Electrical engineering background concepts

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Electrical engineering background concepts
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Instrument Systems
Electrical Engineering Fundamentals
An instrument system is the correct combination
of sensor, controller, and final control element
that will allow a process to operate in an
automatic mode.
The vary first instrument systems were hydraulic
and for the most part major examples of public
works. The Roman aquifers in addition to
supplying drinking water had a system of weirs
and wheels designed to do specific jobs.
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Instrument Systems
Electrical Engineering Fundamentals
you need to figure out how to implant (embed) as
rich vibrant images the following terms and/or
concepts.
Force
Newton
Energy
Joule
Power
Watt
Charge
Coulomb
1 electrons charge
1 protons charge
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Instrument Systems
Electrical Engineering Fundamentals
Force is the push or pull that alters the
energy of an entity (system).
1 Newton of force will be needed to just stop a 1
kg mass object that is accelerating at 1 meter/
second squared.
.
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1 Newton

1 kg
1 meter / sec
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Instrument Systems
Electrical Engineering Fundamentals
Energy is the characteristic of an entity
(system) that is associated with its motion, its
potential motion and/or its lack of motion.
Objects (systems) that are in an identical
environment are grouped together and said to be
in the same Energy State.
( The unit of energy is Joules which are defined
as
The energy used when 1 Newton of force managed
to move the object 1 meter. )
.
1 Joule

1 Newton
meter
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Instrument Systems
Electrical Engineering Fundamentals
Power is a rate concept. Power is the rate
energy is used.
Your guess is as good as mine. BUT here are
some of its properties!!!
1 Watt is the rate when 1 Joule is used in 1
second.
1 watt

1 Joule/ second
Charge
is associated with objects.
What is it?
is packaged in electrons and protons.
is measured in Coulombs.
made Coulombs law famous!
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Instrument Systems
Electrical Engineering Fundamentals
Coulombs Law sort of says that two charge
particles in the same elevator (or any where else
for that matter) will not stay still.
Coulomb determined that the force needed to keep
them from moving was equal to
F (in Newtons)
k
Practice Problem
Show that two 1 Coulomb each charged particles in
free space 1 meter apart need to have 1 million
tons of force ( give or take a few tons) applied
in the correct direction to keep them from moving.
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Instrument Systems
Electrical Engineering Fundamentals
Potential Difference
Note
The second charged particle is not involved in
the calculation but is the reason the first
charged moved in the first place.
If one charged particle moves toward or away
from a second charge particle, the first charge
particle is now in a different energy state.
1 volt 1 Joule/ 1 Coulomb
The second charged particle is sometimes known as
the reference or test charge.
The difference between these two energy states
(the one the first particle is in now and the one
the first particle use to be in) is the potential
difference of the first particle.
Voltage is the potential difference per unit
charge.
Amount of charge on the first particle
Energy difference
V
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Instrument Systems
Electrical Engineering Fundamentals
Electric Field
If one charged particle moves because of the
presence of a test charge, the first charge is
said to move in (through) an electric force
field.
The charged particle can move toward or away from
the test charge but the field is still the region
where the influence of the test charge is felt by
the first charge.
The electric field lines define the electric
field with respect to the test charge.
The direction the first charge travels across the
electric field lines determines if the change in
energy can be used by us to do work.
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Instrument Systems
Electrical Engineering Fundamentals
Electric Field
Once a charge particle is in an electric field,
the only thing of interest is the voltage changes
because the charged particle moved to different
places in the electric field
( Once you have purchased that stock, you only
care about the changes in the price, not what the
stock costs.)
Knowledge of the voltage difference will let you
compute the energy difference between the two
points in the electric field if the charge on the
particle is know.
Energy difference
V
(Amount of charge on the particle)
Many times the charge particle is an electron and
the charge is know.
Use a volt meter for this value.
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Instrument Systems
Electrical Engineering Fundamentals
Current
Current is the rate of movement of electric
charge.
Current is not the rate of movement of the
charged particle.
Current is measured in amperes.
(amount of charge) / ( change in time)
current

