Download PWA_Mod02_Prob03_v04

Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Problems With Assistance
Module 2 – Problem 3
Filename: PWA_Mod02_Prob03.ppt
Go
straight to
the First
Step
Go
straight to
the
Problem
Statement
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Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Overview of this Problem
In this problem, we will use the following
concepts:
• Equivalent Circuits
• Series and Parallel Combinations of
Resistors
Go
straight to
the First
Step
Go
straight to
the
Problem
Statement
Next slide
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
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
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Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Coverage in this Module
The material for this problem is covered in
this module in the following presentations:
• DPKC_Mod02_Part01.
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Dave Shattuck
University of Houston
Problem Statement
© Brooks/Cole Publishing Co.
Find the resistance seen at terminals A and B of the circuit below.
R1=
22[W]
A
R2=
50[W]
R5=
10[W]
R4=
25[W]
B
R3=
15[W]
Next slide
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Solution – First Step – Where to Start?
Find the resistance seen at terminals A and B of the circuit below.
R1=
22[W]
A
R2=
50[W]
R5=
10[W]
R4=
25[W]
B
R3=
15[W]
How should we start this
problem? What is the first
step?
Next slide
Dave Shattuck
University of Houston
Problem Solution – First Step
© Brooks/Cole Publishing Co.
Find the resistance seen at terminals A and B of the circuit below.
R1=
22[W]
A
R2=
50[W]
R5=
10[W]
B
R3=
15[W]
We are asked to find the ratio of voltage to current at the terminals; this is the same
thing as the resistance. What is the best first step?
1. Attach a source to the terminals.
2. Define currents and voltages for each of the elements in the circuit.
3. Write a series of KVL and KCL equations.
4. Combine resistors in series and in parallel to simplify the circuit.
5. Perform a delta-to-wye transformation.
R4=
25[W]
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Your Choice for First Step –
Attach a Source to the Terminals
Find the resistance seen at
terminals A and B of the
circuit given.
R1=
22[W]
A
R2=
50[W]
R5=
10[W]
R4=
25[W]
B
R3=
15[W]
This is not the best choice for the first step.
We could indeed apply a source, with the intention of then finding the ratio of the
voltage at the terminals to the current through the terminals. This ratio would be the
resistance. However, this would require solving the circuit, and we can do the problem
more easily.
Go back and try again.
Dave Shattuck
University of Houston
Your choice for First Step was –
© Brooks/Cole Publishing Co.
Define Currents and Voltages for each of the Elements in the Circuit
Find the resistance seen at
terminals A and B of the
circuit given.
R1=
22[W]
A
R2=
50[W]
R5=
10[W]
R4=
25[W]
B
R3=
15[W]
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.
Dave Shattuck
University of Houston
Your Choice for First Step –
Write a Series of KVL and KCL Equations
© Brooks/Cole Publishing Co.
Find the resistance seen at
terminals A and B of the
circuit given.
R1=
22[W]
A
R2=
50[W]
R5=
10[W]
R4=
25[W]
B
R3=
15[W]
This is not the best choice for the first step.
We could indeed write a set of KVL and KCL equations, once we had defined
voltages and currents. However, without sources all voltages and currents would be
zero. The only way to meaningfully do this would be to apply a source, and then
solve for the ratio of voltage to current at the terminals. There is a better approach.
Go back and try again.
Dave Shattuck
University of Houston
Your Choice for First Step Was –
Combine Resistors in Series and in Parallel to Simplify the Circuit
© Brooks/Cole Publishing Co.
Find the resistance seen at
terminals A and B of the
circuit given.
R1=
22[W]
A
R2=
50[W]
R5=
10[W]
R4=
25[W]
B
R3=
15[W]
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.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Your Choice for First Step –
Perform a Delta-to-Wye Transformation
Find the resistance seen at
terminals A and B of the
circuit given.
R1=
22[W]
A
R2=
50[W]
R5=
10[W]
R4=
25[W]
B
R3=
15[W]
This is not the best choice for the first step.
We could indeed perform a delta-to-wye transformation here. One possible delta
configuration is marked in red in the circuit here. However, this transformation is
complicated; generally we are best served by avoiding this unless there is no other choice.
There is another choice here, combining R4 and R5 in parallel. As we will see, there will be
other simplifications to make after that. We recommend that you go back and try again.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Combining Resistors in Series and in Parallel
Find the resistance seen at
terminals A and B of the
circuit given.
