Filename PWAMod 04Prob 02 ppt Find the Thvenin

Filename: PWA_Mod 04_Prob 02. ppt Find the Thévenin Equivalent of the circuit at terminals A and B. Problems With Assistance Module 4 – Problem 2 Go straight to the First Step Go straight to the Problem Statement Next slide

Overview of this Problem In this problem, we will use the following concepts: • Equivalent Circuits • Thévenin’s Theorem 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 sections: • Circuits by Carlson: Sections #. # • Electric Circuits 6 th Ed. by Nilsson and Riedel: Sections #. # • Basic Engineering Circuit Analysis 6 th Ed. by Irwin and Wu: Section #. # • Fundamentals of Electric Circuits by Alexander and Sadiku: Sections #. # • Introduction to Electric Circuits 2 nd Ed. by Dorf: Sections #-# Next slide

Coverage in this Module The material for this problem is covered in this module in the following presentation: • DPKC_Mod 04_Part 02 Next slide

Problem Statement Find the Thévenin Equivalent of the circuit at terminals A and B. Next slide

Solution – First Step – Where to Start? Find the Thévenin Equivalent of the circuit at terminals A and B. How should we start this problem? What is the first step? Next slide

Problem Solution – First Step Find the Thévenin Equivalent of the circuit at terminals A and B. How should we start this problem? What is the first step? a) Define the open-circuit voltage. b) Replace v. S 1 and R 2 with a current source in parallel with a resistance. c) Define the short-circuit current. d) Replace i. S 1 and R 1 with a voltage source in parallel with a resistance. e) Define the open-circuit voltage and the shortcircuit current.

Your choice for First Step – Define the open-circuit voltage This is a good choice for the first step. Find the Thévenin Equivalent of the circuit at terminals A and B. To find a Thévenin Equivalent, we need to find two of three possible items. The opencircuit voltage is one of these three. Looking at the circuit, though, it appears that finding the short -circuit current may be even easier than finding the open circuit voltage, since R 4 and R 5 will be shorted out when the short is applied. So, even though you made a good choice, we suggest that you try again.

Your choice for First Step – Replace v. S 1 and R 2 with a current source in parallel with a resistance This is not a good choice. Find the Thévenin Equivalent of the circuit at terminals A and B. Generally, it is reasonable to apply source transformations to find Thévenin’s or Norton’s equivalents. However, in this case, having a current source in paralle with a resistance in place of v. S 1 and R 2 will not simplify this circuit. It just will not help. Please go back and try again.

Your choice for First Step – Define the short-circuit current Find the Thévenin Equivalent of the circuit at terminals A and B. This is a good choice for the first step, and the one that we will choose here. To find a Thévenin Equivalent, we need to find two of three possible items. The short-circuit current is one of these three. Looking at the circuit, it appears that finding the short-circuit current may be even easier than finding the open circuit voltage, since R 4 and R 5 will be shorted out when the short is applied. So, let’s try this.

Your choice for First Step was – Replace i. S 1 and R 1 with a voltage source in parallel with a resistance This is not a good choice for the first step. Find the Thévenin Equivalent of the circuit at terminals A and B. The most important point to make here is that i. S 1 and R 4 are not in parallel, and therefore, we cannot replace them with a voltage source in series with a resistance. This is a common error. Some also attempt to replace these with a voltage source in parallel with a resistor, but this is also not valid. Therefore, we recommend that you go back and try again.

Your choice for First Step was – Define the open-circuit voltage and the short-circuit current This is not a good choice. Find the Thévenin Equivalent of the circuit at terminals A and B. The implication of this step is that we should do both things at once, that is, define the open-circuit voltage and the shortcircuit current in the same diagram. This is not possible. When we open circuit terminals A and B, there is no current. When we short circuit terminals A and B, there is no voltage. We cannot do both at once. Please go back and try again.

