Download Sensors Technology MED4: Electron Flow – Current

Electric current
Sensors Technology MED4: Electron Flow – Current
Previously we dealt with electrostatic problems, where field problems are associated with electric
charges at rest.
We now consider the charges in motion that constitute current flow.
There two types of electric current are caused by the motion of free charges.
•
Conduction current, which are governed by Ohm’s law, in conductors and semiconductors are
caused by drift motion of conduction electrons and / or holes.
•
Convection current results from motion of electrons and / or ions in a vacuum or rarefied – such
as in a cathode ray tube.
Basically, what we are interested in electronics, are the possibilities for controlled motion and
transport of electric charge, especially within conductors – where the free electrons as the carriers
of charge are already present in the medium – that means we are interested in conduction
current.
In the case of conduction currents there may be more than one kind of charge carrier (electrons,
holes, and ions) drifting, with different velocities – all of which contribute to what we measure as
current.
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Electric current
Sensors Technology MED4: Electron Flow – Current
Since electric charge is quantized (in discrete multiples of the electron charge), it is instructive to look
at electric current as the movement of multiple microscopic charge carriers as discrete point
particles – although this may not directly correspond to the actual physical reality.
The physical quantity that deals with the description of the motion of electric charge is called electric
current:
- defined physically as the continuous [and directed ] flow of electric charge through a conducting
material
- defined mathematically as the rate of charge flow past a given point in an electric circuit, or in
other words, the quantity of charge  Q passing through some region of space (specific point in a
circuit) in a given time period t
Q
I
t
Electric current is measured in Amperes [A] and 1 Ampere corresponds to a rate of 1 Coulomb of
charge per 1 second, where 1 Coulomb is the charge of 6.24x1018 (6.24 quintillion ) electrons.
Note that the definition for current can be applied to other systems of flowing discrete particles – which
will enable us to relate electric current to flow of water. Also, the electric current definition
demands only mobile charged particles – this does not necesarilly mean only electrons.
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Current, conductors and field
Sensors Technology MED4: Electron Flow – Current
We are already aware of the fact that
- Charge can move under the influence of an electrostatic field
(=potential difference). The direction of electron movement is
from a region of negative potential to a region of positive
potential.
- Charge can freely move in a conductor (material medium), just
as well as in vacuum.
- Conductors which are in electric contact have the same
potential – they share excess charge between themselves (charge
can move between as well as in them), and equalize their
originally different internal potentials.
These findings are confirmed through the fact, that when a conductor is placed in electrostatic field, its
constituent free electrons move and redistribute in such manner that they cancel the field within
the conductor – and there is no further electron movement. This also means that the potential is
constant throughout the conductor.
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Electromotive force - emf
Sensors Technology MED4: Electron Flow – Current
Eventually an internal field due to the repositioned charge cancels an eventual external electrostatic
field resulting in zero current flow.
The conclusion is that we cannot induce directed motion of charge carried by the free electrons in a
conductor, by simply placing the conductor in an external electrostatic field – the free electrons
cancel the effect of the external electrostatic field within the conductor. To move the charge
within the conductor, in a directed fashion, we must set up a field within the conductor, or in other
words, we need to set up potential difference at the ends of the conductor – in that direction that
we want the free electrons to move.
Such a potential difference at the ends of a conductor can be set up by means of what is known as
electromotive force or emf.
So, charge can flow in a material under the influence of an external electric field. To maintain a
potential drop (and flow of charge) requires an external energy source known as electromotive
force – EMF, such as battery, power supply, signal generator, etc.
Another definition could be that emf is a physical quantity which describes the ability of an electrical
source to deliver energy - or the property of the source which creates current in a circuit. The emf
of a battery is responsible for producing a potential difference between the battery's terminals.
In order to understand the concept of electromotive force, we should take a closer look at the
meaning of potential in a conductor medium.
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Potential and charge density
Sensors Technology MED4: Electron Flow – Current
In review:
- An electrostatic field is due to an electrically charged particle.
- A potential gradient indicates an electrostatic field different from zero – and vice versa.
In order to have directed motion partucles in the conductor, we need a field directed in the conductor,
indicated by a corresponding potential gradient.
Locally in space, electrostatic potential is related to the strength of the electrostatic field at that point.
However, the strength of field is related to quantity of charge (or number of electrons) on a
charged body that causes the field, and the distance from it – and thus the potential, locally, is
related to both of these.
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Potential and charge density
Sensors Technology MED4: Electron Flow – Current
This means that if the distance to a charged body is not changed, we can use electrostatic potential
locally as an indication of the quantity of charge (or the concentration of charge carriers) that
produces the field.
Considering that the metal conductors already posess a significant number of free electrons as
charge carriers, the electrostatic potential within a conductor can be related to the measure of the
repulsive electrostatic forces acting between the free carriers themselves – whose strength
depends on the concentration of carriers in the conductor.
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Potential and charge density
Sensors Technology MED4: Electron Flow – Current
Considering that the metal conductors already posess a significant number of free electrons as
charge carriers, the electrostatic potential within a conductor can be related to the measure of the
repulsive electrostatic forces acting between the free carriers themselves – whose strength
depends on the concentration of carriers in the conductor.
The image displays a rendering of the potential (and thus local field) due to the mutual
repulsive forces from a concentration of charges.
Note that in normal conditions in a conductor, there is a given concentration of free carriers, for
which these repulsive forces are compensated by the molecular forces that hold the metal crystal
together.
If that normal concentration is related to a ”zero” potential, then a negative potential means
rarefaction, and positive means densification in relation to the normal density of free charge.
Remember from electrostatics that we can deposit charge on a conductor (charging), which means
effectively that the concentration (density) of charge changes in a conductor!
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Sensors Technology MED4: Electron Flow – Current
Potential and charge density – relation to pressure
Here we can observe one of the correspondances between fluids and free electrons.
Namely molecules in fluids (gases, liquids) have a certain freedom of movement, executed due to
thermal energy being able to cope with molecular forces (Thermal Physics and Properties of
Matter). Due to this, fluids assume the shape of a container. In addition, due to the chaotic
thermal movement, they hit each other and the walls of the container, causing on average a
measure of a pressure – force acting on given area.
The pressure is thus an indication of how much repulsion is there between the (free) molecules due
to collisions during their thermal motion.
Similarly, the potential is an indication of how much repulsion is there between the free electrons due
to the repulsive electrostatic field.
This relation helps with the understanding that the movement direction for free carriers is from a state
of high repulsion (potential / pressure) towards low repulsion (possibly equilibrium).
