Why does resistance reduce current in whole circuit?

[bmhiggs]

TL;DR Summary

ohm's law conceptual understanding for behavior in whole circuit rather than only in the resistor

Ohm's law states that current is inversely proportional to resistance, but on the quantum level, why does that actually slow the current down for the whole circuit? In all of the basic explanations, it talks about how the more densely packed matter in the resistor creates more collisions and therefore slows down electrons and converts the kinetic energy to heat. This conceptual explanation would seem to imply that the current is only reduced for the electrons in resistor, but we know that the current is the same anywhere in the circuit. Is there a way to understand the atomic behavior to explain conceptually why the current is reduced in the whole circuit?

I was recently reading this thread
https://physics.stackexchange.com/q...742#351742?s=14c7dccfb5be47b79675e7afb42579a4
(sorry for diverting to different exchange) which was helpful in clarifying that the electrons after the resistor regain their kinetic energy because they still experience the effect of the field (so the current is the same before and after the resistor). What I still don't quite understand is if we know how/why the current is reduced overall by the presence of the resistor. Based on the prior info, I would assume that there is less kinetic energy overall because of the higher resistor, but I'm not clear why the slow moving electrons in the resistor would also slow down the ones in the rest of the circuit.

 

[Dale]

Ohm's law states that current is inversely proportional to resistance, but on the quantum level, why does that actually slow the current down for the whole circuit?

This is macroscopic and classical. There isn’t a quantum explanation for this.

The current isn’t necessarily slowed down for the whole circuit. If I increase the resistance through one branch of a parallel circuit then it will not change the current in the other branches.

It is only for elements connected in series that the current slows down. For elements in series, the current of all elements is reduced for the simple fact that they all share the same current. So if you reduce the current for one of them then you necessarily reduce the current for all of them. That is what being in series means

 

[bmhiggs]

Sorry - I should have clarified that I was talking about series circuits, and I guess I mean atomic, not quantum.

 

[A.T.]

Is there a way to understand the atomic behavior to explain conceptually why the current is reduced in the whole circuit?

Since no charge is created nor destroyed, the charge flowing per time must be the same everywhere.

 

[Baluncore]

What I still don't quite understand is if we know how/why the current is reduced overall by the presence of the resistor.

What is resistance, or why is ohms law?

 

[Dale]

Sorry - I should have clarified that I was talking about series circuits, and I guess I mean atomic, not quantum.

It doesn’t matter if you say atomic or quantum. You are asking about the behavior of the circuit as a whole. The atomic scale isn’t relevant except perhaps to remember that charge is conserved at that scale too. The conservation of charge is what makes the current the same in all series elements. I just don’t think there is a microscopic explanation that is different in any way from the classical explanation.

 

[Juanda]

Since no charge is created nor destroyed, the charge flowing per time must be the same everywhere.

I think that's the easiest way of conceptually understanding what OP is saying.
Analogies between electrical circuits and pipes can be useful to catch some ideas.

A battery produces a difference in voltage that pushes the electrical charges $\approx$ A pump produces a difference in pressure that pushes the liquid.
Wires from the diagrams with no resistance carry the charges $\approx$ Pipes with no resistance carry the fluid.
Resistances cause a drop in voltage depending on the current through them $\approx$ Bends cause a loss in pressure depending on the velocity of the fluid.

Here comes an awful drawing to explain the concept.

Imagine the only losses in the pipes come from those close bends at the right (resistance shape). Let's keep the section of the pipes constant at all times for simplicity and because changing it adds no value to the point.
A first key point, the fluid is incompressible so mass continuity causes the speed of the fluid to be constant in the whole system. If it were faster before the resistance and slower after it, at some point it'd need to bunch up and that's not allowed because of the incompressibility thing.

Now, the pressure difference in that ideal pump will be the same no matter what. Since the system is stationary (doesn't change with time), the energy input by the pump must be the same as the consumed in the bends. Therefore, the pressure drop in the bendy pipes is the same as the pressure jump in the pump.

