Problems With Assistance Module 1 – Problem 4

1. Problems With AssistanceModule 1 – Problem 4 Filename: PWA_Mod01_Prob04.ppt This problem is adapted from: Quiz #1 – ECE 2300 – February 19, 1997 Department of Electrical and Computering Engineering University of Houston Houston, TX, 77204-4793 Go straight to the First Step Go straight to the Problem Statement Next slide

2. Overview of this Problem In this problem, we will use the following concepts: • Kirchhoff’s Voltage Law • Kirchhoff’s Current Law • Ohm’s Law Go straight to the First Step Go straight to the Problem Statement Next slide

3. Textbook Coverage The material for this problem is covered in your textbook in the following sections: • Circuits by Carlson: Sections 1.3 & 1.4 • Electric Circuits 6th Ed. by Nilsson and Riedel: Sections 2.2 & 2.4 • Basic Engineering Circuit Analysis 6th Ed. by Irwin and Wu: Section 2.1 & 2.2 • Fundamentals of Electric Circuits by Alexander and Sadiku: Sections 2.2 & 2.4 • Introduction to Electric Circuits 2nd Ed. by Dorf: Sections 3-2 & 3-3 Next slide

4. Coverage in this Module The material for this problem is covered in this module in the following presentation: • DPKC_Mod01_Part04 Next slide

5. Problem Statement A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 Next slide

6. Solution – First Step – Where to Start? A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 How should we start this problem? What is the first step? Next slide

7. Problem Solution – First Step A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 • How should we start this problem? What is the first step? • Find the average of the resistor values in the table • Find the power absorbed by the 5[W], 15[W], and 20[W] resistors • Draw the model for the device, with names for the components • Find the current through each of the 5[W], 15[W], and 20[W] resistors • Draw a plot of the voltage versus resistance

8. Your choice for First Step was –Find the average of the resistor values in the table A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 This is not a good choice. The average value of the resistor values in the table cannot be used to obtain any useful information. These values were chosen almost at random. The average of these values has no real meaning. Go back and try again.

9. Your choice for First Step was –Find the power absorbed by the 5[W], 15[W], and 20[W] resistors A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 This is not a good choice. The power absorbed by the resistor values has meaning, but it is very difficult to understand what that meaning is. Say it this way; we don’t have the tools to use this information effectively. Go back and try again.

10. Your choice for First Step was –Find the current through each of the 5[W], 15[W], and 20[W] resistors A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 This is not the best choice. The current through each of these resistor values is useful information, but only if we have a really good understanding of what is happening in this problem. If so, we could plot voltage versus current, and gain some insight. As a beginner, though, it is safer to take a more fundamental approach. Go back and try again.

11. Your choice for First Step was –Draw a plot of the voltage versus resistance A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 This is not the best choice. The plot of the voltage versus resistance for this data will not be a straight line. It does follow a function with meaning, but it is quite difficult to use only 3 points to regenerate a nonlinear curve with an unknown (to us) form. Go back and try again.

12. Your choice for First Step was –Draw the model for the device, with names for the components A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 This is the best choice. The first step is to get this to look like a circuits problem. When it is a circuits problem, we can use our circuits techniques to solve it. This is called modeling. We have been told that we can model the device, and what to use. The key is use this model, and work from there. Let’s try it.

13. Next step Drawing the Model for the Device A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 We want a model for the device, and are told that a voltage source in series with a resistance will work. Let’s draw this model, and assign names to the components. The polarity of the voltage source that we choose does not matter; we just need need to keep that polarity the same with respect to vt and it. These should also be shown on our model, just as they were in Figure 1.4. I have called these values vD and RD. I can pick almost anything. The one thing I cannot pick is vt. This name is already in use, and it is a different voltage.

14. Next slide Drawing the Model for the Device – Note 1 A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 We draw the model, and assign names to the components. We said that the one name we cannot pick for the voltage source we cannot pick is vt. This name is already in use, and it is a different voltage. Is this clear? Is vD different from vt? We can write KVL around the loop, and find that

15. Next slide Drawing the Model for the Device – Note 2 A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 We found that This means that vD and vt are only the same when it is zero. It looks like it is zero, but this is only true until we connect something to the device, like a resistor. Then, the current will not be zero, and vD is not equal to vt . Now, our next step is to use the other information that we have been given. Let’s connect a resistor to the device.

16. Next slide Connecting the Device to the 5[W] Resistor – Step 1 A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 We have attached the 5[W] resistor. We write KVL, to get

17. Next slide Connecting the Device to the 5[W] Resistor – Step 2 A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 Now, we note that it goes through the 5[W] resistor, and write:

18. Next slide Connecting the Device to the 5[W] Resistor – Step 3 A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 And finally, we use the vt value for 5[W], and write: This is one equation in two unknowns. If we do it again with another row from Table 1.4, we will have two equations and two unknowns, which we can solve.

19. Next slide Connecting the Device to the 15[W] Resistor A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 These two equations and two unknowns can be solved. When we do, we get vD = 11.3[V], and RD = -22[W]. Figure 1.4 The two equations we get from the first two rows of the table are:

20. Next slide Negative Resistance A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Can we have a negative resistance? Yes, we can. This is a situation where the ratio of voltage to current is constant, but is negative when the passive convention was used. This can happen when we have a dependent source inside the device. Figure 1.4 Our solution is: vD = 11.3[V], and RD = -22[W].

21. Next slide Solve for the Current Through the 10[W] Resistor A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Our solution is for the device is: vD = 11.3[V], and RD = -22[W]. Figure 1.4 We plug these values in, and we have the device in a form that we can solve. Now we can connect the device to a 10[W] resistor and solve. Writing KVL, and using Ohm’s Law, we have 11.3[V] = it(10-22)[W], which means it = -942[mA].

22. The Solution A device can be modeled using an ideal voltage source in series with a resistance. That device is shown in Figure 1.4. A series of resistors were connected to that device, one at a time, and the results are shown in Table 1.4 below. Then, the device was connected to a 10[W] resistor. Find the power absorbed by this 10[W] resistor, when it is connected to the device. Table 1.4 Figure 1.4 With it = -942[mA], and with pabs,10[W] = it2 (10[W]), we get pabs,10[W] = 8.85[W]. Go to Notes

23. Why do we have to worry about modeling? • Modeling is a very important concept. It really is fundamental to most of the things that we do in circuits. Resistors are models for things where the ratio of voltage to current is constant, but is not exact. We model sources with combinations of resistors and ideal sources. Essentially, everything that we do is a model of reality, which we use because the answers we get for our models are close to the ones for real devices. • In this problem we model a device, and we model the things we connect to the device with resistors. This is a way of thinking we need to be familiar with. Go back to Overviewslide.