1. Problems With Assistance Module 1 – Problem 3
Go straight to the First Step
Filename: PWA_Mod01_Prob03.ppt
This problem is adapted from:
Problem 1.34, page 38 in Circuits by A. Bruce Carlson
Brooks/Cole Thomson Learning
2000
ISBN:
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:
Kirchhoff’s Voltage Law
Kirchhoff’s Current Law
Ohm’s Law
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 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
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 presentation:
DPKC_Mod01_Part04
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 vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
This is the basic problem. We will take it step by step.
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6. Solution – First Step – Where to Start?
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
How should we start this problem? What is the first step?
Try to decide on the first step before going to the next slide.
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7. Problem Solution – First Step
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
How should we start this problem? What is the first step?
Write a series of KVL, KCL and Ohm’s Law Equations
Fill in the given information in the circuit schematic
Define variables for voltages and currents needed to solve the problem
Convert the sources to their equivalent resistances
Click on the step that you think should be next.

8. Your choice for First Step was – Write a series of KVL, KCL and Ohm’s Law Equations
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
This is a reasonable thing to do, but it is too soon to do it.
It is important to define variables before writing equations using them.
It is also useful to include the information given in this problem directly into the circuit schematic. It is a good idea to get used to thinking in terms of these diagrams.
Go back and try again.

9. Your choice for First Step was – Fill in the given information in the circuit schematic
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
This is a good first step. Generally, it is a reasonable first step to include the information that is given in the problem in a way that helps us move forward. Here, this means putting the information about vs and va in the schematic. This has been done here.
Now what is the second step?
Write a series of KVL, KCL and Ohm’s Law Equations
Define variables for voltages and currents needed to solve the problem
Convert the sources to their equivalent resistances

10. Your choice for Second Step was – Write a series of KVL, KCL and Ohm’s Law Equations
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
This is a reasonable thing to do, but it is too soon to do it.
It is important to define variables before writing equations using them.
Go back and try again.

11. Your choice for Second Step was – Define variables for voltages and currents needed to solve the problem
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
This is the best choice. It is important to define variables before writing equations using them.
Which ones should be included?
There is no single answer to this question. The key is to recognize that we must define any variable before using it in an equation. We have included a few that we think that we will need in the diagram here. If we missed any, we just need to add them before writing the equation that uses it. The next step is to actually write the equations.

12. Your choice for Second Step was – Convert the sources to their equivalent resistances
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
This is a bad choice. There is not an equivalent resistance for an ideal source. Sources and resistances are completely different things. Try again.

13. Your choice for First Step was – Define variables for voltages and currents needed to solve the problem
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
This is a good first step. It is important to define variables before writing equations using them.
Which ones should be included?
There is no single answer to this question. The key is to recognize that we must define any variable before using it in an equation. We have included a few that we think that we will need in the diagram here. If we missed any, we just need to add them before writing the equation that uses it. The next step is to actually write the equations.
Now what is the second step?
Write a series of KVL, KCL and Ohm’s Law Equations
Fill in the given information in the circuit schematic
Convert the sources to their equivalent resistances

14. Your choice for Second Step was – Write a series of KVL, KCL and Ohm’s Law Equations
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
This is a reasonable thing to do, but it is too soon to do it.
Generally, it is a reasonable first step to include the information that is given in the problem in a way that helps us move forward. Here, this means putting the information about vs and va in the schematic. Go back and try again.

15. Your choice for Second Step was – Fill in the given information in the circuit schematic
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
This is a good choice. Generally, it is reasonable to include the information that is given in the problem in a way that helps us move forward. Here, this means putting the information about vs and va in the schematic. This has been done here.
Next, we can write the equations.

16. Your choice for Second Step was – Convert the sources to their equivalent resistances
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
This is a bad choice. There is not an equivalent resistance for an ideal source. Sources and resistances are completely different things. Try again.

17. Your choice for First Step was – Convert the sources to their equivalent resistances
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
This is a bad choice. There is not an equivalent resistance for an ideal source. Sources and resistances are completely different things. Try again.

