Electron kinetic energy, movement

[Salvador]

I read that based on temperature , electrons have kinetic energy in metals so they randomly move around the ion lattice.
when we apply current to a room temperature conductor, the electrons being charge carriers align and form current?
but what happens in the plates of a capacitor , when the capacitor is charged the electrons on one plate and the positive charge on the other, do electrons have kinetic energy in such situation or are they locked due to the attraction force?

 

[Drakkith]

I read that based on temperature , electrons have kinetic energy in metals so they randomly move around the ion lattice.
when we apply current to a room temperature conductor, the electrons being charge carriers align and form current?

Not really. Their movements are still random, they just have a small net movement along the direction of current flow. It's kind of like air. When you blow out of your mouth the volume of air is moving fairly slowly, but the molecules themselves are pinging about randomly at around 1100 mph. They just have a small net motion in the direction away from your mouth, leading to airflow.

but what happens in the plates of a capacitor , when the capacitor is charged the electrons on one plate and the positive charge on the other, do electrons have kinetic energy in such situation or are they locked due to the attraction force?

Both. They still have random motions within the plates, but they cannot get off of the plates until you discharge the capacitor.

 

[Salvador]

current decreases in a wire due to the resistance mainly caused by electron collisions with ions, then if the same electrons collide wth the same ions while on the plates of a capacitor , then why doesn't the capacitor loose it's charge as heat in the metal plates ?

 

[ModusPwnd]

For the same reason the current doesn't decrease in a wire over time, because there is a battery supplying a constant voltage. If you remove the battery the accumulated charge will slowly dissipate (as the current will also go to zero in a connected circuit).

 

[Salvador]

so a capacitor looses charge the same way a wire looses current , by electron ion interactions?

 

[nasu]

current decreases in a wire due to the resistance mainly caused by electron collisions with ions, then if the same electrons collide wth the same ions while on the plates of a capacitor , then why doesn't the capacitor loose it's charge as heat in the metal plates ?

The "current decrease in a wire" is a vague statement. If you are thinking about electrical resistance, this is not due to collisions between electrons and ions. You are trying to apply a model which is not appropriate. It is true that this electron-ion collision is presented often in introductory texts.

Your observation may be a hint to the fact that the electrons are not slowed down by electron-ion collisions. The electrons in an atom are not slowed down by collisions with the nucleus, are they?

 

[Drakkith]

so a capacitor looses charge the same way a wire looses current , by electron ion interactions?

No. All capacitors have a small "leakage" current which drains the plates slowly over time. This is because it is impossible to have infinite electrical resistance so there is always a small current flowing.

 

[Drakkith]

current decreases in a wire due to the resistance mainly caused by electron collisions with ions, then if the same electrons collide wth the same ions while on the plates of a capacitor , then why doesn't the capacitor loose it's charge as heat in the metal plates ?

You are talking about two different things.

A plate that is electrically charged simply has an excess of one charge over another. The plate remains charged until those excess chargers are drained away. Remember that the charges are actual particles. You have to physically remove or add them to the plate in order to charge or discharge it. A current carrying wire is usually not electrically charged, and even if it is it has little effect on current flow.

 

[Salvador]

Yes I was thinking about a current in a wire when the power source is disconnected. It stops , due to resistance and the resistance is caused by what then?

 

[Drakkith]

Yes I was thinking about a current in a wire when the power source is disconnected. It stops , due to resistance and the resistance is caused by what then?

See this article: http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity

 

[sophiecentaur]

Yes I was thinking about a current in a wire when the power source is disconnected. It stops , due to resistance and the resistance is caused by what then?

It stops because the PD changes - charges would build up at the ends of the wire, producing a force to stop the flow (as with a charged capacitor). Resistance is not necessary - except to account for the fact that an oscillation does not occur.

 

[Salvador]

Yes , I see , when there is no PD , there is no force that would move the charge, and PD could be described as a separation of opposite charges.Correct?

when current flows due to a PD it encounters resistance in an ordinary conductor.We were talking about ions and electrons interacting wtih them and each other previously, what would happen if we would make a glass tube with electron gas in it as a conductor , would current still have resistance there?

 

[Drakkith]

what would happen if we would make a glass tube with electron gas in it as a conductor , would current still have resistance there?

The electron gas would behave like a plasma, not a normal conductor, so the normal models of electrical conductivity don't apply there any more. That's not to say it doesn't have resistance, it's just that this is beyond the original scope of the thread.

