Why does resistance reduce current in whole circuit?

[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!!!!

 

[Herman Trivilino]

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.

 

[Dale]

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

There are superconducting wires, but yes, for ordinary copper wiring there is a small resistance

 

[renormalize]

...what is the mechanism for the energy transfer in a circuit - say a basic filament lightbulb?

Perhaps my response in this thread from June: Power flow outside a wire - how close? helps to answer this question.

Other than a trivial amount of kinetic energy carried by the low-speed flow of electrons, the vast majority of energy flows between the battery and the light bulb via the electric and magnetic fields outside of, and well removed from, the wires. The electron current in the wires simply serves to establish and guide these fields in the space outside of the wires. Since changes in these fields propagate at the speed of light, the bulb appears to instantly illuminate when the circuit is completed.

 

[vanhees71]

Ok:But:

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...]

Of course, if there's no force on the electrons they come to rest due to friction. There's only a current if there's a force due to an electromagnetic field. If you just have a static electric field along the conductor, after a short while after switching this field on, the electric force, $\vec{F}_{\text{el}}=-e \vec{E}$, is compensated by the friction force $\vec{F}_{\text{fric}}=-\gamma m \vec{v}=-\vec{F}_{\text{el}}=e \vec{E}$, i.e., you have $\vec{v}=-e/(\gamma m) \vec{E}$
$$\vec{j}=-n e \vec{v}=+\frac{n e^2}{\gamma m} \vec{E},$$
where $n$ is the number of conduction electrons per unit volume, i.e., $\rho=-e n$ is the charge density of the conduction electrons.

Now the above is nothing else than Ohm's Law in local form, i.e., you get for the electric conductivity for DC
$$\sigma=\frac{n e^2}{\gamma m}.$$

 

[vanhees71]

There are superconducting wires, but yes, for ordinary copper wiring there is a small resistance

Superconductors cannot described by the usual constitutive relations, i.e., not be Ohm's Law, $\vec{j}=\sigma \vec{E}$ and not with a Drude model as sketched in my previous posting, because obviously you cannot simply set the friction coefficient $\gamma=0$ or the relaxation time $\tau=1/\gamma \rightarrow \infty$.

The reason is that superconductivity is a generic quantum effect, leading to an effective classical theory, which is described by the London equations. For a nice treatment, see

https://www.feynmanlectures.caltech.edu/III_21.html