We have defined in this diagram the short circuit current. It is always important to do this, to show which polarity we are solving for. Defining the Short-Circuit Current Find the Thévenin Equivalent of the circuit at terminals A and B. Next, we are going to simplify the circuit. This step is not necessary, but it makes the solution a little bit easier, so we will do so. Let’s go to the next slide and consider the simplifications possible. Next slide

Which of the simplifications listed here are valid and useful? What Simplifications are Possible Here? Find the Thévenin Equivalent of the circuit at terminals A and B. 1. Remove R 4 and R 5 since they are in parallel with a short circuit. 2. Remove R 1 since it is in series with a current source. 3. Remove v. S 1 and R 2 since they are in parallel with the v. S 2 voltage source. Choices that you may select: a) Just 1. b) Just 2. c) Just 3. d) All of the above. e) None of the above.

You Chose: Just #1 You said that you could remove R 4 and R 5 since they are in parallel with a short circuit. This is true. However, there are more simplifications that could be chosen here. Please go back and try again. Find the Thévenin Equivalent of the circuit at terminals A and B.

You Chose: Just #2 You said that you could remove R 1 since it is in series with a current source. This is true. However, there are more simplifications that could be chosen here. Please go back and try again. Find the Thévenin Equivalent of the circuit at terminals A and B.

You Chose: Just #3 Find the Thévenin Equivalent of the circuit at terminals A and B. You said that you could remove v. S 1 and R 2 since they are in parallel with the v. S 2 voltage source. This is true. However, there are more simplifications that could be chosen here. Please go back and try again.

You Chose: All of the Above Find the Thévenin Equivalent of the circuit at terminals A and B. You said that you could 1. Remove R 4 and R 5 since they are in parallel with a short circuit. 2. Remove R 1 since it is in series with a current source. 3. Remove v. S 1 and R 2 since they are in parallel with the v. S 2 voltage source. These can all be done. Let’s make these changes.

You Chose: None of the Above Find the Thévenin Equivalent of the circuit at terminals A and B. You said that you could not 1. Remove R 4 and R 5 since they are in parallel with a short circuit. 2. Remove R 1 since it is in series with a current source. 3. Remove v. S 1 and R 2 since they are in parallel with the v. S 2 voltage source. These can all be done. Let’s make these changes.

Making the Simplifications Find the Thévenin Equivalent of the circuit at terminals A and B. In the diagram shown, we have 1. Removed R 4 and R 5 since they were in parallel with a short circuit. 2. Removed R 1 since it was in series with a current source. 3. Removed v. S 1 and R 2 since they were in parallel with the v. S 2 voltage source. The much simpler circuit results. We can solve for i. SC, in the next slide. Note that none of these simplifications are needed. You can solve for the shortcircuit current in the circuit before the simplifications. This just makes it easier.

Finding the Short-Circuit Current Find the Thévenin Equivalent of the circuit at terminals A and B. We can write the KCL for the closed surface shown as a dashed red line. We can solve for i. SC, in the equation, as shown below. Note that we have expressed the current through R 3 as v. S 2/R 3. Why is this true? Choose your answer below. Because R 3 is in series with v. S 2. Because R 3 is next to v. S 2. Because the voltage v. S 2 is across R 3, due to the short circuit.

You Chose: Because R 3 is in series with v. S 2 Find the Thévenin Equivalent of the circuit at terminals A and B. We have expressed the current through R 3 as v. S 2/R 3. Why is this true? You said that it was because R 3 is in series with v. S 2. This is not correct because R 3 is not in series with v. S 2. The current source i. S 1 means that they do not have the same current through them. Go back and try again.

You Chose: Because R 3 is next to v. S 2 Find the Thévenin Equivalent of the circuit at terminals A and B. We have expressed the current through R 3 as v. S 2/R 3. Why is this true? You said that it was because R 3 is next to v. S 2. This is not correct because simply having R 3 next to the source v. S 2 does not yield this current. We could write this expression because of Ohm’s Law. Look at the circuit again, and go back and try again.

You Chose: Because the voltage v. S 2 is across R 3 Find the Thévenin Equivalent of the circuit at terminals A and B. We have expressed the current through R 3 as v. S 2/R 3. Why is this true? You said that it was because the voltage v. S 2 is across R 3. This is the correct answer. This is correct because the source v. S 2 being across the resistor R 3 means that Ohm’s Law applies here. By shorting terminals A and B, the bottom terminal of the voltage source is the same as the right hand terminal of the resistor. This is why we can write this equation. Let’s take the next step.