 

[Salvador]

Yes, but if the conductor consists of only electrons and they travel through vacuum , much like in a CRT then were and from what resistance arises?

 

[UltrafastPED]

Yes, but if the conductor consists of only electrons and they travel through vacuum , much like in a CRT then were and from what resistance arises?

Ohm's law is not applicable to electron beams; resistance is a property of _metals_.

 

[sophiecentaur]

Ohm's law is not applicable to electron beams; resistance is a property of _metals_.

'Resistance' is just the ratio of V/I and applies to anything; that's why you can include diodes and other elements in circuit analysis. 'Ohm's Law' is not actually just R = V/I. Ohm's Law applies to metals and means that V/I is constant at a constant temperature. It even applies to Lamp Filaments - or it would, if you could keep the temperature constant.
For an electron beam, there will be a measurable PD and a measurable current. But of course, an electron beam needs to start with a source of electrons (thermionic cathode or lots of volts) the V/I characteristic will be very non-linear

 

[UltrafastPED]

'Resistance' is just the ratio of V/I and applies to anything; that's why you can include diodes and other elements in circuit analysis. 'Ohm's Law' is not actually just R = V/I. Ohm's Law applies to metals and means that V/I is constant at a constant temperature. It even applies to Lamp Filaments - or it would, if you could keep the temperature constant.
For an electron beam, there will be a measurable PD and a measurable current. But of course, an electron beam needs to start with a source of electrons (thermionic cathode or lots of volts) the V/I characteristic will be very non-linear

When I design a photo-electron gun the voltage at the photocathode may be 30 kV, and the anode is grounded. During transit each electron will start with almost zero energy, but by the end each one will have 30 keV.

Depending upon the laser fluence the average current may be anywhere in the range 10^-14 up to 10^-3 amps. By your prescription this vacuum has a resistance varying from:

30,000/10^-14 = 3*10^18 ohms for the low fluence, to
30,000/10^-3 = 3*10^7 ohms for the high fluence.

Funny how the vacuum has a variable resistance!

I believe you are thinking of "transimpedance"; we used this term when studying solid state devices. "Transfer resistance", "transfer conductance", "transfer impedance" ... these are all for non-ohmic devices. See http://en.wikipedia.org/wiki/Transimpedance

When teaching an introductory circuits course I would limit the use of the term "resistance" to when Ohm's law is applicable. I even made some notes about Ohm's law last year - it's available in this thread on resistors: https://www.physicsforums.com/showthread.php?t=740567#15

 

[sophiecentaur]

When I design a photo-electron gun the voltage at the photocathode may be 30 kV, and the anode is grounded. During transit each electron will start with almost zero energy, but by the end each one will have 30 keV.

Depending upon the laser fluence the average current may be anywhere in the range 10^-14 up to 10^-3 amps. By your prescription this vacuum has a resistance varying from:

30,000/10^-14 = 3*10^18 ohms for the low fluence, to
30,000/10^-3 = 3*10^7 ohms for the high fluence.

Funny how the vacuum has a variable resistance!

I believe you are thinking of "transimpedance"; we used this term when studying solid state devices. "Transfer resistance", "transfer conductance", "transfer impedance" ... these are all for non-ohmic devices. See http://en.wikipedia.org/wiki/Transimpedance

When teaching an introductory circuits course I would limit the use of the term "resistance" to when Ohm's law is applicable. I even made some notes about Ohm's law last year - it's available in this thread on resistors: https://www.physicsforums.com/showthread.php?t=740567#15

Yes - I take your point about the 'vacuum' but there will still be a V and an I, measured somewhere and they would, for instance, tell you the power dissipated and how the volts are shared with any series (actual) resistances. And it's not so much the 'vacuum' you are describing as a tube with available electrons in it. They shouldn't be dissipating much power until they hit the end but they are still gaining VI power as they go through the tube.

I though that 'transfer***' described a device with three or more terminals.
What would do about a carbon filament? I wouldn't think you would want to treat that differently from a tungsten filament in a circuit. Also, the resistance of a diode in an RF circuit could be very relevant for small signals.

I really think that "Ohm's Law should be a term reserved for situations where it applies fully. Why not just state Resistance (defined by the ratio), which says nothing about the temperature dependence? You can then include a device in your circuit and solve whatever equations are needed, to get an answer. Amplifiers all have an output and input impedance associated with them and they are definitely not metallic ('ohmic') resistors. (And what about a load resistance, as seen via a transformer?)
We are just coming to this from different directions of experience, I think. I don't think we are disagreeing about anything other than use of terms.