Finally, the pressure drop in the bendy pipes is dependent on the velocity of the fluid. So the greater resistance / bendier pipes will cause an equilibrium point where the flow is running slower / lower intensity.

 

[A.T.]

A first key point, the fluid is incompressible

Yes, this an important simplifying assumption. For short transient periods the charge density and thus the current can vary, especially along a very long circuit. But this is negligible for normal size circuits.

 

[vanhees71]

Sorry - I should have clarified that I was talking about series circuits, and I guess I mean atomic, not quantum.

Of course you are right, if you want to understand this from a fundamental point of view, you have to use quantum theory. However, in this case you get amazingly far by using a classical fluid picture for the conduction electrons, the so-called Drude model. In this model the conduction electrons are just described as particles moving under the influence of the electric field and being subject to friction due to collisions with the ionic lattice.

https://en.wikipedia.org/wiki/Drude_model

 

[Dale]

you get amazingly far by using a classical fluid picture for the conduction electrons, the so-called Drude model

The Drude model is a microscopic “explanation” of resistance at a point, so it answers the lumped-element-level question “how does a resistor work”. But it doesn’t explain the circuit-level fact that current is the same all along a series circuit. I understood the question to be asking that circuit-level question.

 

[sophiecentaur]

TL;DR Summary: ohm's law conceptual understanding for behavior in whole circuit rather than only in the resistor

Ohm's law states that current is inversely proportional to resistance

It's good that you're trying to sort this out in your head. and I hope you get something from this thread. Actually, Ohm stated it the other way round; he said that the current varies proportionally with the applied voltage (in metals at constant temperature) and the constant of proportionality is referred to as Resistance. And it only applies under certain conditions, although we often re-arrange the equation and assume that 'R' stays the same. But 'the Law' is not the same as the equation V=IR because we often apply the equation to non Ohmic components and we usually get away with it until we forget about resistance not always being constant. Include a filament light bulb in your circuit and calculations all go wrong if you ignore the real Ohm's Law.

A battery produces a difference in voltage that pushes the electrical charges

mass continuity causes the speed of the fluid to be constant in the whole system.

You should start thinking in another way, perhaps, about those statements. Voltage is to do with Energy and not force; It's the Energy supplied per unit charge and the Energy is 'used up' around the circuit. Avoid thinking in terms of water flow if you can.
Also, it's not 'speed' but rate of flow of charge. And the speeds, in normal circuits, are in the order of mm's per second - so Kinetic Energy is not significant

 

[vanhees71]

The Drude model is a microscopic “explanation” of resistance at a point, so it answers the lumped-element-level question “how does a resistor work”. But it doesn’t explain the circuit-level fact that current is the same all along a series circuit. I understood the question to be asking that circuit-level question.

Of course, the Drude model also obeys charge conservation, which is behind the fact that the current is the same along any loop of the circuit.

 

[Mister T]

I'm not clear why the slow moving electrons in the resistor would also slow down the ones in the rest of the circuit.

It's conservation of charge. In a typical circuit the charge carriers are electrons. The amount of charge per unit time entering a resistor (the current) has to equal the current leaving the resistor. Otherwise you'd have current either leaking out of the resistor (a sink) or entering the resistor (a source). If you want an explanation on the atomic level, then the resistor would have to be a source or sink of electrons.

This is not what we observe. When we connect an ammeter to either end of the resistor, we find that the current entering the resistor equals the current leaving the resistor.

 

[tech99]

I think with these sort of circuit questions we need to consider what happens at switch on. An EM wave (or impulse) travels from the switch to the resistor, and then bounces back and forth, gradually diminishing until steady conditions obtain. This is how the various parts of the circuit "communicate" with each other, so that current gradually becomes everywhere equal.

 

[Lnewqban]

Avoid thinking in terms of water flow if you can.

Could you please explain why we should avoid that comparison?
I have used it for basic explanations of DC circuits.

