Download ST06 – Electron flow - current, resistance, and elementary circuit

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ST06 –Electron
flow
- current, –resistance,
and elementary circuit
Electron flow - current, resistance, and elementary circuit
Lecturer:
Smilen Dimitrov
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ST06 –Electron flow - current, resistance, and elementary circuit
Introduction
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The model that we introduced for ST
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ST06 –Electron flow - current, resistance, and elementary circuit
Introduction
•
We have discussed
– the microscopic aspects of structure of matter
– interaction of charged particles through the units of electric
(electrostatic) force, field and potential
– definition of electric voltage as difference of potential(s) at different
points
– Effect of external field on two classes of materials: dielectrics
(insulators), and conductors (particularly, metals)
– Process of charging – transfer of free electrons from one material to
another
– The state of electrostatic equilibrium in metals
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ST06 –Electron flow - current, resistance, and elementary circuit
Electric current
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In achieving electrostatic equilibrium if a metal is charged, for a short while
there is a directed motion of particles.
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Directed motion of particles is known as electric current.
•
We are interested under which conditions can electric current occur, that
lasts long in time (is “sustained” – or is in a “steady state”)..
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ST06 –Electron flow - current, resistance, and elementary circuit
Electric current
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Definition of electric current
Q
I
t
Ammount of charge (that crossed in)…
… ammount of time
… through an arbitrary reference plane (or point)
with a defined default orientation.
Since an electron/proton has the
smallest possible ammount of charge,
amount of charge can always be
related to number of free particles that
crossed in a given direction
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•
•
Q  N  q
Has statistical (average) nature – as potential (or voltage) – in the sense of usage
Convection current – flow of charged particles through vacuum
Conduction current – flow of charged particles through a conductor
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ST06 –Electron flow - current, resistance, and elementary circuit
Convection current (CRT)
•
•
Cathode ray tube – prime example of convection current in products
Basis for understanding of the function of an oscilloscope
History of Cathode Ray Tube
•
Kathodenstrahlröhre applet
Oscilloscope video
Two sets of parallel plates, modify the path
of a beam of electrons from a electron gun
(cannon) – by way of electric field; the
electrons move through the vacuum
of the tube
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ST06 –Electron flow - current, resistance, and elementary circuit
Conduction current
•
•
•
Conduction current – directed motion of free electrons (charge) in a
conductive material
As said previously – a charged conductor reaches equilibrium soon, and
directed motion stops
How to enable continuous directed movement of free electrons in a
material?
– What is the mechanism of motion of free electrons through a material?
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ST06 –Electron flow - current, resistance, and elementary circuit
Conduction mechanism
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As the simplest model of conductive movement, we use the Drude model
Assumptions: the conducting electrons
1. do not interact with the cations (the "free electron approximation"), except for
collisions, where the velocity of the electron abruptly and randomly changes
direction as a result of collision ("relaxation time approximation");
2. maintain thermal equilibrium throughout collisions ("classical statistics
approximation");
3. do not interact with each other ("independent electron approximation").
The Drude model approximates the metal to a lattice of cations through which
delocalised electrons flow.
•
(essentially, a billiard-ball type interaction)
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ST06 –Electron flow - current, resistance, and elementary circuit
Conduction mechanism
•
In more detail:
An electron, gaining energy, can become free, and
wander throughout the material... [In metals
(conductors), this happens at room temperature.]
These zones can be perceived as free electron
“gas” or “sea”, in the interatomic space of the
material…
… Thus, there are zones in the material,
where there are many free electrons,
and where they are free to move.
… although we usually simplify the picture, to one
where free electrons and ions are approximated to
hard particles.
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ST06 –Electron flow - current, resistance, and elementary circuit
Conduction mechanism
A free electron, does not necesarilly move freely from
one end of the conductor to the other – instead, it “soon”
enters a previously free valence orbit of an ion…
… and thus, may push another neighboring valence or
free electron. And thus, a ‘push’ from a single electron
is progressively passed on through the conductor. This
can be seen as a electric field interaction, too.
Focusing only on the motion of free electrons, this progressive
motion can be likened to the motion of a tube of marbles – or
alternatively, flow of water (or water molecules) - in a tube.
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ST06 –Electron flow - current, resistance, and elementary circuit
Conduction mechanism
Temperature is a measure of chaotic motion of
atoms and molecules…
Application of external field does not stop the
chaotic motion, but instead adds a directed
component to it…
… and it is also reflected in the free motion of electrons
in metals: their motion is always chaotic, even with no
field applied
… however, in calculations, we can take that the random
components of motion cancel out – and focus only on
the directed component, due to a field.
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ST06 –Electron flow - current, resistance, and elementary circuit
Visualizing potential and charge density in conductors
•
There is a connection between concentration of charge (charge density) and potential locally in a point (or small
space)..
… however, we know that what
matters for movement of free charge,
is not the potential in a point - but the
difference of potential between two
(neighboring) points!
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ST06 –Electron flow - current, resistance, and elementary circuit
Example of conduction current (transient)
•
Connecting two conducting bodies – with different amount of free charge,
with a third conductor (wire) will cause a short transient current through the
wire
There is an analogy with
connecting two water tanks
with differing levels of water –
as soon as the levels are
equal, there is no more
difference of ‘potential’ – and
the flow stops.
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ST06 –Electron flow - current, resistance, and elementary circuit
EMF – electromotive force
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•
•
•
•
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Conductive path and difference of potential – allows for current, but a short
one.
How to enable long running currents (directed motions of free charge)?
We need a non-conservative electric force – electromotive force.
EMF can include can include magnetic, chemical, mechanical, and
gravitational components (non-conservative..)
Measured - through its capability to maintain potential difference = voltage in Volts
Still – without an external circuit (conducting path) – no current yet!
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ST06 –Electron flow - current, resistance, and elementary circuit
Electric circuit
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For a permanent current we need – source of EMF, and a conductor to
connect the terminals
– Electric circuit is a conducting path, external to the battery, which allows
charge to flow from one terminal to the other.
–
•
an unbroken loop of conductive material that allows electrons to flow through continuously without beginning
or end.
Relationship to water flow
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ST06 –Electron flow - current, resistance, and elementary circuit
Short circuit
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Is the previous definition enough for a ‘legal’ electric circuit?
– A source of EMF forces some voltage (difference of potential) on its
ends
– however, a piece of conductor wire has the same potential throughout
=> voltage between any two points of the wire is 0
•
Only a source and a conductor wire is a potentially dangerous circuit known
as a short circuit
Avoid at all cost!!! (in batteries it can potentially result in an explosion)
We thus need something else for a minimal electric circuit
•
•
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ST06 –Electron flow - current, resistance, and elementary circuit
Resistivity, resistance and Ohms Law
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Free electrons, in their motion in the interatomic space of a conductor,
experience hits (collisions, scattering) with the ions of the crystal lattice.
This causes change of the velocity of the electrons, and the excess energy
is given off as heat (thermal energy).
In brief, that effect is the cause of resistivity in conductors
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ST06 –Electron flow - current, resistance, and elementary circuit
Resistivity, resistance and Ohms Law
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Looking at a small piece of a conductor
E
U
L
F  qE
After hit,
v=0
Field in conductor,
L – total conductor length
a
qE
v
t
m


