Help improve my concept of current

[mishima]

I feel like my concept of current is way off. Suppose in a circuit there is a node in which you have a certain amount of charge entering per second. Since charge is quantized, this means you have a certain amount of electrons entering the node per second. Now I would want to say that if, after the node, the wire contains the same elements, then the current would be split exactly. In other words the same current would be flowing in both wires after the node (and their sum would equal the current before the node by Kirchoff's current law).

But if there was an odd number of electrons, wouldn't one current be slightly bigger than the other? For example maybe the initial current was 3 electrons. 2 would go one way and 1 the other. Or even how about 1 initially? Then there wouldn't even be a current in the other wire.

How can I improve my concept of current to get around these thoughts?

 

[berkeman]

I feel like my concept of current is way off. Suppose in a circuit there is a node in which you have a certain amount of charge entering per second. Since charge is quantized, this means you have a certain amount of electrons entering the node per second. Now I would want to say that if, after the node, the wire contains the same elements, then the current would be split exactly. In other words the same current would be flowing in both wires after the node (and their sum would equal the current before the node by Kirchoff's current law).

But if there was an odd number of electrons, wouldn't one current be slightly bigger than the other? For example maybe the initial current was 3 electrons. 2 would go one way and 1 the other. Or even how about 1 initially? Then there wouldn't even be a current in the other wire.

How can I improve my concept of current to get around these thoughts?

A good first step would be for you to look up the charge on an electron. Then use the equation I = ΔQ / Δt (current in Amps = charge flowing through a surface in Coulombs per second) with some reasonable current value like 1mA, and calculate how many electrons per second are flowing in the wire. I think you'll see that the difference of 1 electron here or there doesn't make much difference...

 

[mishima]

Well I know its so incredibly (unfathomably) small as to be insignificant in real electronics. But in theory is that what would really happen in the case of 3 electrons constituting a current?

 

[phinds]

Well I know its so incredibly (unfathomably) small as to be insignificant in real electronics. But in theory is that what would really happen in the case of 3 electrons constituting a current?

This is why nitpickers call Ohm's Law "Ohm's Approximation".

You are picking at nits.

 

[Studiot]

If you have one electron entering a Y junction do you have a current?

As the electron approaches the node there is one electron in the entry leg and zero in the exits legs.

Once the electron is at the node or beyond there are zero electrons in the entry leg so what is the current in the entry leg?
And whilst the electron is at point A in the entry leg, what is the current at points B, C , D etc?

The whole scenario is nonsense.

The whole concept of Current is of a continuum flux. That is it is infinitely divisible or spread out in space and time (in a given conductor).

If you want to work at low electron counts you have to revise your concept to a granular charge flux. Since there are (were) electron tube devices that work at low counts this used to be done for electron ballistics.

But remember that this happens in a vacuum, where we can control the number of electrons.

In a conductor, by definition, there are sufficient 'free' electrons knocking about for the continuum current flux model to hold sway.

This goes to show the importance of always only using a model within its limitations of definition. The conditions are all too often forgotten.

 

[Q-reeus]

Adding a bit to last post - as microelectronics -> nanoelectronics, it is becoming increasingly important to consider 'quantized currents'. Already single-electron transistors have been created: http://luciano.stanford.edu/~shimbo/set.html
http://en.wikipedia.org/wiki/Coulomb_blockade#Single_electron_transistor
When it gets to that level, instead of talking in terms of currents, electronic states or perhaps electron hopping makes more sense - with 'current' then being reserved as a time-averaged concept.

 

[Studiot]

Yes indeed Q-reeus, thank you for bringing me up to date.



If you really want to go the quantum route then your Y junction becomes the quantum equivalent of the two slit experiment and the answer is that the 'electron' goes down both exit legs simultaneously and virtually and only appears in one when you test for it.

 

[mishima]

Ok, that makes sense. I had never heard you needed a certain amount of charge for current to be a valid model.

Does a voltage source create an electric field even when there is no wire? Would a negative charge floating in space move towards the cathode?

Why is it if you put a free wire (not touching) next to a voltage source there is no current, and only when the wire touches the voltage source do you get current? Is there not always an electric field regardless of the wire's location?

 

[CWatters]

Why is it if you put a free wire (not touching) next to a voltage source there is no current, and only when the wire touches the voltage source do you get current? Is there not always an electric field regardless of the wire's location?

Current depends not only on the field but the ability of the material to conduct electricity (eg it's resistance). If you form a gap in a circuit the implication is that the gap is filled with a material that is non conducting. So no current, or very little current flows.

You can also consider a gap in a circuit to be a capacitor. If you charge up one side of a capacitor the electric field pushes charges away from the other plate. So current does flow while you are changing the charge on one side. In short...capacitors pass AC but not DC.

 

[mishima]

That's also clear, thanks. Current density is directly proportional to both conductivity and electric field.

I guess I need to read up on the physical explanation of conductivity/resistivity.

 

[Studiot]

Charge or current density is a concept that allows us to use many powerful theorems from maths such as Gauss' Theorem and assumes that if we hang a net across the flow there is a steady stream passing through the net coming in from one side and going out of the other. This is a bit like water flowing through a hosepipe. Take any section of area A there is water passing through and the volume rate of flow = velocity times A.

Just like with pressure if we shrink the area to a point we obtain a differential equation that we can integrate over the whole stream.