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Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Module 1 – Problem 5
Filename: PWA_Mod01_Prob05.ppt
This problem is adapted from:
Quiz #2 – ECE 2300 – June 17, 1998
Department of Electrical and Computer Engineering
University of Houston
Houston, TX, 77204-4793
Go
straight to
the First
Step
Go
straight to
the
Problem
Statement
Next slide
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
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
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 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
Next slide
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 presentation:
• DPKC_Mod01_Part04
A similar problem is worked in:
• PWA_Mod01_Prob04
Next slide
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Problem Statement
A device can be modeled using a
current source in parallel
with a resistor. This
device was connected to a
5[V] voltage source, as
shown in Figure 1.5a), and
a current i5 of 0.93[A]
resulted.
The same device was then
connected to a 4[A]
current source as shown in
Figure 1.5b), and a voltage
v4 of –34[V] resulted.
Find the voltage v3 if a 3[W]
resistor, as shown in
Figure 1.5c), is connected
to the same device.
i5
Device
+
5[V]
Figure 1.5a)
-
Device
+
v4
-
Figure 1.5b)
4[A]
Device
Figure 1.5c)
Next slide
+
v3
-
3[W]
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Solution – First Step – Where to Start?
A device can be modeled using a
current source in parallel
with a resistor. This
device was connected to a
5[V] voltage source, as
Table 1.4
shown in Figure 1.5a), and
a current
vT in
[V] i5Rofin0.93[A]
[W]
resulted.
-3.32device was5then
The same
connected to a154[A]
-24.2
current source as shown in
-113
Figure 1.5b), 20
and a voltage
v4 of –34[V] resulted.
Find the voltage v3 if a 3[W]
resistor, as shown in
Figure 1.5c), is connected
to the same device.
i5
Figure 1.5a)
Device
+
5[V]
-
Device
+
v4
-
4[A]
Figure 1.5b)
How should
we start this
problem?
What is the
first step?
Device
+
v3
-
Figure 1.5c)
3[W]
Next slide
Dave Shattuck
University of Houston
Problem Solution – First Step
© Brooks/Cole Publishing Co.
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
i5
Figure 1.5a)
Device
Device
+
+
v3
-
5[V]
-
Figure 1.5c)
Device
+
v4
-
Figure 1.5b)
4[A]
How should we start this problem? What
is the first step?
a)
Find the power delivered by the
voltage source and by the current
source
b)
Find the power absorbed by the
device
c)
Draw the model for the device, with
names for the components
d)
Draw a plot of the voltage versus
current
3[W]
Your choice for First Step –
© Brooks/Cole Publishing Co.
Find the power delivered by the voltage source and by the
current source
Dave Shattuck
University of Houston
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
i5
Figure 1.5a)
Device
Device
+
+
v3
-
5[V]
-
Figure 1.5c)
Device
+
v4
-
Figure 1.5b)
3[W]
This is not a good choice.
The power delivered by the voltage
source can be found. Since i5 and
5[V] are in the active convention,
pdel,5[V] = 5[V]i5 = 4.65[W].
Similarly, for the current source
pdel,4[A] = -4[A]v4 = 136[W]. The
device is absorbing this power in
each case, and the values are not the
same. The device is not providing
(or absorbing) the same power to
everything connected to it, so this
information does not help us solve
this problem.
4[A]
Go back and try again.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Your choice for First Step –
Find the power absorbed by the device
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
i5
Figure 1.5a)
Device
Device
+
+
v3
-
5[V]
-
Figure 1.5c)
Device
+
v4
-
Figure 1.5b)
3[W]
This is not a good choice.
The power delivered by the voltage
source can be found. Since i5 and
5[V] are in the active convention,
pdel,5[V] = 5[V]i5 = 4.65[W].
Similarly, for the current source
pdel,4[A] = -4[A]v4 = 136[W]. The
device is absorbing this power in
each case, and the values are not the
same. The device is not providing
(or absorbing) the same power to
everything connected to it, so this
information does not help us solve
this problem.
4[A]
Go back and try again.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Your choice for First Step was –
Draw a plot of the voltage versus current
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
i5
Figure 1.5a)
Device
Device
+
+
v3
-
5[V]
-
Figure 1.5c)
Device
+
v4
-
Figure 1.5b)
4[A]
3[W]
This could be helpful, but is not
the best choice.
