Why is the current the same at points A and B in a resistor?

[OmCheeto]

Yes, if you change the paths, I agree. That's like having some of the current go through each of 2 parallel paths in an otherwise serial loop, which causes no problem but is getting away from my bike chain analogy.

I think this is why a lot of people don't like analogy. You have to be very careful how you explain it.
My analogy doesn't work if the voltage changes. (game time is approaching, people are pointing guns at the ticket counters, telling them to hurry up.)

I discovered this when I went back and "did the maths".

G = # of ticket counters ( called conductance, measured in siemens )
R = 1/G
V = 1 ( constant for simplicity )
I = V/R ( fans per second )

I=VG
G=I/V​

So, the # of ticket counters, conductance, is a bit more complicated than I posted earlier; "Now, the ticket counters would be the opposite of resistance, as each counter can admit one fan per second."

Each counters "conductance" is equal to fans/second(I) divided their level of fear of death(V).

Which even I can't understand.

 

[Dale]

That's like squeezing the garden hose.

Yes, it is very analogous to squeezing the garden hose. When you squeeze the garden hose the flow rate (liters per second passing any point) decreases along the entire hose. You do not have a 4 L/s flow where you squeeze and a 5 L/s flow throughout the rest of the hose, but when you squeeze you reduce the flow rate from 5 L/s to 4 L/s for the entire hose, including "upstream".

 

[Delta2]

Then you have a difference in drift velocity between the conductor and the resistor?

Yes ok it changes depending on wether the coefficient changes. Furthermore the velocity of all the free electrons inside the resistor is not the same for a given time t even at the DC case, it is just the average velocity that remains constant. So yes i guess you were right it is confusing (we are not saying it is wrong but confusing) to think of current in terms of the velocity of the electrons or the drift velocity (and what makes it even more confusing is that we have that linear relationship between the drift velocity and the current ).

Still, if the OP wants to get a good picture of the inner workings of what exactly is happening inside the resistor he should study some notes on the Drude model.

 

[nasu]

Then you have a difference in drift velocity between the conductor and the resistor?

Yes. And the drift velocity may be higher in the resistor than in the conductor. There is no reason to assume that the conduction electrons are slowing down in the resistor.
It all depends on the cross section and carrier concentration.

 

[skepticwulf]

Yes, it is very analogous to squeezing the garden hose. When you squeeze the garden hose the flow rate (liters per second passing any point) decreases along the entire hose. You do not have a 4 L/s flow where you squeeze and a 5 L/s flow throughout the rest of the hose, but when you squeeze you reduce the flow rate from 5 L/s to 4 L/s for the entire hose, including "upstream".

Now I've got it, finally, thank you! :)

 

[Joker93]

Yes,the resistor tends to slow the charges down(the current),and thus initially(before the system reaches steady state conditions) you have charge accumulation near the start of the resistor.As the charge accumulates it creates its own electric field and thus gives some extra "push" to the charge that will tend to also accumulate with them and finally there will not be any more accumulation of charge but a steady state will be reached and you will also have steady current in the resistor.The same mechanism is what drives current when the wire bends within a circuit.So yes,the resistor DOES actually slow down the current,but it does so until the accumulated charge caused by it produce an equal amount of electric force to keep the current steady

 

[Drakkith]

As the charge accumulates it creates its own electric field and thus gives some extra "push" to the charge that will tend to also accumulate with them and finally there will not be any more accumulation of charge but a steady state will be reached and you will also have steady current in the resistor.The same mechanism is what drives current when the wire bends within a circuit.So yes,the resistor DOES actually slow down the current,but it does so until the accumulated charge caused by it produce an equal amount of electric force to keep the current steady

Does this imply that there are negative charges built up on one side of resistive elements?

 

[nasu]

Yes,the resistor tends to slow the charges down(the current),and thus initially(before the system reaches steady state conditions) you have charge accumulation near the start of the resistor.As the charge accumulates it creates its own electric field and thus gives some extra "push" to the charge that will tend to also accumulate with them and finally there will not be any more accumulation of charge but a steady state will be reached and you will also have steady current in the resistor.The same mechanism is what drives current when the wire bends within a circuit.So yes,the resistor DOES actually slow down the current,but it does so until the accumulated charge caused by it produce an equal amount of electric force to keep the current steady

Slow them in respect to what? It seems that you are talking about the transient time, when the circuit is established but still don't see what could be the meaning of this "slowing down". It seem to imply that is takes some time for the electrons to reach the resistor.
Indeed there is surface charge creating the field, in the steady state but this field is what gives the electrons their drift velocity. Is not slowing them down, whatever than means. So if you think about the initial state, before the field is established, the drift velocity is zero and then increases to the steady state value. Where would a slowing down will fit in this?

We can compare the circuit with and without rezistor (just wires) and in this case is clear that the drift velocity in the conductors is lower in the case with resistor than in the case without, given that the same voltage source is used..
If we compare the drift velocity in resistor and in wires for the case with resistor, it can be either way. There is no reason to assume that the drift is slower in resistor.

 

[OmCheeto]

Does this imply that there are negative charges built up on one side of resistive elements?

/me scratches head...
I think it does.

/me thinks about it for another 2.3 seconds
hmm... It makes total sense to me.

Never really thought about it before.

Somebody should build a new analogy model, as I don't think any of the previous ones work here.

Unless of course, all the fans going to the football game have really bad B.O. (You require a mutual repulsive force that fits the square law)
F = k * (Stench₁ * Stench₂)/d²

Science!

Seriously. Why else would they show a voltage drop across a resistor?
Of course, I could be wrong.

 

[Dale]

Does this imply that there are negative charges built up on one side of resistive elements?

Yes. This is an interesting detailed calculation.

EDIT: corrected link
http://depa.fquim.unam.mx/amyd/arch...ia_a_otros_elementos_de_un_circuito_20867.pdf

 

[OmCheeto]

Yes. This is an interesting detailed calculation.

http://mathpages.com/rr/s2-04/2-04.htm

Relativistic doppler shift? Now I'm really confused.

 

[Dale]

Relativistic doppler shift? Now I'm really confused.

Oops. Copy paste error.

Here is what I meant to post.

http://depa.fquim.unam.mx/amyd/arch...ia_a_otros_elementos_de_un_circuito_20867.pdf

 

[OmCheeto]

Oops. Copy paste error.

Here is what I meant to post.

http://depa.fquim.unam.mx/amyd/arch...ia_a_otros_elementos_de_un_circuito_20867.pdf

Delightfully serendipitous mistake though. We've been discussing doppler shift navigation over on the Ceres thread. I think you may have just answered my question. Thanks!

 

[skepticwulf]

Regarding an analogy, from the textbook I'm studying: "
A common misconception is that the electrons are “used up” by the lightbulb. A good analogy
would be water flowing across a water wheel in a flour mill. The water flows onto the wheel at
the top (high potential) and causes the wheel to rotate as the water descends along the wheel. The
amount of water that leaves the bottom of the wheel is the same as the amount that entered at the
top, but it does so at a lower point (low potential). The change in potential energy goes into work
in the wheel. In a lightbulb, electrons at higher potential energy enter the lightbulb and give off
that energy as they pass through the bulb. As with the water on the wheel, the number of
electrons exiting and entering the bulb is the same"