Electrons free to move (metal)
Molecules free to move (fluid)
Less dense – less electrostatic repulsion – less force per
area (or per num. charges )
Less dense – less collisions due to thermal motion – less
force per area (or per num. molecules )
More dense – more electrostatic repulsion – more force
More dense – more thermal collisions – more force
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Sensors Technology MED4: Electron Flow – Current
Potential and charge density – electron gas
In reality, free electrons in a conductor behave a lot like gas
molecules in container. They not only move and redistribute
throughout the conductor – effectively assuming the shape of the
container, but they also exhibit chaotic thermal movement as
well. During such movement they can collide with other free
electrons, or other particles within the conductor – which is why
the free electrons in a conductor are referred to as electron gas.
It is important to realise that a free electron does not remain in free chaotic
movement as a free molecule in gas does. The situation is usually that an
electron gains energy to become free, moves for a short while due to thermal
energy and/or external field, and then experiences a collision where it gives its
energy, and becomes bound to an atom again.
motion of free electrons in
a conductor
The sitation we have is that on average during a given time period, we always
have a given number of free electrons moving, which relates to the gas (fluid)
aspect.
collisions
The fact that the free electrons fill out the conductor (the shape of the
container) as fluid (gas), helps us understand a conductor as a fluid container,
and relate it macroscopically to a pipe filled with fluid (for instance water).
Note that in this analogy, a gas is a compressible fluid, while water is not compressible – however,
due to the electrostatic repulsive force, the “pressure” applied at one part gets transferred to another,
like in liquids.
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Conduction path
Sensors Technology MED4: Electron Flow – Current
The fact that the free electrons fill out the conductor (the shape of the container) as fluid (gas),
helps us understand a conductor as a fluid container, and relate it macroscopically to a pipe filled
with fluid (for instance water).
That means that a conductor’s shape, as a container, also represents a path for its constituent free
electrons – a path where they could freely move – in similar manner a pipe as a container
represents a path where water can freely flow.
If we want electrons to flow in a certain direction to a certain place, we must provide the
proper path for them to move, just as a plumber must install piping to get water to flow.
Remember that electrons can flow only when they have the opportunity to move in the space
between the atoms of a material – and that opportunity is present in a conductive material.
This means that there can be electric current only where there exists a continuous path of
conductive material providing a conduit for electrons to travel through.
A single path is thus related to a single piece of conductor which we know as a conducting
wire.
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Conduction path connection
Sensors Technology MED4: Electron Flow – Current
As mentioned before, whent two (or more) conducting bodies are in electrical contact, they can
share excess charge – which means charge can move between the two. In addition, they attempt to
equalise their potential, so eventually, the system of connected conductors behaves like one
conductor, with one potential shared for all participating conducting bodies.
It is in this way we can connect conductors, and thereby establish a continuous path for the
electrons to move. This can of course be related to a system of connected water pipes, which
establish a path for water flow.
In both cases, at start we have two conductors
Water flow
Electron flow
(pipes) containing different ammounts of particles,
and thus dufferent levels of internal potential
(pressure).
When a counductor (pipe) is connected between the
two, the particles can freely flow between the two,
and aim to redistribute so that the potential
(pressure) is equalized (see Pascal’s Principle), thus
current begins to flow – a mass transport of particles.
Since now the two original bodies, and the
connecting conductor represent one conducting
body (pipe), a disturbance in potential (pressure) will
be gradually transferred to all the particles in the
container – which is the essence of the conduction
mechanism.
Note that when the potential (pressure) is equalised,
the current stops.
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Transient current
Sensors Technology MED4: Electron Flow – Current
Note that we could relate this example to a system of two charged
conducting bodies, which become connected with a conductor (say, a
wire). Since after the connection they must redistribute their excess
charge between themselves, so the field inside is zero, current must
flow through the conductor wire.
As soon as the charge is evenly distributed, there
is no more flow of particles – current. Such current
persists for a very short time and is known as a
transient current.
In the more general applications, currents more persistant in time
are needed – and these are known as continuous currents.
If the rate of the number of free electrons crossing a given point is
constant in a given time interval, it is known as a steady current.
If the direction of the free electron flow does not change in relation to
some referently chosen direction during time, then it is known as
direct current (DC). The direction of the current can be easily
determined through the normal of our ”test surface” – which help us
count the number of electrons past a certain point.
Note that in the most basic case, in order to have current, as flow of particles, we need to have a
difference of potential[pressure], a conducting path and free particles that will move.
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Sensors Technology MED4: Electron Flow – Current
Transient current – capacitor discharge
The given system of two charged conducting bodies separated by a
dielectric is by definition a capacitor, and in a capacitor, deposited charge
means voltage:
C
Q
U
That means that since we have deposited excess charge, it has
redistributed (on the surface) so the field inside is 0, which means there is a
constant potential inside, which we can relate to the average electrostatic
repulsion a free electron might feel from the other free electrons. This
repulsion, is of course dependant on how many free electrons there are –
excess charge included.
In that sense, potential in metals with free carriers is related to
concentration of carriers. And hence for two conducting bodies (separated
by a dielectric – capacitor), a difference in potential, or voltage, means also
a difference of concentration of charge. (Finally, the difference in potential
between two points means existence of an electric field.)
And it is this difference, regardless of how we see is (as difference of potential = voltage, as
difference of concentration or as difference in the repulsive pressure the electron ”sees”) that will
cause the particles to move from more negative (higher pressure) to more positive potential (lower
pressure) – given a conducting path.
These are the minimum requirements for current flow – presence of free carriers, a conducting path,
and potential difference (voltage) at the ends of the conducting path.
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Sensors Technology MED4: Electron Flow – Current
Transient current – capacitor discharge
In the example, in the start, we have two separate conducting bodies,
separated by non conductng medium (dielectric) – which constitutes a
capacitor. There is a difference in concentration, which implies that one of
the bodies carries excess charge. Thus, there exists a difference of
potential or voltage, between the two bodies, due to excess charge.
When the dielectric is replaced with conductive material, we establish a
path between the two bodies, on which ends now there is potential
difference, and the free carriers can move. By moving, we effectively are
taking away excess electrons from one body and placing it on the other, so
the current flow reduces the excess charge – and thus the potential
difference between the two.
When the excess charge is levelled out, there is no more voltage, and thus
there is no more current.
This is the example of a charged capacitor, having its terminals connected with a conductor – and
the transient current that appears is known as capacitor discharge current. Due to the excess
charge there is voltage on its terminals. When the conductor is connected to the terminals, the
excess charge from one body is taken away – discharge – which lowers the potential difference.
Although this illustrates a minimal situation for current, it results only in a transient one - we are
interested in continuous currents – that persist over time, so we should take a closer look at the
conduction mechanism.
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Conduction mechanism
Sensors Technology MED4: Electron Flow – Current
The requirements for a path and free carriers in order to have current are both satisfied by
metals as conductors – since they already contain a number of free electrons.
The mechanism of movement is thus not as straightforward as thinking that one free electron
crosses the entire distance of the conductor.