 

[UltrafastPED]

I don't think we are disagreeing about anything other than use of terms.

Except ... what you are saying is not what is taught in physics or electrical engineering. Ohm's law is a material dependent statement, as pointed out in the notes I referenced.

You are using resistance when the technical word is transresistance:
http://www.answers.com/topic/transresistance

 

[sophiecentaur]

I can only find the term 'transresistance' **used to describe an amplification or mutual effect, along with transconductance. Your link only took me to a page full of adverts. Google the term and there are many pages of hits with references to amplifiers. Where is it taught 'your way'?

Sometimes the resistance of a non-ohmic component is referred to as dynamic resistance (dV/DI)

Of course Ohm's Law is material dependent but Ohm does not actually mention the word Resistance. It is just states that metals have a constant ratio of V/I at constant temperature. You can measure the 'resistance' of anything and get an answer - that doesn't say anything about its Ohmic behaviour. Furthermore, Ohm's Law is not a 'Law'; it just describes a behaviour, as does Hooke's 'Law'.

** Which is where the term 'Transistor' came from, I believe.

 

[nsaspook]

Ohm's law is not applicable to electron beams; resistance is a property of _metals_.

Even metallic conductors only have ohmic conduction regions at low currents IRT conductor size.
You need to rethink this concept at the most basic level. Electron tubes can have very linear I/V (ohmic) regions of operation once potentials overcome space-charge related resistance changes (>100 volts) and secondary electron effects (suppression screen grids).
http://www.oestex.com/tubes/6550ul.gif

Even well designed class A triode amps can be very linear.

 

[UltrafastPED]

I can only find the term 'transresistance' **used to describe an amplification or mutual effect, along with transconductance. Your link only took me to a page full of adverts. Google the term and there are many pages of hits with references to amplifiers. Where is it taught 'your way'?

I'm sorry that you couldn't find the information; when I follow the link I see:

McGraw-Hill Science & Technology Dictionary: transresistance

(′tranz·ri′zis·təns)
(electricity) The ratio of the voltage between any two connections of a four-terminal junction to the current passing between the other two connections.

--------------------------------------------------------
Two connections to measure current, two to measure the voltage ... then divide the voltage by the current ... and that is transresistance.

--------------------------------------------------------

The usual definition of Ohm's law, including it's history and application, can be found here:
http://en.wikipedia.org/wiki/Ohm's_law

And I agree that Ohm's law is empirical - I even discuss this in some detail in the notes referenced earlier in this discussion, which I prepared for an introductory circuits course for sophomore engineering students at the University of Michigan. If you find something in it with which you disagree, please let me know.

 

[sophiecentaur]

I'm sorry that you couldn't find the information; when I follow the link I see:

McGraw-Hill Science & Technology Dictionary: transresistance

(′tranz·ri′zis·təns)
(electricity) The ratio of the voltage between any two connections of a four-terminal junction to the current passing between the other two connections.

--------------------------------------------------------
Two connections to measure current, two to measure the voltage ... then divide the voltage by the current ... and that is transresistance.

You are telling me that every device that is not made of metal needs four connections to it? I was never taught that.

 

[UltrafastPED]

Even metallic conductors only have ohmic conduction regions at low currents IRT conductor size.
You need to rethink this concept at the most basic level. Electron tubes can have very linear I/V (ohmic) regions of operation once potentials overcome space-charge related resistance changes (>100 volts) and secondary electron effects (suppression screen grids).
http://www.oestex.com/tubes/6550ul.gif

Even well designed class A triode amps can be very linear.

What concept should I rethink? I agree that many devices can have a linear region which can be treated like Ohm's law.

 

[nsaspook]

What concept should I rethink? I agree that many devices can have a linear region which can be treated like Ohm's law.

Ohm's law is not applicable to electron beams; resistance is a property of _metals_.

Ionic liquids/electrolytes/membranes have electrical conductivity calculated by measuring resistance between plates.
http://www.aquariustech.com.au/pdfs/tech-bulletins/Electrol_Condct_Thery.pdf

 

[UltrafastPED]

Ionic liquids/electrolytes/membranes have electrical conductivity calculated by measuring resistance between plates.
http://www.aquariustech.com.au/pdfs/tech-bulletins/Electrol_Condct_Thery.pdf

Thanks for the reference; I agree that conductivity (and resistivity) applies to more than metals. I'll have to review the physical principles - I've been stuck in solid state mode for too long.