 

[vanhees71]

I think with these sort of circuit questions we need to consider what happens at switch on. An EM wave (or impulse) travels from the switch to the resistor, and then bounces back and forth, gradually diminishing until steady conditions obtain. This is how the various parts of the circuit "communicate" with each other, so that current gradually becomes everywhere equal.

Yep, and it's the fields the transport energy. That's why a light bulb lights up quasi instantly when turning the switch rather than taking minuts until the electrons could transport the energy there. That's why the nowadays much stressed didacticians' "fluid model" is so bad.

 

[A.T.]

Voltage is to do with Energy and not force

Yes, in the water analogy power supply would be like raising the water higher or adding pressure to it.

Also, it's not 'speed' but rate of flow of charge.

Yes, and in the pipe analogy current is represented by the flow rate of water, which is the same everywhere, while the flow speed can vary, for example when you model the resistor as a narrowing of the pipe

 

[sophiecentaur]

Yes, in the water analogy power supply would be like raising the water higher or adding pressure to it.

Yes. That would be fine but it's usually just done with thin bits of pipe which don't actually account for Energy being used up. Steer Clear of Water is my motto.

 

[Dale]

Steer Clear of Water is my motto.

Especially with electricity!

 

[sophiecentaur]

Could you please explain why we should avoid that comparison?
I have used it for basic explanations of DC circuits.

Because poor models of water flow do not account for Energy Flow because they do not include elements of Energy Used - like a hydraulic motor or a lift pump. Conservation of charge is analogous to conservation of water but the so called circuits are the equivalent of wires with zero resistance and any loss would have to be only inside the pump - but that's never pointed out. Afaiac, any reference to water should be restricted to some general unrecorded arm waving with caveats. What's actually wrong with the term Charge Flow? They only have to Unlearn bad habits later if you use water.
Edit: Oh yes, and going into a thin wire from a thick wire only involves electron speed changing from very very slow to very slow and it's not the KE that is relevant in electric circuits.

 

[Baluncore]

Steer Clear of Water is my motto.

Unless you are dreaming of a cocktail, in the desert.

Especially with electricity!

I only drink water that has been through a hydroelectric turbine and had the electrickery taken out.

 

[sophiecentaur]

That's why the nowadays much stressed didacticians' "fluid model" is so bad.

This is the problem when people who have not understood something try to teach it to others. It's one of many examples where they can do more damage than helping.

 

[nasu]

Yes, and in the pipe analogy current is represented by the flow rate of water, which is the same everywhere, while the flow speed can vary, for example when you model the resistor as a narrowing of the pipe

And even in this model you see that there is no "slowing down" in the resistors.
In the resistor is very likely that the drift velocity is higher than in the copper wires. It depends on the cross sections and mobility too, but the high resistivity of materials used to make resistors is due to lower carrier density (at least few orders of magnitude), and mobility, maybe. This results in increased drift velocity for current density similar to that in the copper wire. The "model" of electrons slowing down in resistor and then speeding up after the resistor (as mentioned in the OP) has no justification.

 

[bmhiggs]

This has been an extremely helpful series of explanations. Thanks for helping me go beyond what I took from two semesters of college physics and rereading several high school textbooks.

One thing that has been especially clarifying is:

And the speeds, in normal circuits, are in the order of mm's per second - so Kinetic Energy is not significant

it's not the KE that is relevant in electric circuits

Thanks @sophiecentaur !

Basic textbooks are always talking about the movement of electrons that are carrying the energy and that resistors "slow them down." I guess I understood electricity to be a form of kinetic energy at the electron level, and that the energy conversion was taking place by them loosing speed within the resistor (bumping into the more densely packed array), and therefore transferring it to heat - analogous to a ball that has kinetic energy slowing down and giving off heat through friction, or hitting a wall that causes it to stop and releasing the energy through heat. A difference would be that the electron immediately jumps back up to speed because it is still under the effect of the electric field, but the transfer of energy still happens in the reduction of kinetic energy.