As each electron moves uniformly through a conductor, it pushes on the one ahead of it,
such that all the electrons move together as a group. The starting and stopping of electron
flow through the length of a conductive path is virtually instantaneous from one end of a
conductor to the other, even though the motion of each electron may be very slow. An
approximate analogy is that of a tube filled end-to-end with marbles.’
The tube is full of marbles, just as a conductor is full of free electrons ready to be moved by an outside
influence. If a single marble is suddenly inserted into this full tube on the left-hand side, another marble will
immediately try to exit the tube on the right. Even though each marble only traveled a short distance, the
transfer of motion through the tube is virtually instantaneous from the left end to the right end, no matter how
long the tube is. With electricity, the overall effect from one end of a conductor to the other happens at the
speed of light: 300 million meters per second!!! Each individual electron, though, travels through the
conductor at a much slower pace.
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Conduction mechanism
Sensors Technology MED4: Electron Flow – Current
Remember that electrons can flow only when they have the opportunity to move in the space
between the atoms of a material.
This means that there can be electric current only where there exists a continuous path of
conductive material providing a conduit for electrons to travel through. In the marble analogy,
marbles can flow into the left-hand side of the tube (and, consequently, through the tube) if
and only if the tube is open on the right-hand side for marbles to flow out.
If the tube is blocked on the right-hand side, the marbles will just "pile up" inside the tube,
and marble "flow" will not occur. [from here]
However, that also means that when we connect such ”blocked” conductors (in our case the
copper conductor would be ”closed” with air – which is why we actually call this situation an
”open” circuit) any eventual ”push” on one side of the conductor (resulting from say an
electric contact with a charged body), will be transferred to the other side of the conductor.
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Sensors Technology MED4: Electron Flow – Current
Conduction mechanism – wave aspect
If we think about what happens from an electrostatic perspective, upon an insertion of an
extra electron (marble): the local density of charge carriers increases, increasing the
repulsive force at that point, and correspondingly, the overall electrostatic field is changed
due to this electron.
Since we know that the electrostatic field travels with the finite speed of light, the information
of the change represented through the field will also travel at the same speed. Note that if the
conductor was in equillibrium previously (and charges did not move due to the field), the
charges further on in the conductor (say 1 cm apart) will start moving only after the
information of the changed field has reached them (for 1 cm, and speed of lights, this is 333
nanoseconds!).
That means that the changed field due to changed density in a conductor travels as a
distrubance through the medium of the conductor, which is by definition a wave.
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Sensors Technology MED4: Electron Flow – Current
Conduction mechanism – wave aspect
This basically means that the starting and stopping of electron flow through the length of a
conductive path is propagates from one end of a conductor to the other with the speed of
light as a wave – the electrons start their actual movement right aftwreards.
For the wave aspect of conduction, read Understanding electrical conductivity in wires
The wave propagation if a cause of reflections in wires (transmission lines), and the need to
account for characteristic impedance of cables.
Applets from the site:
Reflection – mathematically – see tri line applet here
Interaction of electrons – see five el applet here
Physically, via speed of particles – see terminated applet here for terminated wire, see open
applet here for open wire
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Sensors Technology MED4: Electron Flow – Current
Emf potential as power source
We can now consider the two terminals of a source of emf as two conducting bodies – and say that
the negative terminal has more free electrons than the usual number for that particular metal –
which causes a more negative potential in that piece of material, in relation to the positive
terminal – and hence the potential difference, or voltage, between the terminals of the source.
Normal
concentration for the
terminals conductor
The electromotive force tries to maintain this potential difference – and the difference of
concentration of free charge at the terminals - in time.
A useful metaphor is that in order to maintain the difference in concentration of charge, the battery
must take away charge from the positive terminal conductor and move it to the negative terminal –
performing work while doing so – which is how we can provide continouous and steady current.
Since it must maintain this difference over time (otherwise the excess charge will redistribute and
equalise the potential at the terminals) – it must continually perform work as time goes. By definition,
rate of work is power, and it is thus a main characteristic of sources of emf.
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Electromotive force - emf
Sensors Technology MED4: Electron Flow – Current
We could rephrase:
The electromotive force EMF of a source of electric potential energy is defined as the amount of
electric energy per Coulomb of positive charge as the charge passes through the source from low
potential to high potential.
A difference in charge between two points in a material can be created by an external energy source
such as a battery. This causes electrons to move so that there is an excess of electrons at one
point and a deficiency of electrons at a second point. This difference in charge is stored as
electrical potential energy known as emf. It is the emf that causes a current to flow through a
circuit.
A circuit consists of electrons flowing from the negative terminal of a battery to the positive terminal of
the battery. However, these electrons must then return to the negative terminal, or the current will
stop flowing. The electrons are forced into this higher potential by an electromotive force – and
this is intuitively very similar to the notion of the energy of a water pump.
Emf is not a ”force” - the “electromotive force” represents an electric potential or voltage and is
measured in Volts [symbol V].
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Electric circuit?
Sensors Technology MED4: Electron Flow – Current
We mentioned presence of free carriers, a conducting path, and potential difference (voltage) at the
ends of the conducting path as minimum requirements for electric current.
Since we were interested in continuous current, an emf generator can be used as source of potential
difference, and a conductor can be used to provide the free carriers and the conducting path.
Due to the definition of work of the power source – that it takes away charge from one terminal and
moves it to the other, it is obvious that a closed loop conducting path (toward the source) is
needed if energy is to be utilized outside the source; this conducting loop is known as an electric
circuit. This is the basic meaning behind electric circuit.
However, because of the same definition, we need to
consider that if work is put in, that energy must be
used up somewhere – so we need to look at the
power relations.
electric circuit - complete (unbroken) conducting path along which an
electric current exists or is intended or able to flow. A circuit of this type is
termed a closed circuit, and a circuit in which the current path is not
continuous is called an open circuit.
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Power and resistance
Sensors Technology MED4: Electron Flow – Current
Since we defined our source via power, we must recognize the law of conservation of energy. That is,
if the generator put some work in a system, that energy must be somehow used in the system.
This can be visualised on a system made of frictionless track, a ball that can move on the track, and a
power generator which can perform work on the ball pull it toward itself and accelerate it on the
other direction.
If we cover a part of the track with sand or other material that causes friction, then the acceleration
given by the source is used up on compensating the friction forces – which effectively turns the
energy of the source into heat. The ball arrives ”tired” at the source, with reduced velocity, and
the cycle will then continue in a predictable fashion.
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Sensors Technology MED4: Electron Flow – Current
Power and resistance – short circuit
However, if we disregard the resistance, then the ball arrives at the source with the same speed it has
reached during the past acceleration, and as the cycle repeats, it gains more and more energy,
and theoretically, it should reach infinite velocity, which is impossible. (see applet)
Consider that in reality, we do not deal with one particle, but with a number of them – and according to
the conduction mechanism - the energy, without resistance and via progressive transfer of the
push from particle to particle, will simply return to the power source and force it to accept energy
instead of give it – which is a situation that is destructive to the generator.
