1. Electron flow - current, resistance, and elementary circuit
Sensors Technology – MED4
Electron flow - current, resistance, and elementary circuit
Lecturer:
Smilen Dimitrov

2. Introduction
The model that we introduced for ST

3. 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

4. Electric current
In achieving electrostatic equilibrium if a metal is charged, for a short while there is a directed motion of particles.
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”)..

5. Ammount of charge (that crossed in)…
Electric current
Definition of electric current
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
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

6. 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

7. 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?

8. Conduction mechanism
As the simplest model of conductive movement, we use the Drude model
Assumptions: the conducting electrons
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");
maintain thermal equilibrium throughout collisions ("classical statistics approximation");
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)

9. 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.]
… Thus, there are zones in the material, where there are many free electrons, and where they are free to move.
These zones can be perceived as free electron “gas” or “sea”, in the interatomic space of the material…
… although we usually simplify the picture, to one where free electrons and ions are approximated to hard particles.

10. 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.

11. Conduction mechanism
… and it is also reflected in the free motion of electrons in metals: their motion is always chaotic, even with no field applied
Temperature is a measure of chaotic motion of atoms and molecules…
… 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.
Application of external field does not stop the chaotic motion, but instead adds a directed component to it…

12. 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!

13. 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.

14. EMF – electromotive force
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!

15. Electric circuit
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

16. Short circuit
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

17. Resistivity, resistance and Ohms Law
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

18. Resistivity, resistance and Ohms Law
Looking at a small piece of a conductor
Field in conductor, L – total conductor length
For single electron
After hit,
v=0
After time Δt
N - free electrons per unit volume
S – area (cross-sectional, marked as A above)
Average v
total charge crossed
current
Replacements – we define:
Ohms Law
Ohms Law is not a ‘law’ – its an empirical observation for certain kind of materials (like metals) !
resistivity
resistance

19. Resistivity, resistance and Ohms Law
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.

20. Resistivity, resistance and Ohms Law
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
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

21. Resistivity, resistance and Ohms Law
Resistivity of a material is temperature dependent,
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)

22. Elementary electric circuit
So, for a minimal legal circuit, we need
EMF (power source)
Resistance (conductors)
Wire (conductors) that will complete a full circuit
Here, Ohms law is valid
For no resistance, R=0, we would get infinite current - short circuit!
Elementary Electric Circuit

23. Elementary electric circuit
Visualisations

24. Relation to water flow – hydraulic analogy
There is a relationship to water flow: water molecules – free electrons, voltage – pressure, conductors – pipes/hoses

25. Circuit theory
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
Circuit theory – solving a circuit (finding all its voltages and currents) on the basis of circuit diagram (schematic) and conventions..

26. Circuit theory 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:
Elements described through elements equations = UI characteristics
Difference between real and technical direction of flow

27. Power exchange
Although current circulates, power is given from source (power supply) to load (resistor)
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:

28. Electric measurements
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)