Help settle an old dispute

[Seraphiel]

Well, this is a subject I have discussed at length with a friend of mine. Dunno how to express this in any eloquent way, so here goes:

Party A, claims there is a configuration possible (in terms of volts, amps, physical use of wires etc., that'll allow for a current to only pass A or B (at random), but not both of them at the same time.

Party B, claims there is no configuration possible, and that current will have to pass both A and B, to make the circuit effectively work, no matter the configuration or time interval meassured.

It doesn't matter if the circuit will shortcut or destroy itself, only thing that matters is: If both points must be passed or not, configuration doesn't matter.

This is the particular configuration, where the grey area is the power source (regardless of nature), the black part the wires, and A / B the respective paths:

http://img161.imageshack.us/my.php?image=quexb8.jpg


I hope the problem is understood, regardless of how silly the question / problem is. We have asked several physics teachers, and the answers is not quite clear.

Regardless of the correct answer, I have several follow-up questions.

Hope this is not silly and a waste of your time, as this is really a puzzle to me and several others. Please help us to learn the whys, and why nots.

 

[Nathelion]

I'm assuming that I'm interpreting the question wrong (since you have had so much trouble with it), but if the grey part is a power source, the black wires are, well, wires, and there are resistors (of whatever nature) at A and B, then current will flow across both a and b as given by Ohm's law. But I suspect that this is not what you're asking.

 

[Seraphiel]

Originally posted by: Nathelion
I'm assuming that I'm interpreting the question wrong (since you have had so much trouble with it), but if the grey part is a power source, the black wires are, well, wires, and there are resistors (of whatever nature) at A and B, then current will flow across both a and b as given by Ohm's law. But I suspect that this is not what you're asking.

Actually, I don't think you interpret the question wrong at all.

The counter argument is, that if all parts of the wiring part is equal (same thickness, material, resistance), then the current would rather pass one of the points, rather than both. Since it would take half the amount of current to pass either point than both, and if the power supply is restricted enough, then this condition would somehow be met/meet(?).

A point here is, that a lightning bolt (real or man made), would only pass one of many possible paths.

The counter argument to all of this is essentially, that passing through both wires would give less resistance than passing one of them.

Dunno, as this is kinda confusing and I believe it is a quite simple problem, and someone have just misunderstood something.

Don't wanna sound like an idiot, and I think all parties would agree if they somehow saw the problem the same way.

 

[gururu2]

i'm not an electrical engineer, but I would agree that current will reach both A and B and re-converge. if A and B were light bulbs, they would both light up.

 

[irishScott]

Unless you have some sort of switch (transistor?) at the divergence point, I'd say any current would follow both paths equally and re-converge. One thing I remember from basic physics is "current always follows the path of least resistance". If the resistances at the divergence point are equal, then it should travel through both. Even if the resistances were different, it would still travel through both (one more than the other, but still through both). You could (theoretically) have insanely high resistance in one, thus impeding the flow to negligible levels on one side, but some would still pass through.

 

[Seraphiel]

Originally posted by: irishScott
Unless you have some sort of switch (transistor?) at the divergence point, I'd say any current would follow both paths equally and re-converge. One thing I remember from basic physics is "current always follows the path of least resistance". If the resistances at the divergence point are equal, then it should travel through both. Even if the resistances were different, it would still travel through both (one more than the other, but still through both). You could (theoretically) have insanely high resistance in one, thus impeding the flow to negligible levels on one side, but some would still pass through.

No transistor or SS devices of any kind in the circuit. I remember that rule too, and I agree with it. I am party B so to speak, but I am in error in my understanding of this or have simply misunderstood something:

The counter argument to this is, that resistance is not a infinite value, and nor is the minimal amount of current needed to pass either point A or B. If a balance is somehow reached, then the random A/B path should be the result, and not both A/B.

This should somehow, I am told, be related to lighthing. If the atmosphere is used as an example, then there is a finite amount energy charged, and thus there should only be a finite amount of ways it could discharge from - to +, or the other way around. If it should discharge in any path possible, then there should be much more energy charged for this to be possible - it would take infinite energy to travel all the relative infinite paths, and lightning would always fill the sky - which is not the case.

It doesn't make sense, that if one path is slightly less resistant than the another (e.g. 0.5x vs 0.7x), that this should yield only one possible path, when if, both are of equal resistance (0.5x vs 0.5x), then it would yield both possible paths.

Am I taking these counter arguments too seriously, and should just ignore them? They make some sense to me, but I am not smart enough to counter them.