This corresponds to the situation of a short circuit – where the terminals of the power source are
connected only through a conductive wire, which has small resistance – and we must always be
careful to avoid this!
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Electric circuit
Sensors Technology MED4: Electron Flow – Current
We can now put up a more complete basic definition for an electric circuit – one that can sustain
continuous currents due to a power source.
Namely, it is obvious that some sort of friction of the conducting path – resistance to the flow of
current, or user of the provided energy of the source - must be included in the model. Locally, as
property of conductive materials this property is called resistivity (r), and as a property of
conductive objects with finite dimensions – resistance [R].
All conductive materials (such as metals) are resistive – some more, some less. This brings about the
distinction in conductive materials as:
- conductors – good conductive properties, small resistivity (copper, silver, ... )
- resistors – big resistivity (graphite).
Additionally, theoretically we can define an ideal conductor, which has resistivity zero.
.
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Electric circuit
Sensors Technology MED4: Electron Flow – Current
electric circuit - complete (unbroken) conducting path along which an electric current exists or is
intended or able to flow. The term is usually taken to mean a continuous path composed of
conductors and conducting devices and including a source of electromotive force that drives the
current around the circuit.
A closed loop conducting path is needed if energy is to be utilized outside the source; this conducting
loop is known as an electric circuit. The device or circuit component utilizing the electric energy is
called the load.
Note that we now have a situation where free electrons circulate in a conductive medium, which was
not possible solely with an electrostatic field.
.
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Sensors Technology MED4: Electron Flow – Current
Electric circuit – fluid mechanics
The basic notion of an electric circuit can be demonstrated through a fluid example. Most practical
applications of electricity involve the flow of electric current in a closed path under the influence
of a driving voltage, analogous to the flow in a water circuit under the influence of a driving
pressure. A fluid is either a gas (like air) or liquid (like water) that does not hold its own shape.
.
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Sensors Technology MED4: Electron Flow – Current
Ohm’s law
This analogy also gives way for intuitive understanding of Ohm’s law, as formulating the necessity for
the conductive loop, free particles, potential difference and resistance, in order to have a
possible circuit that will sustain steady current – where the energy exchange demanded by power
genator is possible:
U
I
R
U
I
R
Said in other words, all that the power
source needs to “see” on its terminals is
a finite resistance (not zero and not
infinite), in order for continuous current
to flow.
.
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Ohm’s law
U
I
R
Sensors Technology MED4: Electron Flow – Current
U
I
R
In the water analogy we have that greater pressure results with
greater speed – which results with more particles crossed
through a hole per given time interval.
That can be directly applied to electron flow, where increased
voltage results with more free electrons crossed through a point
in the conductor per given time interval.
.
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Ohm’s law and sensors.
Sensors Technology MED4: Electron Flow – Current
Ohm’s law, even on this intuitive level is of essential meaning for sensors.
I
U
R
To transmit information costs energy: Every message is
associated with a material object or radiation, and must thus be
accompanied by some energy.
So, every signal must convey some energy/power — except the
trivial case of the signal “0 Volts”. Thus, when you apply an input
voltage to, say, an oscilloscope, it must also draw a small current
to make it recognise that a signal has arrived.
This can be related to the fact that when current flows, that means
that energy exchange is happening between the generator and the
load.
Any piece of equipment which accepts input signals will require both a voltage and a current to make
it work..All instrumentation modules, which actively gather data, must extract energy from sensors in
order to measure information.
A transduction element will commonly provide a relationship between some physical parameter, and
its own resistance or generated emf. Basically, what we need to do in order to read this information –
(or to interface with the sensor), is to bring the transduction element in a ciruit where current flows –
where there is energy exchange – and transfer this energy to the load – the user circuit.
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Sensors Technology MED4: Electron Flow – Current
Ideal power source – current and voltage
We have already mentioned that the power source produces voltage by moving electrons from the
positive to the negative terminal – this being the energy input in the circuit. Since work is defined
as charge times potential difference, the rate of work which is power will be potential difference
times rate of charge (current), which is:
P UI
On the other hand, we saw that a resistor is necessary to utilize this energy in the circuit – and the
very parameter of a resistance sets up a relationship between voltage and current. That means,
that a voltage applied to a resistor determines the current through it – so we say that when
voltage is applied to a resistor, it draws current – or, when current is forced into a resistor, voltage
appears on its terminals – related to the resistance.
That means that when the power source starts its work, and realizes the resistance, it has two options
on how to proceed – either to keep the potential difference on its ends, and dose the ammount of
charge as according to what the resistor demands, or to keep a constant rate of charge flowing
into the resistor, and develop a potential difference based on what the resistor produces for that
particular current.
.
These
represent idealized electrical sources of power:
1. Ideal voltage source – that keeps a constant potential difference on its ends, no matter what the
current through it – EMF refers to the pot. difference of an ideal voltage source
2. Ideal current source – that keeps a constant rate of charges flowing, no matter what the voltage
across it.
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Sensors Technology MED4: Electron Flow – Current
Ideal power source – current and voltage
These represent idealized electrical sources of power:
1.
Ideal voltage source – that keeps a constant potential difference on its ends, no matter what the
current through it – EMF refers to the pot. difference of an ideal voltage source
An ideal voltage source is an element in which the voltage across its terminals is an
independently specified function of time Vs(t). It is capable of supplying, or absorbing,
infinite current in order to maintain the specified voltage.
2.
Ideal current source – that keeps a constant rate of charges flowing, no matter what the voltage
across it.
The ideal current source is an element in which the current supplied to the system is an
independently specified function of time Is(t). The terminal voltage of a current source is
defined by the system to which it is connected.
These two ideal sources may continuously supply or absorb energy since in each, one power variable
is independently specified while the complementary power variable is determined by the system
to which the source is coupled. Ideal sources are capable of supplying (or absorbing) infinite
power and are idealizations of real sources, which have finite power and energy capability - and
thus only approximate real power-limited sources.
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Sensors Technology MED4: Electron Flow – Current
Power sources and energy exchange
Since we have defined a relation for the power of the source, and since we used resistance to
account for the energy expenditure (heat dissipation) in the circuit – we can now calculate that for
the elementary circuit, the power produced by the source will be the same as the one used by the
load:
+
V
-
i
P=Vi
Produced by Source
Or
Used by Load
i
+
Load V
-
Since the resistance was introduced to account for the energy expenditure, we can rewrite the
relation for the power expenditure in the load through the property of resistance or:
P UI  RI 2
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Real power sources
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The idealised model for the power sources, does not take into account the fact that any power source
has some internal resistance.