What is the Next Step? Find the Thévenin Equivalent of the circuit at terminals A and B. We have found the short circuit current for the circuit below. Now, what is the next step? Choose the next step for this problem. 1. Find the equivalent resistance, REQ. 2. Find the opencircuit voltage, v. OC. 3. Find the Norton current, i. N. 4. Convert all the current sources to voltage sources, and solve.

Your choice for the Next Step – Find the equivalent resistance, REQ This is a good choice for the next step. Find the Thévenin Equivalent of the circuit at terminals A and B. In general, we could do either this or find the open-circuit voltage. Here, where there are no dependent sources, it is probably easier to find the equivalent resistance. This is particularly true when we have several independent sources, because we will set all of them equal to zero in the first step of finding REQ. So, we will choose this step. Let’s do it.

Your choice for the Next Step – Find the open-circuit voltage, v. OC Find the Thévenin Equivalent of the circuit at terminals A and B. This is a good choice for the next step. If we found the open-circuit voltage, we would have everything we need to solve this problem. However, while it is a good choice, it is not the best choice. In this situation, it appears that there is a better choice. Find the better choice, and we will explain why it is better in this case. Go back and try again.

Your choice for the Next Step – Find the Norton current, i. N Find the Thévenin Equivalent of the circuit at terminals A and B. This is not a good choice for the next step. We are not trying to find the Norton equivalent. If we were, we would note that the shortcircuit current, which we already found, is the Norton current. Go back and try again.

Your choice for the Next Step – Convert all the current sources to voltage sources, and solve Find the Thévenin Equivalent of the circuit at terminals A and B. This is not a good choice for the next step. We could use source transformations to convert the current sources to voltage sources. However, that would be to go down a different path, when we are very near the answer on the path we have already chosen. Go back and try again.

Finding the Equivalent Resistance, REQ Find the Thévenin Equivalent of the circuit at terminals A and B. To find the equivalent resistance, the first step is to set all of the independent sources equal to zero. Let’s do it. Remember that the current sources when set equal to zero become open circuits. The voltage sources when set equal to zero become short circuits. This has been done in the next slide.

Setting Independent Sources Equal to Zero Find the Thévenin Equivalent of the circuit at terminals A and B. We have set the independent sources equal to zero. The circuit is much simpler, but it can be simplified further. First, note that resistor R 1 is open-circuited. That is, the resistor is in series with an open circuit. It can be removed. Then, note that resistor R 2 is short-circuited. That is, the resistor is in parallel with a short circuit. It can be removed. Let’s do both simplifications.

Simplifying the Circuit Find the Thévenin Equivalent of the circuit at terminals A and B. After these simplifications, we are left with three resistors in parallel. The solution now is straight-forward. We have an equivalent resistance, which is Next slide

Finding the Thévenin Voltage With these values, we can find the Thévenin voltage, which is Find the Thévenin Equivalent of the circuit at terminals A and B. Because of the polarity we chose when we found i. SC, this will be the voltage at A with respect to B, when these terminals are opencircuited. This leads to the answer on the next slide.

The Solution Go to Comments Slide The solution is given in either of the two circuits, shown below. Note that it is important to know which terminal is A, and which is B, so that the polarity of the voltage source can be interpreted correctly. Find the Thévenin Equivalent of the circuit at terminals A and B.

Was This Worth It? • This is a good question. However, the best answer is, “It depends. ” • We have gone through a fair amount of work, but by doing so we have a simpler circuit. Whether it was worth the work depends on what we were going to use the circuit for. • For example, if we were to connect the circuit to 12 different resistors, or to 12 different current sources, it would be much easier to solve the simpler circuit each time, and in the end it would be worth it. For one resistor, it was probably not a good use of our time. • Note, though, that Thévenin’s Theorem has benefits as a way of thinking about a circuit. This will pay off in many areas, among them when we are designing circuits. Go back to Overview slide.