18. Writing the Equations
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
Now, we have agreed that we are ready to write equations. We can use KVL, KCL and Ohm’s Law. How many do we write? Which ones first?
There are many answers. While there is some benefit to simply writing equations wherever we can, it is better to try to see small steps that take us to the answer. It is easier to write and solve a series of 6 single equations in a single unknown, than to writing all 6 equations and attempting to solve them simultaneously. Let’s try this.
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19. Writing the Equations – Picking the First One to Write
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
We would like to write an equation for a single unknown variable, that has only that unknown in it. The variable should also be useful to me in solving the problem.
Note that we can write a KVL around the left hand loop, and the only unknown will be v12. The loop is shown in red. Let’s write the equation:
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20. Writing the Equations – Picking the Second One to Write
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
So, now we know that v12 = 6[V]. Let’s look for another useful equation.
Note that we can write Ohm’s Law for the 12[W] resistor, and get i12. Let’s write the equation:
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21. Writing the Equations – Picking the Next One to Write
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
Next, knowing i12, we can write KCL at the middle node to get the current through the 4[W] resistor.
However, if we try to write this KCL, we find that we have not yet defined the current through the 4[W] resistor. This needs to be our next step.
We have done this here. In anticipation of needing it shortly, we have also defined the voltage across the 4[W] resistor.
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22. Writing the Equations – Writing the Next One
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
We will write the KCL at the middle node, in red.
Note that our answer for i4 came out negative. Some students are tempted to say that they have defined i4 incorrectly, and need to go back and redefine it. Don’t! You can’t define a reference polarity incorrectly. This is a fine answer.
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23. Writing the Equations – Getting Ohm’s Law Right
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
Next, we write Ohm’s Law, and get
Note that when we defined v4 and i4, we defined them in the active convention for the resistor. Again, we can’t define reference polarities incorrectly; we just need to use the definitions that result correctly. Here, this means writing Ohm’s Law with a minus sign.
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24. Writing the Equations – One Answer
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
Next, we can write KVL for the bottom right hand loop, and get one of our desired answers,
Interestingly, the voltage vb is zero. This is the voltage across the right hand current source. Remember that the voltage across a current source is not always zero; see va for example.
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25. Writing the Equations – Another KVL
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
Next, we can write KVL for the upper right hand loop, and get
Note that the positive answer is the only correct answer.
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26. Writing the Equations – Another KCL
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
Next, we can write KCL for the right hand node, and get
Note that the positive answer is the only correct answer.
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27. Writing the Equations – Second Answer
Find vb and R3 in Fig. P1.34, given that vs=12[V] and va = 6[V].
Finally, we can write Ohm’s Law for R3, and get
Note that here we had defined the reference polarities for i3 and v3 in the passive convention, and the positive sign in Ohm’s Law resulted from that.
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28. How did we know which equations to write, and in what order?
This is an excellent question. In this problem, we looked at the voltages and currents that were given, and saw an equation that we could write for a single unknown. We just started from there.
This will not always happen. When problems become complex, we will want to find a systematic way of knowing what equations we have to write, and write only that minimum number of equations. We will call these systematic ways The Node-Voltage Method and The Mesh-Current Method. We will learn these methods later.
For now, we have no choice but to try writing equations, and seeing what we need to solve. Try to use some insight.
Go back to Overview slide.
Go to Next Note

29. Why do we have to worry about the sign in Everything?
This is one of the central themes in circuit analysis. The polarity, and the sign that goes with that polarity, matters. The key is to find a way to get the sign correct every time.
This is why we need to define reference polarities for every voltage and current.
This is why we need to take care about what relationship we have used to assign reference polarities (passive sign convention and active sign convention).
An analogy: Suppose I was going to give you $10,000. This would probably be fine with you. However, it will matter a great deal which direction the money flows. You will care a great deal about the sign of the $10,000 in this transaction. If I give you -$10,000, it means that you are giving $10,000 to me. This would probably not be fine with you!
Go back to Overview slide.