# How is speed factored in the Amperes calculation?

Discussion in 'General Electronics Chat' started by ptownbro, Nov 8, 2014.

1. ### ptownbro Thread Starter New Member

Sep 28, 2013
17
0
OK. This may be a stupid question but here it goes.

When thinking about the measurement of current in Amperes how is the speed of the current factored in the equation?

Let me try to illustrate using example. Amperes is the measurement of the number if electrons or coulombs passing a given point in one second A = Q/t. However it seems to me that how fast those electrons are moving is missing in the equation.

Here's my (lame) illustration

I this wire at the marked point you have two electrons (coulombs) passing the marked point in one second. So the Amps = 2.

V
-------------------
o
o
-------------------

Now in this example you two electrons agaun but only one is passing the same marked point at a time. But... If they moved twice as fast in that same 1 second time frame you still can get Amps = 2.

V
-------------------
o o
-------------------

So the speed that the electrons are moving be factored somewhere in the equation?

Did I just qualify for a nobel prize? Or what am i missing

2. ### tom_s Member

Jun 27, 2014
287
342
let me just fill this plastic container full of water and manually simulate your experiment. (or just treat it as a stupid answer)

imagine the water as your electrons. punch a hole in the container and the 'electrons' flow through at a constant rate. eg: at a certain frequency

put another same size hole in the same container, fill up with water again and now the 'electrons' flow through twice as fast

in theory, you have doubled the frequency (and quite a lot of water on the floor) eg: twice as fast so i think you have already answered your question.

this (mine) brain works in funny ways, there might be a better / correct solution offered (maybe nobel prize as well if you luckies)

edit: amended last line

Last edited: Nov 8, 2014
3. ### crutschow Expert

Mar 14, 2008
13,482
3,370
The electron speed has nothing to do with it. Your example really doesn't make sense. The current is simply the number of electrons per second passing a given point, independent of speed. For example if 1 mA of electrons where moving in a wire, they would be going very slowly. If you then ran that same mA of current through a vacuum tube, the electrons would be going much faster through the tube due to the electric field from the high positive voltage on the plate, but it's still 1 mA with the same number of electrons passing by a given point in 1 second.

Lundwall_Paul likes this.
4. ### studiot AAC Fanatic!

Nov 9, 2007
5,005
515
Sorry, no prize, it is not quite as simple as that.

In situations like this we normally talk about charge density, because it depends whether the supply of electrons is constant or variable.

If the supply is 'inexhaustible', that is we can get as many as we want, then the faster they go the more we can get past a given point in a given time, so the more will pass per second and the greater the current.

However if the supply is limited, say to a single electron to make it easy, then an electron travelling twice as fast will travel twice as far in one second so the charge density will be averaged over twice the distance and be half that of a slower electron.

Remember also that we live in a three dimensional world and the current path also has a cross sectional area (like Tom's bucket)

So current = Charge per unit time = (Charge density x cross sectional area x travelled length per unit time) times number of charges.

But remember also that the speed is fixed by external factors and you normally only find travelling electron beams in cyclotrons and vacuume tubes and the like, as Crutschow noted.

5. ### BR-549 Well-Known Member

Sep 22, 2013
2,178
418
Speed = distance / time.
A = Q / time.
The reason there is no speed term in current is because there is no distance term in current.
If one coulomb of charge moves 10 foot in one second..........it is one amp.
If one coulomb of charge moves 10 inches in one second.......it is one amp.
Current doesn’t care how far the charge moves, only that it does move.

In most circuits we control the current with voltage and resistance. And the length of circuit does not matter.
However.......there are some circuits where current is controlled by the length of the circuit.
For instance....an antenna. In this instance.......the speed of the current determines the length.

ErnieM likes this.
6. ### ptownbro Thread Starter New Member

Sep 28, 2013
17
0
Thanks everyone for your responses! Very appreciated. Let me try to tackle each one.

Electrons are actual "things". They are beyond microscopic so we cannot see them, but they exist; they have mass. They move, travel distances, and have speed. Now, using an analogy to help further my question. Imagine you are standing on the side of a 4 lane road with a radar gun and over a period of 1 second, 4 cars drive by simultaneously, in each lane, side by side. You radar them and see they are going 5 mph. Now imagine you do the same experiment but on a 1 lane road. The only way you could have 4 cars pass by you in the same 1 second is if each car was moving faster than 5 mph. Now follow my connection between cars and electrons using same definition of Amperes. Even though in both experiments "the number of cars (electrons) passing a given point in 1 second is 4 cars (amps)", the speed of the cars (electrons) are different. The speed matters and there is a formula you could use show how the speed of the cars (electrons) passing a given point will change the number of cars (amps) which passed by that given point.