If that is not the case, what is the mechanism for the energy transfer in a circuit - say a basic filament lightbulb? The electric field does the work on the charge, but how does that get transformed into light and heat? I'm looking for a solid conceptual understanding here.

In basic chemistry, one of the topics is the ideas of electrons jumping orbitals and releasing photons... is there any connection between that and what is happening in a filament?

 

[Dale]

electrons that are carrying the energy

This is incorrect. The energy is carried by the fields. Unfortunately this is an idea that is propagated all too often.

I guess I understood electricity to be a form of kinetic energy at the electron level

The electrons do have kinetic energy, but that is not what carries the energy in a circuit. A mechanical system that demonstrates a similar effect is a bicycle chain. The chain links do have KE, but it is small and largely irrelevant to the energy transfer. The energy is transferred in the tension.

 

[vanhees71]

Basic textbooks are always talking about the movement of electrons that are carrying the energy and that resistors "slow them down." I guess I understood electricity to be a form of kinetic energy at the electron level, and that the energy conversion was taking place by them loosing speed within the resistor (bumping into the more densely packed array), and therefore transferring it to heat - analogous to a ball that has kinetic energy slowing down and giving off heat through friction, or hitting a wall that causes it to stop and releasing the energy through heat. A difference would be that the electron immediately jumps back up to speed because it is still under the effect of the electric field, but the transfer of energy still happens in the reduction of kinetic energy.

This shows that one should stick to Einstein's famous saying: "Explain things as simple as possible but not simpler." Unfortunately, when didactitians think they have found a "good didactical concept" it's hard to convince them otherwise by scientific arguments. So we must live with all kinds of bad simplifications in textbooks.

One should note that the correct understanding of energy transport through electromagnetic interactions originates from the 2nd half of the 19th century, strongly triggered by electrical engineers, who adopted quite quickly Maxwell's theoretical work. These "Maxwellians" were tremendously successful. Most prominently one should mention Heaviside, who brought Maxwell's theory in the form we know today, i.e., in the formulation with fields, using (3D Euclidean) vectors rather then quaternions.

The question about energy transport became particularly interesting to the engineers, who tried to build sea cables for telegraphing, which of course is a tremendous problem given that you deal with sea water etc. From thinking about these problems, Poynting came to his concept of energy transport by analyzing the energy-conservation law for electromagnetic fields and charged matter.

If that is not the case, what is the mechanism for the energy transfer in a circuit - say a basic filament lightbulb? The electric field does the work on the charge, but how does that get transformed into light and heat? I'm looking for a solid conceptual understanding here.

The most simple example, which you can pretty easily calculate analytically is the very long coaxial cable for a constant (DC) current. You'll find that the energy transport from the "battery" at one end and a "resistor" at the other end is due to the electromagnetic field rather than by the "electrons" making up the current.

Another argument is that if you use simple point-particle models a la Drude you'll find that the electrons' drift velocity is tiny for usual household currents, i.e., in the order of mm/s (millimeters per second). Now, if you think that the energy transport is through the electrons, this would imply that for the few meters from the source to a light bulb it would take some minutes to get light when switching it on, which is in clear contradiction to what's observed.

To make this argument quantitative you can use the "telegrapher's equation", which is an approximation to the full Maxwell equations for the coax cable (in terms of these full solutions you get the socalled TEM mode, which is sufficient to get the principle working described right). What you find then solving the time-dependent problem of switching on the DC circuit is that the time it takes to get the light on is given by the speed of the electromagnetic wave along the cable, which is in the order of the speed of light (in the dielectric between the inner and outer conductors making up the coax cable), which explains, why it doesn't take some minutes to get light when switching on the circuit.

In basic chemistry, one of the topics is the ideas of electrons jumping orbitals and releasing photons... is there any connection between that and what is happening in a filament?

That's another question. Indeed, to understand the spectrum of a thermal light source you need quantum (field) theory, leading to Planck's radiation law (for an ideal "black body").