Lets say I have that "insanely" high resistance... how could anything flow through both, if the power supply can only supply enough electrons at any given time, to pass through one of them? There has to be a limit, where there are only current / voltage / whatever aviable, to pass through one of the wires (all of them are equal, so even if the split section A/B has less resistance than the before or after this section, more electrons shouldn't be allowed to pass through this part, than the limit set by the parts before or after minus the amount lost to resistance).

I feel like an idiot

 

[CTho9305]

There will always be current in both. The "always takes the path of least resistance" thing is an oversimplification. Voltage works almost exactly like water pressure. Imagine a bucket of water a few feet above the ground. Poke two equal-sized holes in the bottom and attach equal-size hoses. You'll get the same amount of water flowing through both. Poke a big hole and a small hole, and attach a fire hose to the big one and a coffee stirrer to the other. You'll still get water flowing through both of them. Even under low pressure (shallow water / bucket close to the ground), you'll get the same behavior (just less total current over all).

 

[Nathelion]

Originally posted by: Seraphiel

Originally posted by: irishScott
Unless you have some sort of switch (transistor?) at the divergence point, I'd say any current would follow both paths equally and re-converge. One thing I remember from basic physics is "current always follows the path of least resistance". If the resistances at the divergence point are equal, then it should travel through both. Even if the resistances were different, it would still travel through both (one more than the other, but still through both). You could (theoretically) have insanely high resistance in one, thus impeding the flow to negligible levels on one side, but some would still pass through.

No transistor or SS devices of any kind in the circuit. I remember that rule too, and I agree with it. I am party B so to speak, but I am in error in my understanding of this or have simply misunderstood something:

The counter argument to this is, that resistance is not a infinite value, and nor is the minimal amount of current needed to pass either point A or B. If a balance is somehow reached, then the random A/B path should be the result, and not both A/B.

This should somehow, I am told, be related to lighthing. If the atmosphere is used as an example, then there is a finite amount energy charged, and thus there should only be a finite amount of ways it could discharge from - to +, or the other way around. If it should discharge in any path possible, then there should be much more energy charged for this to be possible - it would take infinite energy to travel all the relative infinite paths, and lightning would always fill the sky - which is not the case.

It doesn't make sense, that if one path is slightly less resistant than the another (e.g. 0.5x vs 0.7x), that this should yield only one possible path, when if, both are of equal resistance (0.5x vs 0.5x), then it would yield both possible paths.

Am I taking these counter arguments too seriously, and should just ignore them? They make some sense to me, but I am not smart enough to counter them.

Lets say I have that "insanely" high resistance... how could anything flow through both, if the power supply can only supply enough electrons at any given time, to pass through one of them? There has to be a limit, where there are only current / voltage / whatever aviable, to pass through one of the wires (all of them are equal, so even if the split section A/B has less resistance than the before or after this section, more electrons shouldn't be allowed to pass through this part, than the limit set by the parts before or after minus the amount lost to resistance).

I feel like an idiot

I think the crux here is that your wires are conductors, so the "lightning bolt" model doesn't apply. Discharges such as lightning typically occur when the electric field between two poles is strong enough to ionize the molecules of an interceding dielectric. The "path" of ionized molecules then becomes conductive (free electrons), and charge flows across it. Naturally, once this happens the potential difference between the two poles will be reduced, so it will only happen once, along one path, such as with lightning.
Conductors, on the other hand, are usually modeled in a continuous fashion, where a small increase in voltage leads to a small increase in current. So the problem seems to be that in option A, the conducting wires are treated as if they were insulators, which is not the case. So B is the correct answer.

 

[BrownTown]

In any sort of real world application the current will flow through both path is inverse proportion to their impedances. However one could posit a system like this in which single electrons are released from the power source and then obviously at any given instant the electron would have to be on one path or the other. I believe such a setup would even be physically possible to construct using nanotubes and such. Another possibility would be for the current paths to nto be modeled as simple linear resistors, but instead something like an airgap which of course has a breakdown voltage. Current will only arc on one path which will be determined randomly by cosmic rays and such. So YES, it is possible to make such a system where the current will flow through only one of two possible paths as determined by random chance.

 

[jagec]

Originally posted by: BrownTown
In any sort of real world application the current will flow through both path is inverse proportion to their impedances. However one could posit a system like this in which single electrons are released from the power source and then obviously at any given instant the electron would have to be on one path or the other. I believe such a setup would even be physically possible to construct using nanotubes and such. Another possibility would be for the current paths to nto be modeled as simple linear resistors, but instead something like an airgap which of course has a breakdown voltage. Current will only arc on one path which will be determined randomly by cosmic rays and such. So YES, it is possible to make such a system where the current will flow through only one of two possible paths as determined by random chance.

I dunno, once we start getting into the quantum level, a single electron will only "choose" a path if we observe it doing so...otherwise, it still "passes through both" with a probability function that depends on the exact configuration.