 

[UltrafastPED]

You are telling me that every device that is not made of metal needs four connections to it? I was never taught that.

I'm not saying anything about metal here ... but if it does take two connections to measure a voltage, and it takes two connections to measure a current - the input to your ammeter, and the return connection.

Perhaps this is a visualization problem; see the diagram for the four-contact sensing:
http://en.wikipedia.org/wiki/Four-terminal_sensing

 

[sophiecentaur]

I'm not saying anything about metal here ... but if it does take two connections to measure a voltage, and it takes two connections to measure a current - the input to your ammeter, and the return connection.

Perhaps this is a visualization problem; see the diagram for the four-contact sensing:
http://en.wikipedia.org/wiki/Four-terminal_sensing

You seem to have got yourself in a corner here, regarding the term 'transrestance'. All this rigmarole about measuring Current and PD in order to find Resistance is well known and you seem be suggesting that, whilst an Ohmic resistor can have a 'Resistance', anything else has to have a 'Transresistance'. That completely baffles me. I have a sealed box and, depending what's inside it (which I don't know) I have to measure it differently - or at least give what I find out a different name.

All I can say is that the Resistance by which I describe a (two terminal) device is given by V/I and that has nothing to do with whether or not it follows Ohms Law. Do you have a problem with that? Were you taught otherwise?

 

[nsaspook]

Perhaps this is a visualization problem; see the diagram for the four-contact sensing:
http://en.wikipedia.org/wiki/Four-terminal_sensing

It's simply a method (Kelvin connection) to eliminate the effect of sensor wiring/contact resistance (causing a voltage drop from the voltage source to the material at the probing points) changing the probed materials voltage reading with very low resistance measurements that need significance current levels to generate a measurable and stable voltage potential.

I think you mean sheet resistance instead of 'Transresistance' as sheet resistance is what we normally use when measuring doping/implant levels in semiconductor wafers with very low resistance levels.

http://en.wikipedia.org/wiki/Sheet_resistance

 

[UltrafastPED]

You seem to have got yourself in a corner here, regarding the term 'transrestance'. All this rigmarole about measuring Current and PD in order to find Resistance is well known and you seem be suggesting that, whilst an Ohmic resistor can have a 'Resistance', anything else has to have a 'Transresistance'. That completely baffles me. I have a sealed box and, depending what's inside it (which I don't know) I have to measure it differently - or at least give what I find out a different name.

All I can say is that the Resistance by which I describe a (two terminal) device is given by V/I and that has nothing to do with whether or not it follows Ohms Law. Do you have a problem with that? Were you taught otherwise?

You can certainly do what you suggest ... anything in the box will have some V/I curve.

But resistivity is a material property: http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity


And you keep asking where I learned this. Some as an undergraduate, and more in my graduate studies. You are welcome to look at my public profile; it lists my general qualifications and background.

 

[UltrafastPED]

It's simply a method (Kelvin connection) to eliminate the effect of sensor wiring/contact resistance (causing a voltage drop from the voltage source to the material at the probing points) changing the probed materials voltage reading with very low resistance measurements that need significance current levels to generate a measurable and stable voltage potential.

I think you mean sheet resistance instead of 'Transresistance' as sheet resistance is what we normally use when measuring doping/implant levels in semiconductor wafers with very low resistance levels.

http://en.wikipedia.org/wiki/Sheet_resistance

I agree with everything you say here; I have even used this technique for measuring the sheet resistance of ultrathin films.

I only posted the link because of the picture: it shows two contacts for measuring current, and two for measuring voltage ... thus four contacts. Our other correspondent was objecting to the requirement for four contacts to obtain an V/I curve as mentioned in the reference for transresistance.

 

[sophiecentaur]

You can certainly do what you suggest ... anything in the box will have some V/I curve.

But resistivity is a material property: http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity


And you keep asking where I learned this. Some as an undergraduate, and more in my graduate studies. You are welcome to look at my public profile; it lists my general qualifications and background.

So you are telling me that you learned that measuring a two terminal device, turns it into a four terminal device? That is bizarre. Does any two terminal device actually exist in your approach?

 

[nsaspook]

Your classic 'Fluke type' two terminal meter uses the constant current method to measure resistance.

The four terminal method can be used when lead resistance values become significant because of higher sense currents for better accuracy measurements of the DUT.

