# What EXACTLY does a resistor do ?

1. Feb 26, 2014

### KingCrimson

according to my understanding of a resistor , all it does is limit the number of charges flowing according to the potential energy possessed by each unit of charge , as the potential energy / charge * aka volts * increase , their ability to * move in large numbers through resistors * increase .
but my teacher says that resistance is * slowing down * charges , its working against their movement through out the wire .
does resistance work against every individual charge ? increasing the work needed to conduct it ?
in other terms slowing it down ?
or does it affect the number of available charge carriers flowing through the conductor ?

2. Feb 26, 2014

### Simon Bridge

The electric current in a circuit is the amount of charge per unit time going past a point in the circuit.
In this model, you are thinking of "charge" as a fluid rather than as a collection of discrete particles.
Thus, a lower current means that the speed of the current has slowed down.

This translates into fewer discrete charges per second past that point.

Resistance is a bulk property of the material that emerges from lots of quantum-level effects and details of the underlying structure of the solid in question. The concept of "resistance" does not actually make much sense on the scale of individual charges.

The force on each unit of charge is proportional to the gradient of the potential through the resistor.
To get the same current through a bigger resistor means you need a bigger voltage, which means a bigger force. The change in energy is bigger, so the work is higher. i.e. the power supply had to do more work lifting the potential energy of each unit of charge high enough to get the same current - the same flow rate.

The number of charge carriers available is fixed by the amount and type of material - i.e. copper supplies two per atom. In the fluid-flow model, though, it is the amount of space that the fluid can flow through that restricts the current, not the amount of fluid. You could think of a resistor as a constriction in a pipe carrying a liquid - this slows the current down in the whole circuit and it means there is less liquid (per unit length) in the resistor at any time, than in the rest of the circuit. Bear in mind that the electrical situation is more complicated.

Also see:

You could also look up "band theory of solids".
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html

If you fancy a look - I found a tutorial that takes a "fine detail" approach to conduction/resistance:
http://arxiv.org/pdf/cond-mat/0408319.pdf
... have fun.

3. Feb 26, 2014

### KingCrimson

that was a very detailed and beautiful reply ! that pdf file is a treasure !! i have been looking for such a thing for quite a while but could not find any .
"The concept of "resistance" does not actually make much sense on the scale of individual charges." this is why i am here :P thanks alot for your answer

4. Feb 27, 2014

### mpresic

You raise an interesting question which I am unprepared to answer at this time. I will have to review some concepts. Here is what I can add. The speed of the electrons in the wire may be a secondary consideration in most applications. It is the speed of the electric fields in the wire that is overwhelming importance to electrical applications. When we talk of an ampere being one coulomb of charge "past a point" in the circuit per second, perhapse we should consider the number of charges across a cross-section of wire (e.g. resistivity).

An interesting analogy is there are numerous cars across a superhighway per hour. An equally wide road may have few cars. In either case the speed of the individual cars could be larger in the case of the wide road than the superhighway.

It is also interesting the heat dissipated in the wire is larger for larger resistance (wasted energy).

I am sorry I am probably adding confusion with these considerations.

5. Feb 27, 2014

### nsaspook

Using the fluid analogy works to a certain extent but it confuses the issue of electron mobility in semiconductors/resistors when you calculate conductance/resistance and the speed of charge carrier movement in response to an applied electric field. The typical drift velocity of a electron in a good conductor is so slow at normal power levels (an hour to move from a car battery to the starter when engaged) using 'slowing down' to describe the effect of resistance on the drift velocity seems redundant even if it were technically true (the actual electron speed "The Fermi Velocity" between collisions is much higher).
http://230nsc1.phy-astr.gsu.edu/hbase/electric/ohmmic.html

https://www.bpa.gov/PublicInvolveme...de_the_surprisingly_slow_electron_express.doc

6. Feb 27, 2014

### Staff: Mentor

That is correct. In simple circuit analysis we ignore the transverse dimension of the wire and treat it as an ideal line, so that's probably how the notion of current as "rate of charge flowing past a point" comes about.

If you do actually want to talk about individual points inside the wire, you have to use the concept of current density, $\vec J$, coulombs per second per square meter transverse to the direction of flow at that point. This is a vector quantity, so as to take into account the direction of flow.

The current density at a point is determined by the resistivity $\rho$ of the material at that point, and the electric field $\vec E$ at that point, via the "point-wise" equivalent of Ohm's Law: $\vec E = \vec J \rho$ or $\vec J = \vec E / \rho$.

This is the classical picture in which we consider the charge as a continuous fluid and the current as a flow of that fluid. It has to be refined further if we can "see" the effects of the individual electrons.

7. Feb 27, 2014

### mpresic

I am now wondering if this question is more complicated than I originally supposed. I may complicate matters in considering the electroplating process. For example plating gold on a copper nail with electricity. (Hypothetical, I do not want to look up whether one or two electrons or the detailed chemical process which is involved). Does the current in the circuit really match up with the number of electrons available for plating. I suspect it does not. Probably the difference in potential (i.e. electrical energy), and it's chemical interactions with the gold and copper is what is relevant. Perhaps our chemist friends can illuminate the discussion, otherwise I may have to review my chemistry

8. Feb 27, 2014

### nsaspook

The gold electrolysis reaction involves gold ions as charge carriers in an electrolyte instead of free electrons in wires or copper nails. The amount of charge moved (current) will be the same in the circuit from the energy source but the carriers will be different inside the plating cell and electrical energy will also be lost from the chemical reaction (moving gold in the electrolyte and depositing it) instead of just resistive heating.