Tom: I haven't really answered my question. We've both explained essentially that electrons move faster; have speed. My question is where is that speed represented in the equation A = Q/t? Or my question perhaps asked in a better way, what is the equation for Amps that has speed as a variable?

Crutschow: Speed of the electrons do matter. As we both described current is simply "the number of electrons per second passing a given point". Both the time (one second) and the area it's passing through (which is implied) are constant. Therefore, if you also hold the number of electrons constant (and all other variables) and only increase the speed, then the amps should increase. However, speed isn't represented as a variable in the equation A = Q/t. There must be a way mathematically to relate/connect speed to Amps.

BR-459: Electrons have speed. In your example, the electrons must be moving faster at a given point within your 10 inches example to make the amps equate to the same as your 10 foot example.

Studiot: Without verifying, I think you answered question. What I'm looking for is (1) confirmation that speed does effect amps and should be a represented variable in the Amps equation and (2) what that equation is. Instead of A = Q/t which doesn't show speed, you given me the formula:

Amps = (Charge density x cross sectional area x travelled length per unit time) times number of charges

If I've understood what you've given here, speed is represented as = traveled length per unit time and you've also added other variables of density and area. This is close to something someone else gave me:

http://en.wikipedia.org/wiki/Drift_velocity
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html

These use velocity (which technically isn't same as speed), but at least I feel more confident that I was right that speed of electrons is a factor in amps.

Thanks again everyone!!!

7. ### kubeek AAC Fanatic!

Sep 20, 2005
4,688
806
I think the drift velocity is what you´re looking for. For a given current it gives you the relation between the wire crossectional area and the speed of the elecrons moving along the conductor.
Lets try another analogy - you can define flow of water in liters per second, similarly to electrical current.. Now can you tell the speed of the water running through a pipe? No you cannot, unless you know the crossectional area of that pipe, then you can easily calculate what the speed of the flow has to be to transfer said number of liters through that pipe in one second.

8. ### crutschow Expert

Mar 14, 2008
13,482
3,370
Of course electrons have speed and speed matters, but not in measuring current, and that's why it doesn't show up in the equation for current. It's not that current is unrelated to electrons speed, it's just that you don't need to know the speed to measure the current. To use your analogy, if you have 4 cars per second passing a given point, then it makes no difference if they are gong 10 MPH or 100 MPH, it's still 4 cars per second. If you want to measure their speed that's fine, but you don't need that measurement to determine how many pass a given point in 1 second. I don't see why that is difficult to understand.

Lundwall_Paul and kubeek like this.
9. ### studiot AAC Fanatic!

Nov 9, 2007
5,005
515
kubeek, that is an exact analogy, you are stating what is known as the continuity equation.

For liquids in a pipe we have

Volume flow rate = Area x velocity

Mass flow rate = density x Area x velocity

For current flow we have

Current density = J = Current/ Area = I/A

J = charge density x velocity = pv

So current/area = pv

So current, I = Apv

10. ### ptownbro Thread Starter New Member

Sep 28, 2013
17
0
Kubeek: Thanks. Yes, I think drift velocity and Studiot's answer leads me to what I'm looking for.

Crutshow: What you're saying is not difficult to understand and is appreciated. I think we're saying similar things but focused on different things. Using your example, if you just and only want to know just how many cars passed by you're absolutely right... I don't need to know the speed of the cars. But if I want to know why those 4 cars passed by in 1 second, then knowing the speed (as well as other things obviously) makes sense and matters. That's all I'm saying, but I get your points and explanations and they make sense. Thanks again.

Studiot: Thanks again.

Sep 28, 2013
17
0
12. ### MrAl Distinguished Member

Jun 17, 2014
2,554
515
Hello there,

A useful equation that relates current to some sort of rate is:
i=dq/dt

which simply means that current is the rate of change of charge with time. So the change of the charge per unit time is what we usually measure with a current meter. If the change of the charge per unit time is constant, then we see a constant current (DC). That means that the same number of electrons are passing a particular point every second. Since this is a summation process (count all the electrons that pass) it's just a matter of counting the electrons that pass within one unit time period, then starting over again once that period has expired, and because it is merely a summation (or counting) process we often dont care how fast they are actually going.
Another way of looking at it is if the cars you talked about passed by one at a time and they were going at different speeds, you would not care how fast each one was going as long as it got counted. You would only care how many got counted in one unit time.