Transresistance is a term normally used with a 4 port device to describe a transfer function (a change in output voltage to a change in input current) in a current source to voltage source device (amplifier).

 

[UltrafastPED]

So you are telling me that you learned that measuring a two terminal device, turns it into a four terminal device? That is bizarre. Does any two terminal device actually exist in your approach?

I'm not clear what you are saying here. How would making a measurement change the nature of a device?

But if I were to use a voltmeter to measure the voltage drop across a resistor - then I need to make two connections, one on each end. If I were to use an ammeter to measure the current flowing through the resistor I would also need to make a connection at each end.

The connections can be shared if you don't require great precision; to get more accurate readings use the Kelvin technique.

But in either case you have four physical connections. The consolidation of wires into nodes implicitly assumes no resistance in the wires.

Is this your point? Nodes on a diagram are logical; connections are physical. The map is not the territory, but it is good enough for an initial analysis.

 

[Salvador]

But if I were to use a voltmeter to measure the voltage drop across a resistor - then I need to make two connections, one on each end. If I were to use an ammeter to measure the current flowing through the resistor I would also need to make a connection at each end.

But you need a series connection for an ammeter not a connection at each end?

I appreciate the discussion but I still don't know why there is resistance for current in a medium made up entirely out of electrons like in a glass tube filled with electron gas?
In a vacuum at first there is infinite resistance right? and when the E field is strong enough a current path out of cathode electrons can be formed and resistance drops to whatever resistance the electron beam has but why it then has a resistance at all ? if there is vacuum and nothing in the way for the electrons? Not to account for the resistance of the hot cathode , just the electron beam itself.

 

[sophiecentaur]

I'm not clear what you are saying here. How would making a measurement change the nature of a device?

But if I were to use a voltmeter to measure the voltage drop across a resistor - then I need to make two connections, one on each end. If I were to use an ammeter to measure the current flowing through the resistor I would also need to make a connection at each end.

The connections can be shared if you don't require great precision; to get more accurate readings use the Kelvin technique.

But in either case you have four physical connections. The consolidation of wires into nodes implicitly assumes no resistance in the wires.

Is this your point? Nodes on a diagram are logical; connections are physical. The map is not the territory, but it is good enough for an initial analysis.

I learned the basics of Resistance measurement at School; nothing has changed about that, since, afaik. NAspook's two diagrams say all that's needed.

My "point" is that you introduced this "transresistance" as if it somehow distinguishes a 'resistor' resistor (Ohmic?) from any other conducting device (the electrons in a vacuum tube, for instance). For some reason, you introduced the 'four terminal' measurement to justify the 'transresistor' term to justify it. But the term is a complete red herring and refers to a four terminal device. It would surely have helped if you had just admitted that the term is not relevant to this thread.
My initial point was that Ohm's Law is not synonymous with the expression R = V/I and that people who know better should really be using the right terminology, in the interests of those who are trying to find out about it.

 

[sophiecentaur]

But you need a series connection for an ammeter not a connection at each end?

I appreciate the discussion but I still don't know why there is resistance for current in a medium made up entirely out of electrons like in a glass tube filled with electron gas?
In a vacuum at first there is infinite resistance right? and when the E field is strong enough a current path out of cathode electrons can be formed and resistance drops to whatever resistance the electron beam has but why it then has a resistance at all ? if there is vacuum and nothing in the way for the electrons? Not to account for the resistance of the hot cathode , just the electron beam itself.

If there is any finite Potential Drop across a device and there is finite current flowing then there must be a value for V/I (i.e what we call Resistance). There is, arguably, a problem in measuring what the Potential Drop is, between different points over the length of the beam but, if the field is linear, the PD would be proportional to the distance along the beam (potential divider equation).
I don't think there is a problem with the fact that introducing electrons into the vacuum would alter the measured resistance. A light sensitive resistor changes resistance when light falling on the LDR alters the number of free electrons. In the case of an electron tube of course, the V/I relationship will be highly non-linear but that doesn't alter the principle.

 

[Salvador]

ok, but apart from low temperature =low kinetic energy of electrons , what else makes a superconductors electrons so resistanceless?

 

[Drakkith]

ok, but apart from low temperature =low kinetic energy of electrons , what else makes a superconductors electrons so resistanceless?

