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```Dave Shattuck
University of Houston
Problems With Assistance
Module 2 – Problem 2
Filename: PWA_Mod02_Prob02.ppt
Go
straight to
the First
Step
Go
straight to
the
Problem
Statement
Next slide
Dave Shattuck
University of Houston
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
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
• Introduction to Electric Circuits 2nd Ed. by Dorf: Chapter
3
Next slide
Dave Shattuck
University of Houston
Coverage in this Module
The material for this problem is covered in
this module in the following presentations:
• DPKC_Mod02_Part01.
Next slide
Dave Shattuck
University of Houston
Problem Statement
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
R3=
150[W]
A
R2=
300[W]
R4=
100[W]
B
Next slide
Dave Shattuck
University of Houston
Solution – First Step – Where to Start?
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
R3=
150[W]
A
R2=
300[W]
R4=
100[W]
B
How should we start this
problem? What is the first
step?
Next slide
Dave Shattuck
University of Houston
Problem Solution – First Step
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
R3=
150[W]
A
R2=
300[W]
R4=
100[W]
B
Problems such as this one ask us to analyze a part of a circuit, one that is probably
going to be connected to sources in some way in the future. We are asked to
find the ratio of voltage to current at the terminals; this is the same thing as the
resistance. How should we start this problem? What is the 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.
Dave Shattuck
University of Houston
Your Choice for First Step –
Attach a Source to the Terminals
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
R3=
150[W]
A
R2=
300[W]
R4=
100[W]
B
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 –
Define Currents and Voltages for each of the Elements in the Circuit
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
R3=
150[W]
A
R2=
300[W]
R4=
100[W]
B
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
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
R3=
150[W]
A
R2=
300[W]
R4=
100[W]
B
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
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
R3=
150[W]
A
R2=
300[W]
R4=
100[W]
B
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
Combining Resistors in Series and in Parallel
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
R3=
150[W]
A
R2=
300[W]
R4=
100[W]
B
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 R3 in series.
d) Combine R1 and R2 in parallel.
e) Combine R2 and R4 in parallel.
Dave Shattuck
University of Houston
You Said that We Should Combine R1 and R2 in Series
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
R3=
150[W]
A
R2=
300[W]
R4=
100[W]
B
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. 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 R3, so R1 and R2 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 R3 and R4 in Series
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
R3=
150[W]
A
R2=
300[W]
R4=
100[W]
B
This is correct. The resistors R3 and R4 are in series. They can be combined, and replaced
by a resistor with the value (R3 + R4).
Let’s redraw this circuit and look for the next step.
Dave Shattuck
University of Houston
You Said that We Should Combine R1 and R3 in Series
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
R3=
150[W]
A
R2=
300[W]
R4=
100[W]
B
This is not possible. The problem is that R1 and R3 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 R2 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 R2, so R1 and R3 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
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
R3=
150[W]
A
R2=
300[W]
R4=
100[W]
B
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 R2 and R4 in Parallel
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
R3=
150[W]
A
R2=
300[W]
R4=
100[W]
B
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. 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 a
voltage across R3, so R2 and R4 are not in parallel.
This is not a correct step. Go back and try again.
Dave Shattuck
University of Houston
Combining Series Resistors
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
A
R2=
300[W]
R5=
250[W]
B
We have combined the series resistors, and replaced them with an equivalent resistor,
which we called R5. Our next step is to combine R2 and R5 in parallel.
Next slide
Dave Shattuck
University of Houston
Combining Parallel Resistors
Find the resistance seen at terminals A and B of the circuit below.
R1=
200[W]
A
R6=
140[W]
B
We have combined the parallel resistors, and replaced them with an equivalent resistor,
which we called R6. Remember to use the parallel combination rule for this step.
At this point, it is probably clear that R1 and R6 are in series. Next we will replace R3 and
R8 with their series equivalent.
Next slide
Dave Shattuck
University of Houston
Combining Resistors Yet Again
Find the resistance seen at terminals A and B of the circuit below.
A
R7=
340[W]
B
We have combined the series resistors, and replaced them with an equivalent resistor,
which we called R7. At this point it is clear that the resistance between the terminals
A and B, which we will call REQ, is just R7, or
REQ  R7  340[W].
Go to
Slide
Dave Shattuck
University of Houston
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 still
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.
```
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