 

[bmhiggs]

I'm trying to understand it from a conservation of energy standpoint... how does the resistor pull energy from the field and turn it into heat/light?

A mechanical system that demonstrates a similar effect is a bicycle chain. The chain links do have KE, but it is small and largely irrelevant to the energy transfer. The energy is transferred in the tension.

This was a helpful example - but then the energy gets transferred by the work of the chain on the gear. Where does the work occur in a resistor?

 

[Dale]

Where does the work occur in a resistor?

In the resistor there is a current and an E field both pointing in the same direction. The work is $\vec E \cdot \vec J$.

 

[bmhiggs]

In the resistor there is a current and an E field both pointing in the same direction. The work is $\vec E \cdot \vec J$.

But isn't that happening everywhere in the circuit? Why does a filament light up but the copper wire carrying the current does not? The current and E field are the same everywhere in the circuit, as has been amply shown by this thread.

@sophiecentaur Any help here?

 

[Dale]

But isn't that happening everywhere in the circuit?

No. In ideal wires $\vec E=0$ so no work is done there. In a capacitor $\vec J=0$ so no work is done there either.

 

[bmhiggs]

Ok:

In ideal wires E→=0

But:

the so-called Drude model. In this model the conduction electrons are just described as particles moving under the influence of the electric field and being subject to friction due to collisions with the ionic lattice.

How can there be a current without an electric field?? Or is that vector E referring to something more specific?
[Keep on exercising patience with me here if that should be obvious...]

 

[bmhiggs]

Ok, before anyone wastes time on that last one, I did a quick search and found this:

Why is the voltage drop across an ideal wire zero? - Reddit​

Reddit
https://www.reddit.com › AskPhysics › comments › why...

So disregard. But then I am back to the question of WHY a resistor DOES do work.

 

[Dale]

How can there be a current without an electric field??

Not everything is a resistor. Ohm’s law says that you need an electric field to have a current, but it only applies for resistors. You can have current without an E field and you can have an E field without a current and you can have an E field which points in a different direction than the current.

Your original question is about resistors, but not everything is a resistor.

 

[bmhiggs]

I did some more reading (ref this post:
https://physics.stackexchange.com/q...re has the same,voltage and no electric field. )

Also some hyperphysics: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elewor.html
Key idea: "The electric field is by definition the force per unit charge"

Let's see if I have refined my understanding...
Situation: Simple circuit with a battery and a resistor.
An electric field is propagated by the potential difference of a battery in a closed circuit. Then I believe this happens...

I think with these sort of circuit questions we need to consider what happens at switch on. An EM wave (or impulse) travels from the switch to the resistor, and then bounces back and forth, gradually diminishing until steady conditions obtain. This is how the various parts of the circuit "communicate" with each other, so that current gradually becomes everywhere equal.

(thanks @tech99 - that definitely filled a gap for me)

Once that happens, the electrons are moving, but if the wire that connects the battery to the resistor is ideal, it needs to exert no force on the electrons to keep them moving, so there is no work done, so no E field.
[Still a teensy confusion about how they get going in the first place without a force, but I guess the idea is that it is so instantaneous, it can be disregarded. Or we basically pretend like the idea wire isn't there to make out calculations easier. Or we can use the flawed marble in a tube analogy? But no analogies.]

However, in the resistor, the material is such that the electrons do need force to make them move (they encounter resistance). The force exerted by the field on these elections to overcome the resistance and keep moving therefore does work, and the collisions that created the resistance convert the electrical energy to heat/light. No KE of significance involved.

In actuality, no wire is idea, so all wires put up a certain amount of resistance, "using" a small amount of the energy of the field, contributing to the overall resistance and creating a field throughout the wire.

Thanks for the crash course in E&M!!!!

 

[Mister T]

If that is not the case, what is the mechanism for the energy transfer in a circuit - say a basic filament lightbulb?

The charge carriers (electrons in this case) collide with atomic nuclei.