Last edited: Feb 27, 2014
9. Feb 27, 2014

### Simon Bridge

no - it is simpler.
When you field these sorts of question it is a good idea to consider what level the question is being asked at.
Otherwise every question could be taken as extremely deep.

i.e. "1+1=2" could be read as from a basic arithmetic course, or an extremely advanced level mathematical course, focusing on the Peano axioms for the natural numbers which formalised mathematics in the late 19th century. This course would culminate with Gödel's second incompleteness theorem which shows that the consitency of the Peano axioms cannot be formalised within Peano arithmetic itself.

Context is everything.

10. Feb 27, 2014

### mpresic

The paper you included to answer the question is also very involved. Your answer to King Crimson was the electrical situation is not simple.

I am sympathetic to the POV from nsaspook that the teacher's description (If King Crimson is understanding the teachers answer accurately) of the charges slowing down is not complete. Occasionally as an instructor I have answered questions posed on the spur of the moment and found out later upon reflection the answer I gave is inaccurate.

King Crimson is satisfied with your answer with the papers you provided so I will leave it at that.

11. Feb 27, 2014

### KingCrimson

To be honest the principle of resistance is not as * simple * as it seems , i have done much reading on the matter and i was fairly confused about it , but i decided to understand resistance as an opposition to the number of flowing charges , just that , this is what resistance means anyhow , how does it do so though is a bit more complicated , for instance low cross sectional area means lower number of charge carriers and thus , lower number of chargers
a hot resistor would have more * collisions * of electrons with atoms as books say , so that offers a kind of slower flow of charges thus less charges / sec and thus lower current .
My problem was with how the resistance "sucked out" potential energy out of charges , but this was due to a misunderstanding of the problem , the way i think about it is that potential energy of charges is there to carry charges through resistance , so as the charge has passed the resistor , the energy is dissipated somehow .
now how the energy is dissipated is what i am after , the pdf file is pretty detailed on the matter but i still lack alot of knowledge to be able to fully comprehend the paper , so i will give it some time .

12. Feb 27, 2014

### KingCrimson

yea i guess you could decrease the number of cars in the road by either introducing bumps which slow down cars , increasing the distance so cars would have to move slower to be able to get to the end of the road with the amount of fuel they possess * potential * , Or you can just decreasing the width of the road .

13. Feb 27, 2014

### KingCrimson

it actually does , the number of electrons in a cross section of a copper wire is ENORMOUS ! each electron might be actually slower than a snail , but imagine the end of the copper wire , each second billions of billions of electrons that were just on the edge of the wire , take a jump out of the wire to do the reduction process
@nsaspook
it involves both the flow of ions and flow of electrons , the gold rod is oxidized , and then the electroplated substance is reduced , the electrons flow from the gold rod to the electroplated substance where it meets a gold ion and forms a gold atom which is then stuck on the surface of the electroplated substance

14. Feb 27, 2014

### Simon Bridge

Electrical PE gets converted to some other form of energy in a component through some intermediate processes - it is not usually a direct conversion. Charges lose electrical PE the same way masses lose gravitational PE.

It is worth remembering that there are positive as well as negative charges in a solid.

Charges in a solid dissipate electrical energy by interaction with other charges in the solid - usually by scattering (bouncing off each other) or by radiation (giving off light). The usual result of this is increased heat, and something else ... i.e. a light bulb dissipates electrical energy by giving off light as well as heat.

The exact details depend on what sort of "resistor" you have.

Consider an analogy:
If a ball rolls down a slope - you notice it loses gravitational potential energy.
Is there anything "sucking" the PE out of the ball?
But you've discarded this picture so - moving on...

If it goes over a rough slope, it goes slower than over a smooth slope.
If it travels through a bit with grass on it, or a bunch of pinball bells, it also takes loner to get to the bottom.
Is the gravitational PE of the ball there to get the ball through the rough patches?
Is that a useful way to think about gravity?

Lots of balls flowing down the hill would form a ball-current, we can count the number of balls past a particular height per unit time, and we can even average it out as a continuous mass-current.

We can work out the "resistance" of the slope by taking the ratio of the difference in PE the ball went through (the ball-PD) with the mass current.

So what is this resistance - exactly?

Caution: Like all analogies it is not an exact match.
However, the general concept of "resistance" is the same: it is the ratio of a change in potential with the rate of flow through the potential change. You should now be able to apply the concept to various situations besides electricity.

Note: the detailed PDF talks a lot about conduction - you can think of conductance as the inverse of resistance. On the particle level we think of "transport processes" - which can be quite varied. The transport processes, acting on lots of particles, gets you a bulk current, then you can talk about conduction and resistance properly.

And that PDF should show you that we cannot avoid leaving something out in these descriptions.
As you advance through your education you will get more of the background you need to get a bigger picture. Be aware that nobody has a Complete picture since we do not have a grand unified theory - so there will always be something left out.

15. Feb 28, 2014

### UltrafastPED

I wrote a brief explanation of resistance for an introductory circuits course - it is based on the Drude model, which is an application of the kinetic theory of gasses to electrons in a metal. It gives a nice picture, without getting into the complexities of quantum theory.

See attached: "Physical Origins of Electrical Conductivity and Resistivity".

Your instructor is welcome to share it with his class.

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