This internal resistance can be modelled as a resistor in series with an ideal voltage source, and a
resistor in parallel with an ideal current source.
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Resistivity and resistance
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However, in order to understand Ohms law better, we need to take a look a closer look at resistivity –
on the molecular scale (more: Ohms Law and Materials Properties).
This is because we have introduced resistance in order to model some sort of friction, to account for
the impossibility of infinite velocity; however there is no friction on the molecular scale – only
effects of fields. In addition, Ohm’s law, as it is given, is limited to only a class of conductive
materials called ohmic materials – where the resistivity is generally not dependant on the electric
field (and thus the voltage).
The best way to model resistivity is through free electrons, as particles, being able to experience a hit
or collision with another particle. During this hit, the momentum that the particle has can be given
to the other particle, and transferred as heat, and the particle may continue in a different
direction.
This behaviour is very similar to gas in a container,
which is why free electrons in conductors are referred to
as the “electron gas”.
.
Even without influence of a field, the free electrons are in
a state of chaotic movement and collision, due to the
thermal energy of the crystal. During these an electron
may lose energy and even fall back into a shell of the
crystal ion – possibly giving energy to another bound
electron so it becomes free.
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Resistivity and resistance
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The free electron might collide with (and scatter from):
-
Another free electron
-
A defect in the crystal lattice
-
A vibration of the crystal latice called a phonon
which essentially represents the Drude model of conduction.
.
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Resistivity and resistance
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Under the influnce of electric field, the chaotic movement does not stop – instead, the overall
movement gains a direction – as in a swarm of bees. This net directional velocity is called drift
velocity.
drift
drift
.
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Resistivity and resistance
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The influence of the chaotic movement can be averaged out, and then we can work only with the drift
velocity, which is due to the field:
.
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Resistivity and resistance
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This gives us the possibility to use a test surface, normal to the direction of flow of current, and have a
concept of number of electrons that crossed the surface amongst all that random movement –
and a numerical value for current.
This is also a good place to note that generally, it doesn’t have to be only free electrons that move –
those could be positive particles, such as lacks of shell electrons in a crystal due to impurities! In
that case, we add the effects of the positive and the negative particles.
.
Actually, it is much easier to think in terms of current of free electrons, as a
flow of positive particles from the positive to the negative terminal of the
battery! Although that is not the case, this direction is widely used and is
known as technical direction of current.
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Resistivity and resistance
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We needed the previous steps because we need to see what happens on average, in between the
collisions. As the source performs work and begins to insert electrons, electrons further on in the
conductor sense the field and begin to move, repelled by it. However, some of those will
experience collisions, and they might end up in the opposite direction of where they are
supposed to go. These on average, make the drift velocity lower.
That at the same time means that locally, those that have gone back, are contributing to the greater
density of free charges at that point – and thus greater electrostatic repulsion, and greater
potential. So, because of collisions and scattering with other particles – which is our cause of
resistivity – during current, there appears a accumulation of charge locally at the conductor, which
on average move slower – have a lower drift velocity.
.
However, greater density
means also stronger
potential – and stronger
repulsion for those that
actually did “cross the
surface” and contributed
to the current. That means
that they will be locally
less dense, and faster!
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Resistivity and resistance
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The situation that we have now in the conductor is that due to the resistance due to collisions - a
difference in concentration of free charge is established, due to deposited charge that went back
from the collision, along the line of flow of current – and the corresponding potential gradient, due
to which, there is also a difference in the speed of particles.
This concept of hits and deposition can be directly related
to the macroscopic multilayered sieve (the one pictured is
on the right for materials analysis).
It can also be related to flow of water, in the sense of a
sieve(strainer) intercepting the flow of water.
The sieve can be related to the static crystal lattice of
the conductor, and the water molecules to the free
electrons.
Basically, the effect of the crystall latice on the electron flow
as a sieve would relate to our measure for resistivity, locally
in the conductor.
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Resistivity and resistance
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If water was compressible, it would not be difficult to relate a “deposition” of water molecules and
increase of water pressure because the molecules on their way hit the walls of the sieve and try
to turn back. Thus, effectively the sieve can be seen as a nozzle – which effectively lowers the
area through which water can flow.
Due to the principle of conservation of mass –
whatever flows in must flow out, regardless if the
cross section area is smaller – and that is
possible only if the molecules move faster (being
too close together, they will start repelling and
increase the pressure – which on microscopic
level is close to the logic of the electrons
repelling).
Thus a smaller cross sectional area in direction
of the flow represents resistance to flow, and
causes particles to move faster.
In spite of the fact that there is a gradient of concentration
of carriers – it will still result in the same current – as
average number of electrons that crossed a certain point throughout the conductor.
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Resistivity and resistance
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Another visual rendering of the interaction of free electrons with the crystal lattice that results with hits
and slowdown, can done be through the following macroscopic model – which might represent for
instance a “top” view at the “sieve” structure of the lattice, while the electrons are moving through
it. The analogy is also that the “sieve” effect of the lattice is distributed throughout the conductor
material:
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Resistivity and resistance
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The most important finding is that for ohmic materials, resistivity – as parameter of expected hits due
to the specific build up of the conductor – does not depend on the electric field. In that case, we
can treat a given conductive object as a whole, and express ts resistivity and its geometry (which
we have seen also influences the flow of current) through one parameter called resistance: Note
that this is the resistance which is called real resistance, which attributes for the development of
heat and dissipation of the energy of the source.
The resistivity r is a
parameter which would
describe the specific “sieve”
of a conductor – however, it is
r throughout
R as “box”
reapplied throughout the
dimensions of the material.
l
Rr
S
S
Therefore, we basically
“lump” physical processes
involved with resistivity inside
a single package – ”black
box” - called a resistor,
described with only one
parameter - resistance (R).
The resistance is the overall
effect of resistivity (effect of
all the “sieves”) within the
resistor’s entire volume on
the flow of current.
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Resistivity and resistance
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l
Rr
S
S
For ohmic materials, both resistivity and R are independent of the el. field (and voltage), and
means that the resistive effect upon the flow of current is constant in relation to voltage.
So, for these materials, Ohms law will become a linear equation – and the relationship between
the voltage across and the current through a resistor will be a linear one – linear UI
characteristic. Ohm’s Law now provides a numerical relationship between current, voltage and
resistance of a resistor.
R
U
I
R
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Current flow simulation
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Applets:
Resistance at molecular level – demostration of collisions
Electrons in metal simulation – demonstration of how the crystal lattice (the ”sieve” geometry) and
thus collisions, depend on temperature.
Light Bulb applet Resistance applet
Consider the simple circuit applet for
demonstration
of the gradient of potential
.
and concentration, as well as the change
in speed according to density of particles,
and wave propagation of the field – and
power relations between source and load.