However, adding an air gap or other device that requires a semi-random breakdown voltage would allow us to restrict the current to only a single path at a time.

 

[Born2bwire]

Originally posted by: BrownTown
In any sort of real world application the current will flow through both path is inverse proportion to their impedances. However one could posit a system like this in which single electrons are released from the power source and then obviously at any given instant the electron would have to be on one path or the other. I believe such a setup would even be physically possible to construct using nanotubes and such. Another possibility would be for the current paths to nto be modeled as simple linear resistors, but instead something like an airgap which of course has a breakdown voltage. Current will only arc on one path which will be determined randomly by cosmic rays and such. So YES, it is possible to make such a system where the current will flow through only one of two possible paths as determined by random chance.

I don't think a single electron is a valid thought experiment. Circuits do not work by just injecting electrons, they work foremost by applying an electric field across a set of points. The electric field induces movement in the free and bound charges of the media. When you initially turn on a circuit, the electrons that appear moving are not the ones that are being injected into the medium, but are the electrons (and other charges) that were floating around in the conductors initially. This is why the propagation of voltage and current signals in waveguides can be faster than the velocity of the carriers. You end up injecting carriers because the electric field causes a net drift, but this is only in the case of a DC voltage. If you have a purely AC signal, then the charges are just oscillating about fixed points (barring any secondary drifts due to static fields and such).

 

[Biftheunderstudy]

"[/quote]I don't think a single electron is a valid thought experiment. Circuits do not work by just injecting electrons, they work foremost by applying an electric field across a set of points. The electric field induces movement in the free and bound charges of the media. When you initially turn on a circuit, the electrons that appear moving are not the ones that are being injected into the medium, but are the electrons (and other charges) that were floating around in the conductors initially. This is why the propagation of voltage and current signals in waveguides can be faster than the velocity of the carriers. You end up injecting carriers because the electric field causes a net drift, but this is only in the case of a DC voltage. If you have a purely AC signal, then the charges are just oscillating about fixed points (barring any secondary drifts due to static fields and such).[/quote]"

Exactly, I remember my E&M course where we determined the electron velocity in a circuit and found that it is some very slow speed, somewhere in the region of a few meters per second. Even so, when you flick your light switch its still almost instantaneous, this is because its not that the electron has to travel through the wire. Remember, the definition of current is coulombs/second, this does not mean its the same electron--just some amount of charge.



Edited for my inept quotation practices.

 

[Seraphiel]

Thanks everyone. I really appreciate it.

Lots of info to think about, and I'll probably ask a few questions later.

 

[PowerEngineer]

This debate about dropping single electrons into this circuit with two possible paths is essentially a recasting to the classic "double slit" experiment with electrons.

See Dr. Quantum

The particle notion that the electron takes only one of several possible paths turns out to be wrong (unless you peek!).

 

[Modelworks]

Read up on kirchoff's law.
It pretty much explains the answer.
http://cnx.org/content/m0015/latest/
http://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws

 

[acidpad]

the only issue I'm taking with the initial question is the "randomly choose" part, but there are certainly ways that party b could be correct, especially in practice more than in theory. As stated above, it will come down to a function of resistance. In theory, there will always be some current over both, but if the resistance is very high on one, and very low on the other, there are cutoff thresholds where the electricity that would theoretically pass through is negligible. Going back to the water example, it would be like if there was a big hole and a small hole, but the small hole was plugged with so much mud that the water just couldnt get through. Mud is porous enough that water can theoretically get through, but in practice, the water will simply divert if you are at the extreme.

Another thing to account for, however, is that if the wires are close together at all, the wire that has electricity flowing through it will likely induce a magnetic field, which will then likely induce an electric field onto the other wire, thus making the other wire live, even though the electricity did not originally flow through it. This is a function of many things, especially distance of the wires.

There are certainly more answers if you involve more pieces (like transistors, capacitors, etc).

 

[BrownTown]

Originally posted by: acidpad
the only issue I'm taking with the initial question is the "randomly choose" part, but there are certainly ways that party b could be correct, especially in practice more than in theory. As stated above, it will come down to a function of resistance. In theory, there will always be some current over both, but if the resistance is very high on one, and very low on the other, there are cutoff thresholds where the electricity that would theoretically pass through is negligible.

But that isn't random at all, if you have a billions ohms of resistance on one path and .001 ohms on the other than the current will ALWAYS flow mostly through the .001 ohm path. The air gap example is alot better in that its is entirely random which path is chosen because the two paths have the exact same resistance (in theory) until some random gamma ray comes by and set off an avalanche breakdown of the air between the contacts and sets ALL the current going through that one path purely by random chance.