1 ampere
1 Coulomb / second
Decision time !
We have to pick the sign of this 1 Coulomb charge.
Positive? Or negative?
Yep, Ben Franklin wins, the reference charge is
the positive charge, even though the electron is
the most common carrier of charge in systems we
will deal with.
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Instrument Systems
Electrical Engineering Fundamentals
Concepts that might seem confusing.
A charge moving from point b to point a
(lower voltage to higher voltage) requires energy
from the outside world and the charge is moving
up the field
A charge moving from point b to point a
produces an electrical current that itself
produces a net force. This force produced by an
electric current is referred to as magnetic
force, and it possess many of the properties of
the magnetic force associated with an ordinary
bar magnet.
A charged particle has a static electric field
around it.
A moving charged particle creates a current and
has a magnetic field around the path, usually a
wire, it is traveling on.
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Instrument Systems
Electrical Engineering Fundamentals
Conventions that might seem confusing.
But by drawing convention
When a charge moves from point b to point a
(lower voltage to higher voltage) energy is
required from the outside world and the charge
is moving across the field lines as it goes up
the field
Terminal a is assigned to be point at higher
voltage
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
The passive sign convention for labeling the
voltage and current of a two-terminal electric
circuit element.
When the element current and voltage are labeled
with the assumed current to enter the terminal of
assumed higher voltage the element is labeled
using the passive sign convention

b
i(t)
If the actual current and voltage agree with
their passive assignment the element is absorbing
energy
v(t)
Terminal a is assigned to be point at higher
voltage
a
-
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
If either (but not both) the current or voltage
differ from the assumed passive assignment, then
that negative component is opposite in direction
of its assumed orientation and the energy is
flowing in the opposite direction. (The two port
element is delivering power.)
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Practice Problem-- Assume the passive
labeling system is being practiced.
If the actual current and voltages are in the
orientations as shown, which two-terminal element
device is delivering power?
The one on the left
Terminal a is assigned to be point at higher
voltage
True terminal a is high energy point
False terminal a not high energy point
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Practice Problem-- Assume the passive labeling
system is being practiced.
If the actual current and voltages are in the
orientations as shown, what is the power and
direction of power for each of the following?
1)
2)
p(t) -v(t) i(t)
p(t) v(t) i(t)
p(t) (-3V)(4A) -12 Watts
p(t) (3V)(2A) 6 Watts
6W of power absorbed by this element
12W of power delivered by this element
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Practice Problem-- Assume the passive labeling
system is being practiced.
If the actual current and voltages are in the
orientations as shown, what is the power and
direction of power for each of the following?
3)
4)
p(t) -v(t) i(t)
p(t) v(t) -i(t)
p(t) (-3V)(-3A) 9 Watts
p(t) (5V)(-2A) -10 Watts
10W of power delivered by this element
9W of power absorbed by this element
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Is there a voltage gain or drop across the
following resistors?
This two terminal electric circuit element is the
resistor. The resistance of material used to
make a resistor is always a positive number.
1)
2)
v(t) -i(t)R
v(t) i(t)R
v(t)
v(t)
v(t) is positive indicating a voltage drop
v(t) is negative indicating a voltage gain
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Is there a charge gain or drop in each of the
following capacitor?
This two terminal electric circuit element is the
capacitor. The capacitance of a capacitor is
always a positive number
1)
2)
i(t) dv/dt)C
-
i(t) dv/dt)C
b
b
Energy being stored
Energy being released
a
a
i(t) is negative indicating the charge in the
capacitor is dropping.
i(t) is positive indicating a gain in the charge
of the capacitor.
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Are the following inductors absorbing or
releasing energy?
This two terminal electric circuit element is the
inductor. The inductance of practical inductors
is always a positive number
1)
2)
v(t) di/dt)L
-
v(t) di/dt)L
b
-
Energy being stored
v(t)
Energy being released