Consider the Venturi Tube simulation applet for
demonstration that the local pressure, during
current flow, acts in all directions – and given a
conduit at that position, that “push” will be
propagated through the conduit. The same
concept applies for potential in electric circuits –
and allows us to measure voltage (as potential
diff. on the ends of a piece of cond. material)
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Circuit theory – graphs and network topologies
We have already realised that the flow of current, first and foremost means that there is energy
exchange of some sort, and in the simplest possible setup, this is an exchange between source -- a provider of energy in the circuit, such as a generator, and load – a user of energy in the circuit,
such as a resistor.
Systems for transport of free electrons (current flow), can of course be more complicated than the
basic case. Nonetheless, the above findings must still be valid. As the complexity of the transport
system grows, it can be difficult to keep track of all the parameters which influence the flow of
current – especially since the geometry of the connections influences possibilities for flow.
In general: The internal flow of fluids through pipes, vessels, and pumps,
and the external flow around vehicles, aircraft, spacecraft, and ships are
complex phenomena involving flow variables that are continuous functions
of both space and time.
As such they generally cannot be represented in terms of pure lumped
elements.
.
With some simplifying assumptions, however, a number of significant
characteristics of the dynamic behavior of fluid systems, particularly for one
dimensional pipe flows, can be adequately modeled with lumped parameter
elements.
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Circuit theory – graphs and network topologies
With some simplifying assumptions, however, a number of significant characteristics, can be
adequately modeled with lumped parameter elements. :
• In circuit analysis, important characteristics are grouped together in “lumps”
(separate circuit elements) connected by perfect conductors (“wires”)
• An electrical system can be modeled by an electric circuit (combination of
paths, each containing 1 or more circuit elements) if
l = c/f >> physical dimensions of system
l = Distance travelled by a particle travelling at the speed of light in one period
Example: f = 100 Hz
l = 3 x 108 m/s / 100 = 3,000 km
We define a set of lumped parameter elements that store and dissipate energy in network-like fluid
systems,
that is systems which consist primarily of conduits (pipes) and vessels filled with
.
incompressible fluid. These definitions are analogous to those for mechanical and electrical system
networks.
A transportation network enables flows of people, freight or information, which are occurring along links.
A graph is a symbolic representation of a network. It implies an abstraction of the reality so it can be
simplified as a set of linked nodes. Graph theory is a branch of mathematics concerned about how
networks can be encoded and their properties measured.
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Circuit theory – graphs and network topologies
A transportation network enables flows of people, freight, information – or free electrons, which are
occurring along links. A graph is a symbolic representation of a network. It implies an abstraction
of the reality so it can be simplified as a set of linked nodes. Graph theory must thus offer the
possibility of representing movements as linkages.
The goal of a graph is representing the structure, not the appearance of a network. The conversion of
a real network in a planar graph is a straightforward process which follows some basic rules: The
most important rule is that every terminal and intersection point becomes a node. Each
connected nodes is then linked by a straight segment.
.
The outcome of this abstraction, as portrayed in the above figure, is the actual structure of the
network. The real network, depending on its complexity, may be confusing in terms of revealing
its connectivity (what is linked with what). However, the graph representation reveals the
connectivity of a network in the best possible way.
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Circuit theory – graphs and network topologies
As the complexity of the transport system grows, it can be difficult to keep track of all the parameters
which influence the flow of current – especially since the geometry of the connections influences
possibilities for flow.
Since it is only the geometry of connections that matter - the structure, not the appearance of a
network - what we have obtained with the graph is the topology of a network. And we can redraw
it until it reveals the connectivity of a network in the best possible way.
The ideas involved in network topology come from a branch of geometry (topology), which is
concerned with the properties of a geometrical figure that do not change when the figure is drawn
in alternate forms, where those alternate forms do not involve taking apart or joining together any
parts of the figure. In the case of a given electric circuit, it can be redrawn in many ways, and it
still is the same circuit. So regardless of the way the circuit is drawn, it can be analyzed in the
same fashion.
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Sensors Technology MED4: Electron Flow – Current
Circuit theory – graphs and network topologies
We have already realised that the flow of current, first and foremost means that there is energy
exchange of some sort, and in the simplest possible setup, this is an exchange between source
and load.
As the complexity of the transport system grows, it can be difficult to keep track of all the parameters
which influence the flow of current – especially since the geometry of the connections influences
possibilities for flow.
That is why it is useful to go back to the elementary circuit of energy exchange between source and
load – and realise the basic aspects of representation of topologies of electric circuits.
The figure displays three representations superimposed upon one another - of the
topology of an elementary circuit between
a source and a load:
.
- branches & nodes (graph representation)
(red)
- Connection of elements with ports
(schematic representation) (gray)
- Connection of networks with ports (black)
all of which are based on, and related to,
the graph representation of this circuit.
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Circuit theory – graphs and network topologies
Generally
A branch may consist of more than one element
A network may encompass a more complex connection than just a single branch
(In the elementary circuit, one branch consists of one element each, and each network consists of one element)
The graph representation is the basics for the remaining two. It basically represents the path of
transport – which in our case is conductive path for transport of free electrons or current – without
any regard to the special conditions on that path. Each path segment is modelled with a branch
(wire / pipe), each end (termination) of a path is modelled with a node (end of wire / pipe - terminal).
+
.
The nodes of both branches are connected (that
is why we are focused on topology of
connections), so we form a circular (closed)
conducting path for current flow – a circuit. So,
we need at least two branches to close a circuit.
Since our definition for current – elementary
circuit – demands at least two types of elements
(source and load) – neither of them can alone
represent a circuit – so they must each have (at
least) two terminals.
The two terminals then correspond to the two
nodes each branch has.
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Circuit theory – graphs and network topologies
Terms from graph theory:
Graph. A transportation network, like any network, can be represented as a graph.
Vertex (Node). A node v is a terminal point or an intersection point of a graph. It is the abstraction of a
location such as a city, an administrative division, a road intersection or a transport terminal
(stations, terminuses, harbors and airports).
Edge (Link - Branch). An edge e is a link
between two nodes.
+
.
Path. A sequence of links that are traveled in the
same direction.
Circuit. A path in where the initial and terminal
node corresponds. It is a cycle where all the links
are traveled in the same direction.
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Circuit theory – graphs and network topologies
The schematic representation of a circuit, adds the possibility of modelling the transport conditions
(such as resistivity) of a path (branch) to the graph representation.
This is done by assigning a lump model (such as resistance) to the branch in the form of an element.
The element must retain its two terminals, and these are modelled by ideal conducting paths – in our
terms, ideal conductors.
The schematic diagram consists of idealized
circuit elements each of which represents
some property of the actual circuit.
It thus has its own symbolic language for
representation of these elements on the
graph: circuit schematic symbols
.
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Circuit theory – graphs and network topologies
The flow of current through the elements can be modelled
with arrows.