See the following articles:

http://en.wikipedia.org/wiki/Cooper_pair
http://en.wikipedia.org/wiki/Bcs_theory

 

[UltrafastPED]

My initial point was that Ohm's Law is not synonymous with the expression R = V/I and that people who know better should really be using the right terminology, in the interests of those who are trying to find out about it.

So you disagree with this lesson from "All About Circuits"?
http://www.allaboutcircuits.com/vol_1/chpt_2/6.html

"Ohm's Law is not very useful for analyzing the behavior of components like these where resistance varies with voltage and current. Some have even suggested that "Ohm's Law" should be demoted from the status of a "Law" because it is not universal. It might be more accurate to call the equation (R=E/I) a definition of resistance, befitting of a certain class of materials under a narrow range of conditions."And for just for fun, read this long discussion on the same topic; all of the arguments are hashed over multiple times.

Conclusion: if you define resistance as whatever the V/I curve says for that (V,I) then you have an "Ohm's law" that is a tautology.

However if we consider only the linear behavior (regions of V/I curves of constant slope), then Ohm's law describes the behavior well within this region of applicability - it is an empirical law for which experimental results will be consistent with the predictions.

 

[Salvador]

If an electron beam in a glass tube much like in CRT would be put into extremely low temperature , would it then too become superconducting like various metals when under low temperatures?

Wikipedia states that...

In a normal conductor, an electric current may be visualized as a fluid of electrons moving across a heavy ionic lattice. The electrons are constantly colliding with the ions in the lattice, and during each collision some of the energy carried by the current is absorbed by the lattice and converted into heat, which is essentially the vibrational kinetic energy of the lattice ions. As a result, the energy carried by the current is constantly being dissipated. This is the phenomenon of electrical resistance.

in a vacuum once a current path has formed , the electrons flow but they have nothing in their way unlike in a metal conductor so what is the reason for them to experience resistance still?

 

[Drakkith]

If an electron beam in a glass tube much like in CRT would be put into extremely low temperature , would it then too become superconducting like various metals when under low temperatures?

The term "superconducting" doesn't apply to free particles traveling through space/vacuum. It specifically applies to the lack of electrical resistance in conductors. (A vacuum is not a conductor, it is actually an insulator)

 

[nsaspook]

Wikipedia states that...


in a vacuum once a current path has formed , the electrons flow but they have nothing in their way unlike in a metal conductor so what is the reason for them to experience resistance still?

The electrons in a vacuum can accelerate (in a specific direction instead of very fast random velocities with slow drift speeds like in conductors) to near light speed easily. (~10% of c in a small o-scope CRT with 2kv acceleration voltage) Electrons have a rest mass so it takes energy (work) to make them move faster. So we can think of electrical resistance in part as a indicator how much work is being used to accelerate them (along with the beam EM fields themselves ) to those speeds and the kinetic energy in each electron at that speed (2keV for the o-scope)
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ev.html

So we have a static beam with kinetic energy filled electrons moving at high speed, what do you think happens when we start switching that beam on/off, changing it's density and moving it around to display information? We then also have energy (a small amount usually) in EM waves that can radiate out and be detected from considerable distances.
EMR

 

[sophiecentaur]

So you disagree with this lesson from "All About Circuits"?
http://www.allaboutcircuits.com/vol_1/chpt_2/6.html

"Ohm's Law is not very useful for analyzing the behavior of components like these where resistance varies with voltage and current. Some have even suggested that "Ohm's Law" should be demoted from the status of a "Law" because it is not universal. It might be more accurate to call the equation (R=E/I) a definition of resistance, befitting of a certain class of materials under a narrow range of conditions."And for just for fun, read this long discussion on the same topic; all of the arguments are hashed over multiple times.

Conclusion: if you define resistance as whatever the V/I curve says for that (V,I) then you have an "Ohm's law" that is a tautology.

However if we consider only the linear behavior (regions of V/I curves of constant slope), then Ohm's law describes the behavior well within this region of applicability - it is an empirical law for which experimental results will be consistent with the predictions.

I would disagree with that lesson because it fails to include Temperature in its implied definition of Ohm's Law. To my mind that is sloppy. I agree that it is not a "Law" but a description of behaviour (I already wrote as much, earlier on).

You are not responding to my comments about that transresistance thing you introduced. Do you still think you are 'right' about it? I can't see how you can introduce four terminal devices in your view of resistance. The measurement method is not relevant here because you could produce a resistance of, say 1kΩ, from an appropriately shaped piece of conductor, without ever needing to connect it up to your four terminals. R doesn't care how it's measured.