1. Problems With Assistance Module 2 – Problem 1
Go straight to the First Step
Filename: PWA_Mod02_Prob01.ppt
You can see a brief introduction starting on the next slide, or go right to the problem.
Go straight to the Problem Statement
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2. Overview of this Problem
In this problem, we will use the following concepts:
Equivalent Circuits
Series and Parallel Combinations of Resistors
Voltage Divider Rule
Go straight to the First Step
Go straight to the Problem Statement
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3. 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.
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4. Coverage in this Module
The material for this problem is covered in this module in the following presentations:
DPKC_Mod02_Part01, and DPKC_Mod02_Part02.
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.
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5. Problem Statement
Find the power delivered by the source in this circuit.
Find the voltage vX.
This is the basic problem. We will take it step by step.
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6. Solution – First Step – Where to Start?
Find the power delivered by the source in this circuit.
Find the voltage vX.
Try to decide on the first step before going to the next slide.
How should we start this problem? What is the first step?
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7. Problem Solution – First Step
Find the power delivered by the source in this circuit.
Find the voltage vX.
Click on the step that you think should be next.
How should we start this problem? What is the first step?
Write a series of KVL equations.
Write a series of KCL equations.
Combine resistors in series and in parallel to simplify the circuit.
Define currents and voltages for each of the elements in the circuit.

8. Your Choice for First Step – Write a Series of KVL Equations
Find the power delivered by the source in this circuit.
Find the voltage vX.
This is not the best choice for the first step.
We could indeed write a set of KVL equations, once we had defined currents for the resistor elements. This would result in a set of simultaneous equations that could be solved. However, there are better approaches. We advocate an approach that allows us to avoid simultaneous equations.
Go back and try again.

9. Your Choice for First Step – Write a Series of KCL Equations
Find the power delivered by the source in this circuit.
Find the voltage vX.
This is not the best choice for the first step.
We could indeed write a set of KCL equations, once we had defined voltages for the resistor elements and the current through the voltage source. This would result in a set of simultaneous equations that could be solved. However, there are better approaches. We advocate an approach that allows us to avoid simultaneous equations.
Go back and try again.

10. Your Choice for First Step Was – Combine Resistors in Series and in Parallel to Simplify the Circuit
Find the power delivered by the source in this circuit.
Find the voltage vX.
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.

11. Your choice for First Step was – Define Currents and Voltages for each of the Elements in the Circuit
Find the power delivered by the source in this circuit.
Find the voltage vX.
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.

12. Combining Resistors in Series and in Parallel
Find the power delivered by the source in this circuit.
Find the voltage vX.
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 R5 and R6 in series.
Combine R2 and R4 in parallel.
Combine R4 and R6 in parallel.

13. You Said that We Should Combine R1 and R2 in Series
Find the power delivered by the source in this circuit.
Find the voltage vX.
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.
This is not a correct step. Go back and try again.

14. You Said that We Should Combine R3 and R4 in Series
Find the power delivered by the source in this circuit.
Find the voltage vX.
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.
This is not a correct step. Go back and try again.

15. You Said that We Should Combine R5 and R6 in Series
Find the power delivered by the source in this circuit.
Find the voltage vX.
This is correct. The resistors R5 and R6 are in series. They can be combined, and replaced by a resistor with the value (R5 + R6).
Let’s redraw this circuit and look for the next step.

16. You Said that We Should Combine R2 and R4 in Parallel
Find the power delivered by the source in this circuit.
Find the voltage vX.
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.
This is not a correct step. Go back and try again.

17. You Said that We Should Combine R4 and R6 in Parallel
Find the power delivered by the source in this circuit.
Find the voltage vX.
This is not possible. The problem is that R4 and R6 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 R5 is between two of the terminals.
This is not a correct step. Go back and try again.

18. Combining Series Resistors
Find the power delivered by the source in this circuit.
Find the voltage vX.
Find the power delivered by the source in this circuit.
We have combined the series resistors, and replaced them with an equivalent resistor, which we called R7. What should our next step be?
Combine R4 and R7 in series.
Combine R4 and R7 in parallel.
Combine R3 and R4 in series.

19. You Said the Next Step was to Combine R4 and R7 in Series
Find the power delivered by the source in this circuit.
Find the voltage vX.
Find the power delivered by the source in this circuit.
This step would not be a valid one.
The resistors R4 and R7 are not in series in this circuit, due to the current through R3.
Go back and try again.

20. You Said the Next Step was to Combine R4 and R7 in Parallel
Find the power delivered by the source in this circuit.
Find the voltage vX.
This step would be the correct choice. The resistors R4 and R7 are in parallel, and replacing them by their equivalent would result in a simpler circuit, as seen by the source.
Let’s replace the parallel resistors by their equivalent.

21. You Said the Next Step was to Combine R3 and R4 in Series
Find the power delivered by the source in this circuit.
Find the voltage vX.
This step would not be a valid one.
The resistors R3 and R4 are not in series in this circuit, due to the current through R7.
Go back and try again.

22. Combining Parallel Resistors
Find the power delivered by the source in this circuit.
Find the voltage vX.
We have combined the parallel resistors, and replaced them with an equivalent resistor, which we called R8. Remember to use the parallel combination rule for this step.
At this point, it is probably clear that R3 and R8 are in series. Next we will replace R3 and R8 with their series equivalent.
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23. Combining Resistors Again
Find the power delivered by the source in this circuit.
Find the voltage vX.
Find the power delivered by the source in this circuit.
We have combined the series resistors, and replaced them with an equivalent resistor, which we called R9. Next we will replace R2 and R9 with their equivalent. We should be careful, though. It looks as if the voltage vX is inside the parallel equivalent, and would be lost when taking the equivalent. Is this true?
Yes. The voltage vX will not be present after we take the equivalent. We need to solve for vX in this circuit.
No. The voltage vX will still be present after we take the equivalent. We can solve the simpler circuit for vX.

24. You Said That vX Would Not Be Present
Find the power delivered by the source in this circuit.
Find the voltage vX.
Find the power delivered by the source in this circuit.
After we will replace R2 and R9 with their equivalent, will the voltage vX still be present?
Your answer was that the voltage vX would not be present after we take the equivalent. While this approach will get the correct answer, it will take longer to get it. The voltage can be moved outside the equivalent. The correct answer is that it will still be present. Let’s consider that answer.

25. You Said That vX Would Still Be Present
Find the power delivered by the source in this circuit.
Find the voltage vX.
Find the power delivered by the source in this circuit.
After we will replace R2 and R9 with their equivalent, will the voltage vX still be present?
Your answer was that the voltage vX would still be present after we take the equivalent. This is correct. The voltage can be identified to the left of the resistor R2, and so the correct answer is that it will still be present.
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26. Combining Resistors Yet Again
Find the power delivered by the source in this circuit.
Find the voltage vX.
We have combined the parallel resistors, and replaced them with an equivalent resistor, which we called R10.
At this point it is straightforward to solve for part b), using the Voltage Divider Rule. We can write,
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27. Combining Resistors Yet One More Time
Find the power delivered by the source in this circuit.
Find the voltage vX.
We have combined the series resistors, and replaced them with an equivalent resistor, which we called R11.
At this point it is straightforward to solve for part a), using Ohm’s Law to find the current through the voltage source, iS. We can write,
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28. What if I chose another method? Is that a big deal?
If you picked another method, such as writing a set of equations using KVL and KCL, it does not make that much difference. One advantage of the approach taken here is that we do not have to solve simultaneous equations. However, if we have access to a good calculator or a computer, the solution can be done easily taking many other approaches.
While this is true, we still recommend that you learn this approach to solving 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.