On the other hand, we are aware that current is related to
potential difference between the terminals of an element.
Since we must retain the difference in potentials, we must
index the nodes - number (name) them, so that we can write
that “node A is on higher potential that node B”.
This allows us to interpret the value of nodes as potentials – and assign current (flow) as
through variable, and voltage (difference in potential) as across variable to any element with the
two end terminals (and in the general sense - any branch with the two end nodes). This is again
related to energy exchange and brings about the concept of causality.
.
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Circuit theory – graphs and network topologies
Causality - Each of the primitive elements is defined by an elemental
equation that relates its through and across-variables. This equation
represents a constraint between the across-variable and the through-variable
that must be satisfied at any instant. An immediate consequence is that the
across-variable and the through-variable cannot both be independently
specified at the same time. One variable must be considered to be defined by
the system or an external input, the other variable is defined by the elemental
equation. This is known as causality.
.In the energy storage elements the constraint is expressed as a differential or integral relationship, that
defines the element as having integral or derivative causality. Dissipative elements always operate in
algebraic causality because the through and across-variables are related by algebraic equations.
Causality leads to the possibility of using an equation (or a UI characteristic [comes from U for voltage and I for
current – graphical representation of the equation]) to find out the current if the voltage is known – or vice versa. It
also leads to acknowledgment that power can either be specified to voltage or current supplied, but not
both.
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Circuit theory – graphs and network topologies
Causality leads to the possibility of using an equation (or a UI characteristic [a graphical representation of
the equation - comes from U for voltage and I for current]) to find out the current if the voltage is known – or
vice versa. It also leads to acknowledgment that power can either be specified to voltage or current
supplied, but not both.
For each element:
-There are two terminals, and there is a potential assigned to each (Va1 and Va2; or VA and VB).
.
- By reference we can assign one terminal potential to be higher (+) (above Va1 or VA ) than the other
- which determines a reference voltage across the element and
VAB = VA – VB
or
Va = Va1 – Va2
- the reference current flowing through the element (from + to -)
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Circuit theory – graphs and network topologies
For each element:
-There are two terminals, and there is a potential assigned to
each (Va1 and Va2; or VA and VB).
- By reference we can assign one terminal potential to be
higher (+) than the other
- The difference in between the terminal potentials is the
voltage across the element:
V = V+ – V-
or
Va = Va1 – Va2
- The current through the element, can be determined from the equation / UI characteristic.
If the element is a resistor, its elemental equation algebraically is
and geometrically relates to a linear UI characteristic.
I
U
R
.
We have to solve this equation – graphically or
numerically - in order to get the current through
the element.
1
I  U
R
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Circuit theory – graphs and network topologies
I
1
U
R
The definition of voltage as “across” variable, and current as “through” variable, indicates the way
measuring instruments should be interfaced:
- Ammeter (ampermeter) measures current : so we must break a circuit at a given branch, and insert
the ampermeter as an additional branch that completes the given branch (and the circuit) in order to
measure current through the given branch
- Voltmeter and Oscilloscope measure voltage – or the difference in potentials at the terminals : so
we must position the voltmeter probes so they are in electric contact with the terminals of the
element.
.
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Circuit theory – graphs and network topologies
The network representation is meant to provide means for simplified representation of more complex
network systems – focused on the simple fact that energy must be exchanged if current is to flow,
no matter how complex the system. So, it geometrically recognizes the fact that we need at least
two terminals for an element that can participate in energy exchange in current flow.
This recognition comes in the form of a port, which is nothing but a pair of terminals through which the
system can exchange energy with another system. Note that also othe energy systems than
electric can be modelled with this approach – mechanical, fluid etc.
So, in the elementary circuit we will have two
networks exchanging energy, one
representing the generator element, and the
other – the resistor. Since both of these
networks sport only two terminals each, they
are both one-port networks.
.
Note that again, we need at least two oneport networks to close a circuit – so a network
in this sense does not represent a circuit –
although internally – since they can represent
complex circuits – there could be current
flowing and energy exhange going on. The
port just represents the energy that has been
exchanged with the “outside”.
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Circuit theory – graphs and network topologies
The benefit of network
representation is more obvious
when we consider that we can
represent more complex
connections through one or
more port networks.
If we remember the intuitive
interpretation of Ohms Law, all that
a source needs to see on its
terminals is some finite resistance
for current to start flowing – no
matter how complex the network
may be.
.
Network representation makes
this perception of a source
”seeing” resistance on its
terminals easier – which is the
core of the method known as
Thevenin/Norton theorem,
which simplifies complex
networks down to a one-port
network.
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Circuit theory – graphs and network topologies
We can compare the different representations – in the case of the elementary circuit – on the figure
below:
.
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Circuit theory – graphs and network topologies
On the figure above, the shaded areas represent the branches in
the same elementary circuit, drawn when the generator and
resistor switch places.
Here we can see the topological aspect – that the connection
structure doesn’t depend on how we draw.
.
Namely, the fact that for the generator branch, current flows from – to + node, means that it is giving
energy – and the same is valid for the resistor branch - current flowing from + to - node, means that it
is using/receiving energy.
This is a valid conclusion for a models of branch (& its nodes), as well as for elements and their
terminals, and networks and their ports – and is the basic method for recognizing energy exchange.
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Circuit theory – graphs and network topologies
V
+
-
i
P=Vi
Produced by Source
Or
Used by Load
i
+
Load
-
V
.
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Circuit theory
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These theories bring about circuit theory as a way of solving electric circuits – analysis of more
complex topologies than the elementary circuit. As the complexity of a circuit grows, we can
expect a great number of branches to be interconnected in different ways, resulting in a number
of currents through and voltages across hose branches. To solve a circuit means to determine all
currents and voltages in a circuit in a given instant.
Circuit theory applies graph theory – for the graph representation of the conductive transport network
which constitutes the electric circuit. The graph is supplied in the form of a schematic diagram,
with the corresponding schematic symbols.
Then, a correspondence between the graph and a system of equations can be developed, and the
system solved, basically using only three laws:
-
-.
First and second Kirchoff law (laws of conservation of charge and energy)
Ohms law (for a resistor, or any UI relation that exists for a given element – represented on the
graph with a schematic symbol)
(Additionaly Thevenin/Norton theorem may be used)
The algebraic system of equations can determine each current and voltage in the circuit. For strictly
ohmic elements, these equations are also linear, and enable us to quickly solve circuits.
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Circuit theory
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Circuit theory means that now we can work approximatively, and instead of taking into account local
properties (such as concentration of charge, potential distribution and resistivity), we can solve a
set of linear equations connected to a graph, and quickly gain integral, general measures – such
as current and voltage.
In addition, we do not need to care how the circuit physically appears – all we have to be careful
about is that we have correctly represented the connection between the elements (connection
topology) in the schematic as in the physical circuit.
.