R1=
22[W]
A
R2=
50[W]
R5=
10[W]
R4=
25[W]
B
R3=
15[W]
We have decided to simplify this circuit by combining resistors in series and in parallel.
Where should we start this process?
a) Combine R1 and R2 in series.
b) Combine R3 and R4 in series.
c) Combine R1 and R2 in parallel.
d) Combine R4 and R5 in parallel.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
You Said that We Should Combine R1 and R2 in Series
Find the resistance seen at
terminals A and B of the
circuit given.
R1=
22[W]
A
R2=
50[W]
R5=
10[W]
R4=
25[W]
B
R3=
15[W]
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 are
currents through R4 and R5 that prevents this. Do not be confused by the fact that at
present, with no source, all currents are zero. Remember that we are assuming that a
source will be applied later. When it is, there will be a current in R4 and R5, so R1 and R2
are not in series.
This is not a correct step. Go back and try again.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
You Said that We Should Combine R3 and R4 in Series
Find the resistance seen at
terminals A and B of the
circuit given.
R1=
22[W]
A
R2=
50[W]
R5=
10[W]
R4=
25[W]
B
R3=
15[W]
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. Do not be confused by the fact that at present, with
no source, all currents are zero. Remember that we are assuming that a source will be
applied later. When it is, there will be a current in R5, so R3 and R4 are not in series.
This is not a correct step. Go back and try again.
Dave Shattuck
University of Houston
You Said that We Should Combine R1 and R2 in Parallel
© Brooks/Cole Publishing Co.
Find the resistance seen at
terminals A and B of the
circuit given.
R1=
22[W]
A
R2=
50[W]
R5=
10[W]
R4=
25[W]
B
R3=
15[W]
This is not possible. The problem is that R1 and R2 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 terminal A is not connected to terminal B. Do
not be confused by the fact that at present, with no source, all voltages are zero.
Remember that we are assuming that a source will be applied later. When it is, there
will be different voltages across R1 and R2.
This is not a correct step. Go back and try again.
Dave Shattuck
University of Houston
You Said that We Should Combine R4 and R5 in Parallel
© Brooks/Cole Publishing Co.
Find the resistance seen at
terminals A and B of the
circuit given.
R1=
22[W]
A
R2=
50[W]
R5=
10[W]
R4=
25[W]
B
R3=
15[W]
This is correct. The resistors R4 and R5 are in parallel. We can see this, since their two
terminals are the same. The terminals in this circuit are marked in red.
Thus, we find the equivalent circuit, and replace these two resistors with that parallel
equivalent. Let’s do this now.
Dave Shattuck
University of Houston
Combining Series Resistors
© Brooks/Cole Publishing Co.
Find the resistance seen at
terminals A and B of the
circuit given.
R1=
22[W]
A
R2=
50[W]
R6=
7.1[W]
B
R3=
15[W]
We have combined the parallel resistors, and replaced them with an equivalent
resistor, which we called R6. We assume at this point, that you are getting the
idea of how to do these problems. Therefore, without quizzing you, we note
that our next step is to combine R3 and R6 in series.
Next slide
Dave Shattuck
University of Houston
Combining Parallel Resistors
© Brooks/Cole Publishing Co.
Find the resistance seen at
terminals A and B of the
circuit given.
R1=
22[W]
A
R2=
50[W]
R7=
22.1[W]
B
We have combined the series resistors, and replaced them with an equivalent resistor,
which we called R7.
At this point, it is probably clear that R2 and R7 are in parallel, so we will replace them with
their parallel equivalent.
Next slide
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Find the resistance seen at
terminals A and B of the
circuit given.
Combining Resistors Yet Again
R1=
22[W]
A
R8=
15[W]
B
We have combined the parallel resistors, and replaced them with an equivalent resistor,
which we called R8. At this point it is clear that the resistance between the terminals
A and B, which we will call REQ, is the series combination of R1 and R8, or
REQ  R1  R8  22[W]  15[W]  37[W].
Go to
Comments
Slide
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
What if I chose another method?
• If you picked another method, such as writing a set
of equations using KVL and KCL, it requires that
attach a source. Otherwise all currents and voltages
will be zero. While this can be done, we
recommend that you learn the approach we have
taken here to solving these 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.