a
v(t) is negative indicating the inductor is
releasing energy.
v(t) is positive indicating the inductor is
absorbing energy.
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Instrument Systems
Electrical Engineering Fundamentals
Other concepts that might seem confusing.
The perfect world.
The ideal voltage supply
v(t)
The ideal current source
i(t)
Is a car battery an ideal voltage supply?
The voltage developed in an ideal voltage supply
is a dictated value that does not change with
age, use (misuse), application, snow, sleet,
rain, or etc, it just keeps providing the voltage
it was advertised to provide.
Is a lighting bolt, (like the one Ben Franklin
felt when he was flying his kite) an ideal
current supply?
An ideal current source will provide the stated
amount of current (a specific number of moving
charges/unit time) no matter what the demand for
that flow of charge becomes or how long that
demand lasts.
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Instrument Systems
Electrical Engineering Fundamentals
Other concepts that might seem confusing.
Is the energizer bunnies battery an ideal voltage
supply?
Hmmmmmm! Life does seems to be full of difficult
questions!
Circuit configurations
Voltage as function of time that is available for
use.
1)
Voltage value profile as a function of time
remains the same.
2)
Voltage value profile can be fixed value, dc,
shaped like a sine wave, ac, or any other desired
shape. The main point is that the specific
voltage value of the ideal supply at a specific
instant in time is always that exact value
desired no matter what the circumstances are.
3)
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Instrument Systems
Electrical Engineering Fundamentals
Other concepts that might seem confusing.
Ideal voltage supplies connected in series.
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Instrument Systems
Electrical Engineering Fundamentals
Other concepts that might seem confusing.
Ideal voltage supplies connected in parallel.
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Instrument Systems
Electrical Engineering Fundamentals
Other concepts that might seem confusing.
Ideal current source
Circuit configurations
Ideal current sources connected in series.
Ideal current sources connected in parallel.
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Things to remember about transformer passive
diagram symbolism.
This four terminal electric circuit element is a
coupled inductor (transformer).
1)
2)
M
(Mutual inductance)
b
d

3)



-
-
a
c
4)
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Things to remember about transformer passive
diagram symbolism.
5)
This four terminal electric circuit element is a
coupled inductor (transformer).
v (t)

2
1)
2)
M
(Mutual inductance)
b
d

3)



-
-
a
c
4)
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Things to remember about transformer passive
diagram symbolism.


M

The voltage difference v1(t) between point b and
point a is the sum of the voltage, v 1 induced
by the change
in current i1 and the mutually induced voltage
v 1 produced by the change in the flow of
current i2.
The voltage difference v2(t) between point d and
point c is the sum of the voltage, v 2 induced by
the change
in current i2 and the mutually induced voltage v
2 produced by the change in the flow of current
i1.
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Passive diagram example


An example of a three coupled coil system that is
complaint with the passive diagram symbolism.
A) how many equations are needed to describe this
three coupled inductor system?
-
-
-

i (t)
3
But it is more convenient to arrange them
this way!
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Passive diagram example
i (t)
1





An example of a three coupled coil system that is
complaint with the passive diagram symbolism.
-

-


-




i (t)
3
After a bit more manipulation and substitution we
get.


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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Passive diagram example
i (t)
1


v (t)

v (t)
v (t)
L (d /dt)


1
An example of a three coupled coil system that is
complaint with the passive diagram symbolism.
1
1
-
v (t)

v (t)
-


L (d /dt)
2
2
-
v (t)

v (t)


L (d /dt)
3
3

i (t)
3
Note
After a bit more manipulation and substitution we
get.









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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Passive diagram example
i (t)
1


The equations below model the three inductor
circuit to the right.
An example of a three coupled coil system that is
complaint with the passive diagram symbolism.
-
-
If the circuit you have to deal with is not wired
this way, you can manipulate the equations by
multiplying specific components by (-1) to get
the correct model.
-

i (t)
3
Try the next practice problem to see how this
works.









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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Practice Problem-- Assume the passive labeling
system is being practiced.
If the actual current and voltages in the
following diagram are in the orientations as
shown, what are the three equations that
determine the voltages across each of the coils,
respectively?
Note that either
A) the defined voltages and corresponding
currents do not all conform to the passive
sign convention.
or
B) the positive voltage terminal is not at the
dot.
To get to the correct set of equations, use
negative signs in the model equation set
everywhere such a sign corresponds to a reversal
of an item in the diagram to return the diagram
to its passive diagram form. 4 reversals must be
accomplished.
1) Reverse direction of i1
2) Reverse direction of i2
3) Reverse direction of v2
4) Reverse direction of v3
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Practice Problem-- Assume the passive labeling
system is being practiced.
If the actual current and voltages in the
following diagram are in the orientations as
shown, what are the three equations that
determine the voltages across each of the coils,
respectively?
-
-
-
-
-

-

-
-
-
-

-
1) Reverse direction of i1
-

-
2) Reverse direction of i2

i (t)
3
3) Reverse direction of v2
4) Reverse direction of v3
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Instrument Systems
Electrical Engineering Fundamentals
Other conventions that might seem confusing.
Practice Problem-- Assume the passive labeling
system is being practiced.
If the actual current and voltages in the
following diagram are in the orientations as
shown, what are the three equations that
determine the voltages across each of the coils,
respectively?
Thus the voltages for the three coupled coils are
modeled with the following three equations.
-



-



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