The speed in the wire can be calculated but its not usually of concern in most of electronics. The velocity is basically:
v=ds/dt

where s is the distance one representative electron travels linearly along the wire in one unit time. One representative electron would be a hypothetical electron that represents the average motion of a large group of electrons in the wire.
There are various ways to calculate this based on the number of available electrons per mole of substance, but it usually comes out quite slow. For example, 1cm/sec. If you could see electrons, you'd see that group progress slowly along the wire even though each one moved in a somewhat random way. It would look like a huge swarm of bees flying through a clear plastic pipe except the bees would be very tiny, so maybe a swarm of fruit flies would look more like it. They would be separated by somewhat large distances, so we'd need a large diameter plastic pipe to see this, and have some small stationary marbles mounted inside the pipe to act as the nuclei.

13. ### ptownbro Thread Starter New Member

Sep 28, 2013
17
0
Good stuff. Like with Crutshow, you're explaining (among other things) why most typically don't care about speed. Which is great, and I understand. I just wanted to know if you did care about how speed effected Amps, where and how would you factor it in the equation A=Q/t.

This may create string of more replies, but... If you take this farther... Here are the thoughts that led me to ask "hmmm... what about speed?"

Amps also is represent as volts divided by ohms: A=V/R.

Given that. The thought that cross my mind was: If you held Volts and Ohms constant and just increased the speed of the electrons, wouldn't that increase the Amps? But looking at the equation I saw there wasn't a speed variable there or even in the A=Q/t equation either. That's when I realized, I'm missing and not quite understanding something. My (faulty) line of reasoning was somewhere, somehow I could connect Volts, Resistance, and Speed and Amps.

14. ### kubeek AAC Fanatic!

Sep 20, 2005
4,688
806
Well the thing is that resistance basically reflects the speed of the electrons, given the rest of the physical parameters remain the same. So if you wanted the speed to increase, the resistance would have to decrease.

15. ### crutschow Expert

Mar 14, 2008
13,482
3,370
True for the resistance of a given material. But for two wires of difference resistivity material but the same resistance per unit length, obviously the electrons in the low resistivity material will be moving faster since the cross-section area of that wire would be less to achieve the same resistance per unit length.

16. ### studiot AAC Fanatic!

Nov 9, 2007
5,005
515
Those who are saying that current = number of electrons passing a given point in unit time are not wrong.

They are only telling part of the story and not fully answering the question, "Under what circumstances is velocity important?"

The point is the difference between total flux and flux density and is true of any time dependent flux.

For an electron flux, the total flux is as defined above.

But we can also work in terms of flux density, as I previously described, and in this case velocity needs to be included as it is the link between distance and time.

17. ### Austin Clark Active Member

Dec 28, 2011
409
44
Electron speed has nothing to do with current. Amps are measured in Q/T. That is, CHARGE (not electrons, even though electrons have charge) per second time. In fact, technically it's possible to have current without moving electrons whatsoever, with protons moving instead.

18. ### studiot AAC Fanatic!

Nov 9, 2007
5,005
515
If you stood on a motorway overbridge looking down at the traffic and counted cars passing under the bridge for exactly one hour are you telling me that you would not count more cars if their speed was 60mph than 10mph?

Last edited: Nov 10, 2014
19. ### ptownbro Thread Starter New Member

Sep 28, 2013
17
0
I believe your statement that Amperes is not (I'm paraphrasing) counting "Electrons", but instead counting "Charge" is misunderstood. In the measurement of Amps, Charge and Electrons are the same things (as well as Protons depending on the context). Look at it this way: 1 ampere is 6.241×1018 electrons (or one coulomb) per second... key in on the word "electrons"... Often times the "6.241×1018 electrons (or one coulomb)" will be called "charge" or even the "charge carrier", but its really still talking about the Electrons (or, again, the Protons depending on the context of discussion).

So, in this context, Amperes is a count of Electrons (aka Charge, aka Coulombs, aka Charge Carriers) per Second. And, velocity and speed do play a part in the calculation of Amps.

I found this video (as well as many others) which may be of help in the connection between Amps and Velocity (which in turn connects speed).

20. ### studiot AAC Fanatic!

Nov 9, 2007
5,005
515
ptownbro

Yes you are getting there, but I wouldn't recommend pursuing this model too far.
And yes the idea of little balls travelling along like cars on a motorway, each carrying one charge is just a model.

This is because there are other ways to transport electricity that are more efficient.
In a few cases like an electron beam in a cathode ray tube there really is such a stream of electrons.
But most electricity is carried by each carrier bumping their neighbour along a chain.