2. Problems With Assistance Module 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 Next slide Go straight to the Problem Statement Go straight to the First Step

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

4. 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 6 th Ed. by Nilsson and Riedel: Sections 2.2 & 2.4 Basic Engineering Circuit Analysis 6 th 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 2 nd Ed. by Dorf: Sections 3-2 & 3-3 Next slide

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

6. Table 1.4 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Next slide Figure 1.4 R in [  ] v t in [V] 5-3.32 15-24.2 20-113

7. Solution – First Step – Where to Start? How should we start this problem? What is the first step? Next slide 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4Figure 1.4 R in [  ] v t in [V] 5-3.32 15-24.2 20-113

8. Problem Solution – First Step How should we start this problem? What is the first step? a)Find the average of the resistor values in the tableFind the average of the resistor values in the table b)Find the power absorbed by the 5[  ], 15[  ], and 20[  ] resistorsFind the power absorbed by the 5[  ], 15[  ], and 20[  ] resistors c)Draw the model for the device, with names for the componentsDraw the model for the device, with names for the components d)Find the current through each of the 5[  ], 15[  ], and 20[  ] resistorsFind the current through each of the 5[  ], 15[  ], and 20[  ] resistors e)Draw a plot of the voltage versus resistanceDraw 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4Figure 1.4 R in [  ] v t in [V] 5-3.32 15-24.2 20-113

9. Your choice for First Step was – Find the average of the resistor values in the table 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.try again 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4Figure 1.4 R in [  ] v t in [V] 5-3.32 15-24.2 20-113

10. Your choice for First Step was – Find the power absorbed by the 5[  ], 15[  ], and 20[  ] resistors 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.try again 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4Figure 1.4 R in [  ] v t in [V] 5-3.32 15-24.2 20-113

11. Your choice for First Step was – Find the current through each of the 5[  ], 15[  ], and 20[  ] resistors 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.try again 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4Figure 1.4 R in [  ] v t in [V] 5-3.32 15-24.2 20-113

12. Your choice for First Step was – Draw a plot of the voltage versus resistance 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.try again 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4Figure 1.4 R in [  ] v t in [V] 5-3.32 15-24.2 20-113

13. Your choice for First Step was – Draw the model for the device, with names for the components 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 itLet’s try it. 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4Figure 1.4 R in [  ] v t in [V] 5-3.32 15-24.2 20-113

14. Drawing the Model for the Device 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 v t and i t. These should also be shown on our model, just as they were in Figure 1.4. I have called these values v D and R D. I can pick almost anything. The one thing I cannot pick is v t. This name is already in use, and it is a different voltage.I cannot pick is v t. 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4Figure 1.4 Next step R in [  ] v t in [V] 5-3.32 15-24.2 20-113

15. 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Drawing the Model for the Device – Note 1 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 v t. This name is already in use, and it is a different voltage. Is this clear? Is v D different from v t ? We can write KVL around the loop, and find that Table 1.4Figure 1.4 Next slide R in [  ] v t in [V] 5-3.32 15-24.2 20-113

16. Drawing the Model for the Device – Note 2 We found that This means that v D and v t are only the same when i t is zero. It looks like i t 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 v D is not equal to v t. Now, our next step is to use the other information that we have been given. Let’s connect a resistor to 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4Figure 1.4 Next slide R in [  ] v t in [V] 5-3.32 15-24.2 20-113

17. Connecting the Device to the 5[  ] Resistor – Step 1 We have attached the 5[  ] resistor. We write KVL, to get 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4 Figure 1.4 Next slide R in [  ] v t in [V] 5-3.32 15-24.2 20-113

18. Connecting the Device to the 5[  ] Resistor – Step 2 Now, we note that i t goes through the 5[  ] resistor, and write: 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4 Figure 1.4 Next slide R in [  ] v t in [V] 5-3.32 15-24.2 20-113

19. Connecting the Device to the 5[  ] Resistor – Step 3 And finally, we use the v t value for 5[  ], 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. 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4 Figure 1.4 Next slide R in [  ] v t in [V] 5-3.32 15-24.2 20-113

20. Connecting the Device to the 15[  ] Resistor The two equations we get from the first two rows of the table are: 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4 Figure 1.4 These two equations and two unknowns can be solved. When we do, we get v D = 11.3[V], and R D = -22[  ]. Next slide R in [  ] v t in [V] 5-3.32 15-24.2 20-113

21. 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4 Figure 1.4 Our solution is: v D = 11.3[V], and R D = -22[  ]. 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. Next slide R in [  ] v t in [V] 5-3.32 15-24.2 20-113

22. Solve for the Current Through the 10[  ] 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4 Figure 1.4 Our solution is for the device is: v D = 11.3[V], and R D = -22[  ]. 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[  ] resistor and solve. Writing KVL, and using Ohm’s Law, we have 11.3[V] = i t (10-22)[  ], which means i t = -942[mA]. Next slide R in [  ] v t in [V] 5-3.32 15-24.2 20-113

23. 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[  ] resistor. Find the power absorbed by this 10[  ] resistor, when it is connected to the device. Table 1.4 Figure 1.4 With i t = -942[mA], and with p abs,10[  ] = i t 2 (10[  ]), we get p abs,10[  ] = 8.85[W]. Go to Notes R in [  ] v t in [V] 5-3.32 15-24.2 20-113

24. 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 Overview slide. Overview