The plot of the voltage versus
current for this data will be a
straight line. However, you
may or may not know why
this is true. If you don’t
know why it is true, then all
you really get are two points
in an unknown relationship.
If you do know why the
relationship is a straight line,
then this approach will move
you towards the answer. For
now, let’s assume that you do
not know that v vs. i is
straight line.
Go back and try again.
Your choice for First Step was –
© Brooks/Cole Publishing Co.
Draw the model for the device, with names for the components
Dave Shattuck
University of Houston
This is the best choice.
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
i5
Figure 1.5a)
Device
Device
+
+
v3
-
5[V]
Let’s try it.
-
Figure 1.5c)
Device
+
v4
-
Figure 1.5b)
4[A]
3[W]
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.
Dave Shattuck
University of Houston
Drawing the Model for the Device
© Brooks/Cole Publishing Co.
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
i5
Figure 1.5a)
Device
Device
+
v3
-
+
3[W]
5[V]
-
Figure 1.5c)
Device
+
v4
-
Figure 1.5b)
4[A]
iD
RD
We want a model for the device,
and are told that a current
source in parallel with a
resistance will work. Let’s
draw this model, and assign
names to the components.
The polarity of the current
source that we choose does
not matter; we just need need
to keep that polarity the same
with respect to the voltages
and currents connected to it.
I have called these values iD and
RD. I can pick almost
anything. The one thing I
cannot pick is i5. This name
is already in use, and it is a
different current.
Next step
Dave Shattuck
University of Houston
Drawing the Model for the Device – Note
© Brooks/Cole Publishing Co.
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
i5
Figure 1.5a)
Device
Device
+
v3
-
+
3[W]
5[V]
-
Figure 1.5c)
Device
+
v4
-
Figure 1.5b)
4[A]
iD
RD
We draw the model, and assign
names to the components.
We said that the one name we
cannot pick for the current
source we cannot pick is
i5. This name is already in
use, and it is a different
current. Is this clear?
Is iD different from i5? Yes, it
is. For example, when we
connect the 5[V] voltage
source to the device, the
current entering the top
terminal of the device is i5.
However, some of this
current goes through the
resistor RD. So, iD is
different from i5.
Next slide
Dave Shattuck
University of Houston
Connecting the Device to the 5[V] Voltage Source
© Brooks/Cole Publishing Co.
Next slide
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
i5
Figure 1.5a)
Device
We have attached the 5[V] voltage
source. We write KCL at the
top node, to get
i5  5[V]
 iD  0, or
0.93[A]  5[V]
Device
+
RD
+
v3
-
RD
 iD  0.
3[W]
5[V]
-
Figure 1.5c)
i5
Device
+
v4
-
Figure 1.5b)
4[A]
We used Ohm’s
Law to write the
current in the
resistor in terms
of the voltage
across it, which is
5[V].
iD
RD
+
5[V]
-
Dave Shattuck
University of Houston
Connecting the Device to the 4[A] Current Source
© Brooks/Cole Publishing Co.
Next slide
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
i5
Figure 1.5a)
Device
We have attached the 4[A] current
source. We write KCL at the
top node, to get
4[A]  34[V]
RD
 iD  0.
Device
+
+
v3
-
3[W]
5[V]
-
Figure 1.5c)
Device
+
v4
-
Figure 1.5b)
4[A]
We used Ohm’s
Law to write the
current in the
resistor in terms
of the voltage
across it, which is
-34[V].
+
iD
RD
v4
-
4[A]
Dave Shattuck
University of Houston
2 Equations and 2 Unknowns
© Brooks/Cole Publishing Co.
Next slide
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
We have obtained two equations
with two unknowns. They
are:
4[A]  34[V]
RD
 iD  0,
and
i5
Figure 1.5a)
Device
Device
+
+
v3
-
5[V]
3[W]
0.93[A]  5[V]
-
RD
 iD  0.
Figure 1.5c)
Thus, we can solve these
equations.
Device
+
v4
-
Figure 1.5b)
4[A]
After some algebra, our
solution for the model is:
iD = -0.3[A], and
RD = 7.9[W].