N - free electrons per unit volume
S – area (cross-sectional, marked as A above)
vd 
total charge crossed
current
Q  q  N  V  q  N (S  vd  t )
Q q 2 Nt S
I

 U
t
2m L
Replacements – we define:
2m
 2
q  N  t
resistivity
L
R
S
resistance
qE
m
For single electron
After time Δt
qE 
v
  t
 m 
q  E  t Average v
2m
Ohms Law
U  I R
Ohms Law is not a ‘law’ – its an
empirical observation for certain kind
of materials (like metals) !
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ST06 –Electron flow - current, resistance, and elementary circuit
Resistivity, resistance and Ohms Law
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Resistivity is a local parameter, that changes from point to point (due to
impurities) and is specific to a given material; 
Resistance is an averaged parameter for a block of material, with known
resistivity and geometry. R   L
S
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ST06 –Electron flow - current, resistance, and elementary circuit
Resistivity, resistance and Ohms Law
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Elements that obey Ohms law are ohmic elements/materials
– a linear dependency between voltage and current: increasing the voltage
across the element in equal steps, will cause increase of current through the element in
equal steps, and vice versa, given by Ohms Law U  I  R
•
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Not all materials or elements are ohmic !! (diodes are not, for example)
Two important classes of ohmic materials (that is, conductive materials):
– conductors - good conductors, metals, low resistivity, used for wire,
approximated as ideal conductors
– resistors - poor conductors, high resistivity
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ST06 –Electron flow - current, resistance, and elementary circuit
Resistivity, resistance and Ohms Law
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Resistivity of a material is temperature dependent,    1   T  T 
– due to the increased vibrational motion of the atoms (“phonons”) that
make up the lattice - further inhibiting the motion of the charge carriers.
•
Sensing principle (how to sense temperature)
0
0
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ST06 –Electron flow - current, resistance, and elementary circuit
Elementary electric circuit
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So, for a minimal legal circuit, we need
– EMF (power source)
– Resistance (conductors)
– Wire (conductors) that will complete a full circuit
Elementary
Electric
Circuit
U
Here, Ohms law is valid I  R
– For no resistance, R=0, we would get infinite current - short circuit!
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ST06 –Electron flow - current, resistance, and elementary circuit
Elementary electric circuit
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Visualisations
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ST06 –Electron flow - current, resistance, and elementary circuit
Relation to water flow – hydraulic analogy
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There is a relationship to water flow: water molecules – free electrons,
voltage – pressure, conductors – pipes/hoses
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ST06 –Electron flow - current, resistance, and elementary circuit
Circuit theory
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In practice, we do not analyze the microscopic state of electric circuits
directly;
– instead the effects are seen through macroscopic, lumped parameters
(voltage, current, resistance) which are then used in connection with
circuit diagrams
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Circuit theory – solving a circuit (finding all its voltages and currents) on the
basis of circuit diagram (schematic) and conventions..
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ST06 –Electron flow - current, resistance, and elementary circuit
Circuit theory
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Conventions
– Network topology vs. appearance – it matters not how the connections
look like, what matters is which point is connected to which
– Wire is an ideal conductor with R=0
– Standardized use of circuit diagram (schematic – pictorial representation of an
electrical circuit) using schematic symbols:
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Elements described through elements equations = UI characteristics
Difference between real and technical direction of flow
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ST06 –Electron flow - current, resistance, and elementary circuit
Power exchange
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Although current circulates, power is given from source (power supply) to
load (resistor)
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This leads to definition of active elements (power supplies – can supply
energy in the circuit) and passive elements (can use it / dissipate it as heat)
– Active and passive have different conventions for default directions of
voltage and current:
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ST06 –Electron flow - current, resistance, and elementary circuit
Electric measurements
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Voltage is measured across an element, current is measured through an
element
Thus, for the corresponding meters
– volt-meter is connected at the points whose potential difference we want
to measure – without breaking the circuit
– Circuit must be broken so that an amper-meter is attached
An oscilloscope is a type of a volt-meter (it measures potential difference –
voltage – between two points)
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