this point, that you are getting the idea of how to do these problems. Therefore, without quizzing you, we note that our next step is to combine R3 and R6 in series. Next slide

Combining Parallel Resistors Find the resistance seen at terminals A and B of the circuit given. We have combined the series resistors, and replaced them with an equivalent resistor, which we called R7. At this point, it is probably clear that R2 and R7 are in parallel, so we will replace them with their parallel equivalent. Next slide

Combining Resistors Yet Again Find the resistance seen at terminals A and B of the circuit given. We have combined the parallel resistors, and replaced them with an equivalent resistor, which we called R8. At this point it is clear that the resistance between the terminals A and B, which we will call REQ, is the series combination of R1 and R8, or Go to Comments Slide

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 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.