What happens to the speed of charge carriers when going through a resistor

[ezadam]

Hi everyone,

I hope this question hasn't be asked and answered already in this forum, I searched through all related threads but I couldn't find an answer specific enough to my question.

Consider a simple circuit with a DC battery and resistor. When the electrons (the charge carriers in this situation) move through a resistor, does their speed decrease or increase ? It would be better if you could explain using both physical and mathematical interpretations.

Here's what I've thought of:

Using the physical interpretation, I concluded that by making use of the water pipe analogy (water flows faster in tighter sections of the pipe), the electrons in a resistance would speed up.

Using the mathematical interpretation however, I get the opposite results. We know that :
I = nevA
with: - n the number of electrons per unit volume,
- e the charge of an electron,
- v the drift speed of an electron
- A the cross-sectional area.
Using Ohm's law: V=RI
Thus: V/R=nevA and so: v = (V/neAR)*(1/R)
With the first terms in parentheses constant, the drift speed of electrons decreases as resistance increases (when a resistance is present). In other words, the electrons slow down in a resistor

Please explain to me where my misconceptions lie.

Thanks

 

[Feldoh]

Initially when electrons move in a circuit with a resistor their drift velocity is decreased.

Physically, electrons traveling through a resistor will collide with atoms of the resistor which causes their average (drift) velocity to decrease. *BUT* (and it's a huge but) we know that is we have a circuit the current through a resistor is that same as along a wire that is attached to the resistor.

What happens is that the resistor impedes electron flow but this impedance causes the electrons to initially build which causes an electron field which causes electrons to slow down in the rest of the circuit. It's actually a rather complex process involving not only drift of electrons but also the diffusion of electrons, but suffice to say:

Initially: Electrons will slow down in a resistor.
At equillibrium: Drift velocity is equal everywhere in a circuit loop.

Mathematically the simplest model we can use is called the Drude model. http://en.wikipedia.org/wiki/Drude_model

Note: The Drude model is independent of position, or in other words the theoy tells us that the current flow should be the same regardless of if the electron is in the resistor or in the wire.

 

[schip666!]

One should note that the hydraulic analogy for electricity breaks down precisely where one begins to think of charge as being carried by moving electrons... Electron motion is very slow, the charge is carried by the field which moves at the speed of light. There was a bit of discussion recently here:
https://www.physicsforums.com/showthread.php?t=491130

 

[ezadam]

Great explanation Feldoh ! My physics professor was assuring me that electrons speed up in resistors, so I got really confused ...

However, this leads me to another question: How can current stay constant in my simple DC circuit if electrons slow down in resistors ? I mean, doesn't the slowing down of electrons in resistors mean that there will be less charges passing through a cross-sectional area in the resistor during a given time period than in a cross-sectional area in a normal wire in the circuit ? And thus, current would be less in resistors than in the wires ?

On a side note, does my mathematical interpretation (I = nevA) hold ? I know it tells that electrons wil be slowing down in resistors, but that doesn't necessarily mean that it's a right method, so I just want to make sure.

 

[Feldoh]

That's my point *initially* there is a build-up. The build-up of electrons causes an electric field which causes the electrons everywhere in a circuit to distribute themselves as to cancel out the electric field.

In order for the electrons to distribute themselves the current flow outside of the resistor must decrease as electrons are repelled from the buildup of electrons at the resistor. After a relatively short time the circuit finds a balance between charge build-up and drift velocity. Effectively the current in the circuit will equalize out to a constant value.

 

[ezadam]

Could you explain more the situation of balance that you're talking about ? Your idea of electrons build up makes great sense but I still do not understand how the circuit achieves the state of balance you've mentioned.

Also, could you (or anyone else) comment on the second part of my last reply ?

 

[willem2]

Could you explain more the situation of balance that you're talking about ? Your idea of electrons build up makes great sense but I still do not understand how the circuit achieves the state of balance you've mentioned.

The balance is achieved, because there will be a few more electrons on the positive side of the resistor, and a few less on the negative side. This will produce a bigger electric field in the resistor than in the wires around it, and that can give the electrons higher speeds.

Also, could you (or anyone else) comment on the second part of my last reply ?

Your equation (I=nevA) is correct, but it does not mean that the electrons will slow down in
resistors.

- High resistance materials often have a much lower number of charge carriers per volume.
The current density (I/A) can be lower even if the drift speed is much higher.

-In a wire made of the same material with sections of different thicknesses, the current will be the same everywhere, so the drift speed is inversely proportional to the crossectional area, so the drift speed is higher in sections with a higher resistance.

 

[willem2]

electrons but also the diffusion of electrons, but suffice to say:

Initially: Electrons will slow down in a resistor.
At equillibrium: Drift velocity is equal everywhere in a circuit loop.

I think it's (drift velocity) * (crossectional area) * (density of charge carriers) is equal everywhere in a circuit loop.

 

[ezadam]

Initially: Electrons will slow down in a resistor.

so the drift speed is higher in sections with a higher resistance.

Aren't you guys proving opposite points ?

 

[willem2]

Aren't you guys proving opposite points ?

The first point contains "Initially". If the material is harder to pass through for electrons, they won't move as quickly. Buildup of charges on both ends of this section will increase the electric field in them which will make the drift speed the same everywhere (if the crossectional areas are also the same)

What I wrote is about the steady-state situation, in the case that you have a wire with a section that is thinner. The drift speed must be greater in a thinner section.

 

[ezadam]

Thanks willem2, I got it now. I don't know why professors do not focus much on electrostatics in explaining this things, relying instead more on circuit theory.

 

[Quinzio]

Thus: V/R=nevA and so: v = (V/neAR)*(1/R)

Note that:

$${V \over R}=nevA$$

$$v = {V \over R \ n \ e \ A}$$

The speed of electrons changes with the cross area.
If a wire where a current is flowing changes its section, the electrons must go faster.
I don't see many options.

 

[mohamedihab]

Thinner wires (of smaller area) are of larger resistance than those thicker wires (of larger area). Think of the area as parallel connection of resistors for example let 1/Rt = 1/10 + 1/10 then Rt = 5Ω as an example for smaller area wire. Now for larger area wire 1/Rt = 1/10 + 1/10 + 1/10 then Rt=3.3Ω
so as area decrease the resistance increase and vice versa. so electrons will speed up in thinner wires (of larger resistance and smaller area) and slows down in thicker wires (of smaller resistance and larger area) to keep constant current in series connection of wires or in other words keep constant current along a single wire of different areas. Think of flow of current in a wire of different thickness as flow of water in single tube of different thickness it speeds up in thinner parts and slow down in thicker parts but at the end the amount of water that enter from one end of the pipe is equal to the amount of water that exits from the other end.