 

[Seraphiel]

So theoretically, if matched capacitors are put in the circuit at point A and B, it would be possible to have the current flow across one point and not the other?

Such a circuit sounds simple enough in theory, but how difficult would it be, to make it work in practice?

 

[Born2bwire]

Originally posted by: Seraphiel
So theoretically, if matched capacitors are put in the circuit at point A and B, it would be possible to have the current flow across one point and not the other?

Such a circuit sounds simple enough in theory, but how difficult would it be, to make it work in practice?

No, it would not be possible for the current to go through one branch over another. As long as you have two branches with possible paths of current you will always have currents through both.

 

[Nathelion]

This is devolving into a comparison of classical and modern physics.

In classical physics, unless there was an air gap or some other dielectric involved, you would have currents flowing across both paths as explained in multiple posts above.

In modern physics, "current" is more tricky to define. Do you define current as the potential existence of an electron traveling along a certain path? In that case, you would have "current" along all possible paths, but with varying probability densities. Unless there are infinite potentials involved, any given electron could be anywhere until the wavefunction is collapsed, so you'd have "current" even outside the wires.
The modern perspective is only useful if you are looking at a system on a very small scale, such as the case of a single electron traveling the circuit. Classical physics is really an approximation of modern physics on a "large" scale. As such, the answer depends on whether you want the "classical" answer or the "modern" answer. In other words, do you want to consider a current of gzillions of electrons, or are you interested in a current of, say, a couple of hundred electrons, or even a single one?

 

[KIAman]

Born2bwire hit the nail on the head.

The movement of current through a wire is due to the electric field generated by the potential. Assuming equal values on both paths, the field is uniform and thus the same amount of current flows.

The water in pipe example is great but there is one thing that people always forget. The whole pipe is prefilled with water already but nothing is moving that water. Now, pump more water from the source and there is movement in both pipes as the pressure is applied to both paths.

 

[BrownTown]

That is a nice model that they try and teach you in freshmen "Circuits I" class, however it doesn't take into account a whole lot of the properties of electric fields, and in this case electric fields in non-linear materials. For example lets say we had the two paths here, one with a diode with threshold voltage 0.7V and another with threshold voltage 1V and both with internal resistance of 100 ohms. Now if we go and apply 0.8V the vast majority of the current will be going through the path with the 0.7V diode and not with the 1V diode even though they both have the same nominal resistance (in reality they don't have the same resistance because their resistance is a function of applied voltage and not a constant which is the whole point here). Now the instance people here are discussing of an air gap is exactly the same thing, as you increase the electric field the resistance stays the same (incredibly large value) until you reach the breakdown threshold and an arc forms across only ONE of the two paths. At this point the resistance in that path decreases 10+ orders of magnitude as the air is ionized while the other path is still very high in resistance. At that point ALL (99.9999999999%) of the electricity is going through the arc. The important thing is that this is more or less random as to which way it goes, but the point is that initially both paths have the same resistance and the same electric field applied across them and yet in the end 99.999999999999% of the current is flowing in one path and not the other.

 

[gururu2]

the way you guys physically manipulate one side to direct current to the other kind of defeats the purpose of the idea. the important reality is that if all things are equal, both sides will carry current. if 1 side is messed up, then the other side will be the preferable route.

 

[Seraphiel]

Originally posted by: BrownTownNow the instance people here are discussing of an air gap is exactly the same thing, as you increase the electric field the resistance stays the same (incredibly large value) until you reach the breakdown threshold and an arc forms across only ONE of the two paths. At this point the resistance in that path decreases 10+ orders of magnitude as the air is ionized while the other path is still very high in resistance. At that point ALL (99.9999999999%) of the electricity is going through the arc. The important thing is that this is more or less random as to which way it goes, but the point is that initially both paths have the same resistance and the same electric field applied across them and yet in the end 99.999999999999% of the current is flowing in one path and not the other.

Isn't that contrary to the statement: "Assuming equal values on both paths, the field is uniform and thus the same amount of current flows." ???

Damn, so confused by this, sorry. Are all of you right, and talking about different things?

How can air behave any different than wires made of say poorly conducting materials (relative to the rest of circuit), still all things being practically equal? Isn't the difference just a matter of the powersource (voltage I guess) and time?

Also, would it matter if the powersource is continious or is shutdown/restarted everytime any meaningful current has passed?

Sorry for the (probably) dumb questions, and I am grateful for the answers you have all given, and that you have taken the time to do so. If you think the questions too dumb to answer, no offence is taken (I feel dumb about this subject). Thank you, anyways.

 

[Nathelion]

Yes, we are all right, and yes, we're all just talking about different things - or really the same thing, but at different levels of accuracy and with different assumptions about the premises.