Dave Shattuck
University of Houston
Solve for the Voltage Across the 3[W] Resistor
© Brooks/Cole Publishing Co.
Next slide
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
i5
Figure 1.5a)
Device
Device
+
+
v3
-
3[W]
We plug these values in, and we have
the device as a circuit model. Now
we can connect the device to a 3[W]
resistor and solve. Writing KCL, and
using Ohm’s Law, we have
  0.3[A] 
v3

v3
7.9[W]
3[W]
Solving this for v3 yields
 0.
v3  0.66[V].
5[V]
-
Figure 1.5c)
+
Device
+
v4
-
4[A]
iD=
-0.3[A]
RD=
7.9[W] v3
Figure 1.5b)
-
3[W]
Dave Shattuck
University of Houston
Why is the plot of voltage vs. current for the device a
straight line? Part 1
Next slide
© Brooks/Cole Publishing Co.
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
i5
Figure 1.5a)
Device
Device
+
v3
-
+
We mentioned that for this problem a
plot of the voltage across the device
versus the current through the device
is a straight line. The key in this
problem is understanding why this is
true for this device.
We can prove this by writing KCL for
the device below, having assigned
names for the voltage and current.
3[W]
5[V]
-
it
Figure 1.5c)
+
Device
+
v4
-
Figure 1.5b)
4[A]
We can write:
v
 0.3[A]  t

iD 

vt
RD
iD=
 i  0, or -0.3[A]
7.9[W] t
 it  0.
RD=
7.9[W] vt
-
Dave Shattuck
University of Houston
Why is the plot of voltage vs. current for the device a
straight line? Part 2
Next slide
© Brooks/Cole Publishing Co.
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
i5
Figure 1.5a)
Device
We look at the equation we obtained
in this case. As long as the device can
be modeled as current source in
parallel with a resistor, the equation
will have this form. Note, that the
equation
iD 
Device
+
v3
-
+
3[W]
vt
RD
 it  0.
is the equation for a straight line, as
long as iD and RD are known.
5[V]
-
it
Figure 1.5c)
+
Device
+
v4
-
Figure 1.5b)
4[A]
We can write:
  0.3[A] 
iD 
vt
RD
vt
7.9[W]
 it  0, or
iD=
-0.3[A]
RD=
7.9[W] vt
 it  0.
-
Dave Shattuck
University of Houston
Why is the plot of voltage vs. current for the device a
straight line? Part 3
Next slide
© Brooks/Cole Publishing Co.
A device can be modeled using a current source in
parallel with a resistor. This device was connected to a
5[V] voltage source, as shown in Figure 1.5a), and a
current i5 of 0.93[A] resulted. The same device was
then connected to a 4[A] current source as shown in
Figure 1.5b), and a voltage v4 of –34[V] resulted. Find
the voltage v3 if a 3[W] resistor, as shown in Figure
1.5c), is connected to the same device.
i5
Figure 1.5a)
Device
+
iD 
vt
RD
 it  0
which can be rewritten as
vt  it RD  iD RD .
Device
+
v3
-
So, as long as the device can be
modeled as current source in parallel
with a resistor, the equation will be a
straight line. Note that we can write
3[W]
5[V]
-
it
Figure 1.5c)
Device
+
v4
-
Figure 1.5b)
4[A]
Note that in this case, if we plot vt vs.
it, then we have a straight line with a
slope of RD and an intercept of iDRD.
The signs of the slope and intercept
depend on the signs of the values of
iD and RD, and on the way we chose
polarities for it and vt.
+
iD=
-0.3[A]
RD=
7.9[W] vt
-
Dave Shattuck
University of Houston
Why is the plot of voltage vs. current for the device a
straight line? Part 4
© Brooks/Cole Publishing Co.
it
vt in [V]
10
5
0
-5
-10
-15
-20
-25
-30
-35
-40
+
5
-2.37
iD=
-0.3[A]
RD=
7.9[W] vt
-34
-5
-4
-3
-2
-1
0
1
2
it in [A]
We wrote
vt  it RD  iD RD .
We have a straight line with a slope
of RD (7.9[W]) and an intercept of
iDRD. (-0.3[A].7.9[W] = -2.37[V])
Go to notes
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
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.