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Circuit theory – schematic symbols
circuit schematic symbols
Resistor
Conductive wires
Power source
.
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Circuit theory – basic laws
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We can see that all the elements are modelled as two terminal or one port elements. This is related to
the graph concept of a branch, and analogous to a conducting path – for each branch we can
have an across and through variable, related to voltage and current, and then the actual behavior
can be attributed to a particular idealized model – say a resistor.
With this in mind, in circuit theory we work in essence with branches and nodes on schematic
diagrams – graphs that represent electric circuits, which use schematic symbols for depicting
elements. Thus we will rephrase the terms from graph theory in circuit theory context.

  


.

A circuit with 5 branches.




A circuit with 3 nodes
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Circuit theory – basic laws

  




A circuit with 5 branches
and 2 (principal) nodes



Sensors Technology MED4: Electron Flow – Current
A circuit with 3 nodes (2 principal)
and 3 branches
We redefine an electric circuit as a connection of electrical devices that form one or more closed paths.
A branch: A branch is a single electrical element or device.
A node: A node can be defined as a connection point between two or more branches. (principal node or
junction – at least three branches.)
If we start at any point in a circuit (node), proceed through connected electric devices back to the point
.
(node)
from which we started, without crossing a node more than one time, we form a closed-path.
A loop is a closed-path.
An independent loop is one that contains at least one element not contained in another loop.
Ground is a reference node located at an arbitrary point in the circuit to which for convenience is assigned
a potential of zero volts.
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Circuit theory – basic laws
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To solve a circuit, means to determine currents through and voltages across all branches in the
circuit. Three laws govern the distribution of currents and voltages in a circuit with resistors:
Ohms law:
U
I
R
which basically governs the voltage across and current through a
branch that is modelled by a resistor. For non ohmic elements, we
need a corresponding relation between the current and voltage!
Kirchoff laws:
the 1st or current law (KCL) or the junction rule: for a given
junction or node in a circuit, the sum of the currents
entering equals the sum of the currents leaving. This law is
a statement of charge conservation – what goes in must
come out.
the
. 2nd or voltage law (KVL) or the loop
rule: around any closed loop in a circuit, the
sum of the potential differences across all
elements is zero. This law is a statement of
energy conservation, in that any charge that
starts and ends up at the same point with
the same velocity must have gained as
much energy as it lost.
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Circuit theory – basic laws
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An important corollary of 1st KL:
A current through a branch remans the same, no matter where in the branch it is measured.
.
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AC Current
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So far, we have drawn our conclusions based on a steady current – one that does not change its
magnitude or direction in time. Such a current is known as DC (Direct Current) to point at the fact
that the current does not change direction. However, a direct current might also be changing in
magnitude and not be steady.
To realise the behaviour of current or
voltage in time, we use time diagrams.
A voltage source that creates a
constant potential difference on its
ends (which cases steady current in a
resistor) is a DC voltage source.
A voltage source that creates a
sinusoidal potential difference on its
ends (which is changing in magnitude
and direction, but is mathematically
predictable) is a AC voltage source.
A voltage source that creates a
potential difference on its ends, which
is changing in magnitude and direction,
and is random (only statistically
predictable) is a random voltage
source.
Information signals (speech) also appear random in time, so if information is encoded in the
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change of voltage in time, generally we have a signal voltage source.
Sensors Technology MED4: Electron Flow – Current
AC Current – Interpreting sinusoidal time graphs
The image
displays a sine
function that
represents a
sinusoidally
changing current.
Here the function
graph gives
information on
how many
particles crossed a
given point in
circuit at a given
point in time.
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Sensors Technology MED4: Electron Flow – Current
AC Current – Interpreting sinusoidal time graphs
The image displays a sine function that
represents a sinusoidally changing voltage.
Here the function graph gives information on the
potential difference between two points in a
circuit (such as element terminals) at a given
point in time.
Note that we could obtain such a sinusoid from
for example as a result from a measurement with
an oscilloscope.
By that we obtain information only about the
potential difference on the terminals – not their
exact potentials! They depend on the point that
we use as reference (ground – 0 Volts) and on
the circuit topology itself.
Thus, when we obtain voltage for a given
moment, it could mean any kind of potential
distribution – until we connect that voltage to the
rest of the circuit and obtain node potentials.
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Sensors Technology MED4: Electron Flow – Current
AC Current – Using the UI characteristic.
Once we start working with
voltages which are changing
in time, it can become
difficult to relate the
equations to what is
happening in the circuit.
However, since the UI
characteristic is a geometric
rendering of the equation of
the element, it can be used
to graphically determine the
look of the signals.
The image displays a UI characteristic of a resistor (linear UI characteristic). We
know the resistance doesn’t change with voltage, so the resistor will “resist” all
the same, no matter what voltage is applied. So the look of the sine will remain –
only its amplitude will reflect Ohms law.
Graphically, we can align the graphs for change of voltage (and current) in time,
with the corresponding sides of the UI characteristic. Then, at each moment in
time we have definite values for U and I called a working point.
As the voltage changes, the working point moves on the UI char, and traces out
the changes of current in time. So, we now have a graphical method for obtaining
voltages and currents in time.
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Soldering
Sensors Technology MED4: Electron Flow – Current
Basic Soldering photo guide
Electric contact - a physical contact that permits current flow between conducting parts.
A. Solder is used to hold two (or more) conductors in electrical contact with each other.
B. Solder is not used to make the electrical contact.
C. Solder is not used to provide the main mechanical support for a joint.
D. Solder is used to encapsulate a joint, prevent oxidation of the joint, and provide minor mechanical
support for a connection.
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Final Remarks
Sensors Technology MED4: Electron Flow – Current
-
Electricity CAN be dangerous – read the following document on electrical safety: Electrical Safety
and How can electric current *NOT* cause a shock?
-
The magnetic field is an effect that appears around charges in movement – and is per defintion an
ffect that follows electric currents – as phenomena of transport (movement) of free electrons. The
magnetic field will however not be looked at during this part of the course.
-
A conductor which is not a part of a loop in a circuit, yet is connected to some source of (AC)
current, will experience that a charge will be deposited on it – according to some equivalent
capacitance it might have in relation with some other conductor. If this deposited charge changes
due to a changing current, then it becomes a source of a changing electrostatic (and thus also
electromagnetic) field – which we are aware propagates through space like a wave with the speed
of light. The the conductor becomes an antenna.
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Resources
Sensors Technology MED4: Electron Flow – Current
Conductors in Electric Field
All About Circuits - basic concepts of electricity
Fluid Dynamics
Hydrostatics
Direct-Current Circuits
Direct current circuits
Understanding electric flow on the quantum level
Graphs, matrices and circuit theory
Circuit models
Lecture - Circuit Theory
Circuit Variables
Network Models
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