st06 –electron flow - current, resistance, and elementary circuit 1 electron flow - current,...

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

Electron flow - current, resistance, and elementary circuit

Lecturer:Smilen Dimitrov

Sensors Technology – MED4

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Introduction

• The model that we introduced for ST

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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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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”)..

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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

t

QI

qNQ

Ammount of charge (that crossed in)…

… ammount of time

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

… through an arbitrary reference plane (or point) with a defined default orientation.

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Convection current (CRT)

• Cathode ray tube – prime example of convection current in products

• Basis for understanding of the function of an oscilloscopeHistory of Cathode Ray Tube Kathodenstrahlröhre applet Oscilloscope video

• Two sets of parallel plates, modify the pathof 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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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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Conduction mechanism

• As the simplest model of conductive movement, we use the Drude model

• Assumptions: the conducting electrons1. 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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• 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.

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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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Temperature is a measure of chaotic motion of atoms and molecules…

… and it is also reflected in the free motion of electrons in metals: their motion is always chaotic, even with no field applied

Application of external field does not stop the chaotic motion, but instead adds a directed component to it…

… 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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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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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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• 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!

EMF – electromotive force

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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

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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

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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

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• Looking at a small piece of a conductor

L

UE

EqF m

Eqa

tm

Eqv

tm

Eqv

m

tEqvd 2

)( tvSNqVNqQ d UL

S

m

tNq

t

QI

2

2

tNq

m

2

2S

LR

RIU

Field in conductor, L – total conductor length

For single electron

After hit,

v=0

After time Δt

Average v

total charge crossed

current

Replacements – we define: Ohms Law

resistivity

resistance

Ohms Law is not a ‘law’ – its an empirical observation for certain kind of materials (like metals) !

N - free electrons per unit volume

S – area (cross-sectional, marked as A above)

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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.

S

LR

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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

• 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

RIU

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• 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)

00 1 TT

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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!

ElementaryElectricCircuit

R

UI

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Elementary electric circuit

• Visualisations

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Relation to water flow – hydraulic analogy

• There is a relationship to water flow: water molecules – free electrons, voltage – pressure, conductors – pipes/hoses

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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..

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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

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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:

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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)

st06 –electron flow - current, resistance, and elementary circuit 1 electron flow - current,...

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