# Where is speed factored in the Amperes calculation?

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1. Nov 8, 2014

### ptownbro

OK. This may be a stupid question but here it goes. :D

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
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o
o
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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
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o o
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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. Nov 8, 2014

### dlgoff

Check out this reference for more about electron drift velocity. Microscopic View of Ohm's Law

3. Nov 8, 2014

### Staff: Mentor

You've almost answered your own question. If the speed is greater and the density (number of electrons per unit volume) is the same, then more electrons per unit time will be passing a given point. So the speed is already factored into the number of electrons passing by.

4. Nov 8, 2014

### ptownbro

Thanks for the response. But, I don't think I have answered my own question as you described it. Look at the formula for amperes to understand what I mean. A = Q/t

There are no variables for speed in that mathematical equation.

As you said in your response "If the speed is greater...". Where is (are) the speed variable(s) in the equation A = Q/t? You should be able to prove mathematically "speed is greater" in the formula.

5. Nov 8, 2014

### DrGreg

There is insufficient information. You can get the same current from a large number of electrons moving slowly or a small number of electrons moving quickly.

What is missing is the charge density.

6. Nov 8, 2014

### Staff: Mentor

The amperage at a given point is given by the amount of charge $Q$ passing that point in a time $t$: $A=Q/t$ just as you say.

So what is the value of Q? It's the product of $e$, the charge on one electron, times the number of electrons passing that point. And how many electrons is that? Well, consider the electric current as a stream of electrons separated from one another by distance $d$; the number of electrons passing the point per unit time is $v/d$, so in this case $Q=ve/d$ and the velocity is, as I said, already in the quantity Q. You can try other configurations of electrons and the arithmetic will be more complicated, but the $v$ will always be in there somewhere.

There's an analogy with the flow of water in a pipe. If the pipe has a cross-sectional area of one square meter and the water is moving at one meter per second, the flow past any point along the pipe is 1000 liters per second. If the water is moving at two meters per second, the total flow is 2000 liters per second. This, if I know the rate of flow, I don't need to worry about the velocity - it's already in the flow rate.

The reason we write these equations in terms of total flow (liters per second for water, coulombs per second for the electric current) instead of particles (water molecules in the case of water, electrons in the case of charge) times speed divided by distance is that it is much easier to measure the total flow.

7. Nov 8, 2014

### ptownbro

Thanks everyone for your responses. You've both partially answered my question. I guess what I was looking for is the equation that shows the speed variable factored in along with confirmation that speed is actually a factor of Amps even though the traditional equation A = Q/t doesn't explicitly show it.

Someone else also provided these references which confirms that speed is a factor and provides a formula (though it discusses velocity which is related but technically different than speed):

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

8. Nov 8, 2014

9. Nov 8, 2014

### jerromyjon

There are many factors to calculate which can get very confusing, the temperature of the conductor and the molecular structure which determines its resistance as well as its drift velocity which is a lot of electrons bouncing around much faster than that but in a collective order towards "ground".

When you refer to AC, the net velocity over time is 0 because the Alternating Current switches back and forth at a rate referred to in Hz (Hertz) denoting the wave frequency in seconds.

And last but not least the connection which has to be realized to cause electrical current to "flow" transfers "information" through a field at nearly the speed of light "telling" every free electron which way its closest attractive deficient atom is and vise versa strengthening the attraction. A good example is how your body creates and collects excess energy and the static potential dissipates to a system which is lacking energy very quickly but the flow is brief and therefore the "work" which occurs, being your desired transaction velocity, is much slower leading to the "zap" you experience as entropy efficiently facilitates equilibrium.

10. Nov 8, 2014

### jerromyjon

In the other thread you mentioned 4 cars a second at once in parallel (four lanes) versus 4 cars a second in series (one lane) which, realistically, the velocity you seek to understand doesn't change and the cars are all bouncing around the lanes much faster with some trying to get back to the entrance ramp and some trying to run off the road and more, in a current, trying to continue along the highway to a nice vacation from the rat race.

11. Nov 8, 2014

### Staff: Mentor

I think the problem here is you want to combine two things that are already combined:
Speed is already a part of Amps. It makes no sense to put something into an equation that is already there. If you want to see how it is in there, you need to take it out. You make a separate equation describing it, such as: A=SD where S is speed (in m/s) and D is (linear) charge density in Coulombs/m.

Last edited: Nov 8, 2014
12. Nov 8, 2014

### Staff: Mentor

If you want to think about speed then you probably want to think about current density rather than current. Current density is simply charge density times velocity. Then current is current density times area.

13. Nov 8, 2014

### sophiecentaur

Although we would normally produce an electric current by using a flow of electrons, it is by no means the only way. A beam of positive Ions (multiply charged perhaps, even) also corresponds to an Electric Current. An Amp is still an Amp and, with that beam being included somehow in a circuit, all the calculations would be the same. (Ideally, at least).

14. Nov 9, 2014

### ptownbro

Thanks everyone for your responses! I'll try to briefly address each.

jerromyjon: Good responses and all understood. I guess what I'm looking for in regards to what you've said is the equation which represents with these and more importantly for me, the speed variable. In regards to your comment about my 4 cars example: I'm not seeking velocity, I'm seeking speed.

russ watters: Speed is not already a part of Amps and hey are not effectively one in same as you suggest. I used an anology/example to explain the difference before. Here's an edited version:

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. 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. Amps is the number of electrons (cars) passing a given point, while Speed is how fast those electrons (cars) are going while passing that point. Two different things

dalespam: I think that's what the formula given in the two links I gave are referring to as well. Though I'm really looking for speed versus velocity, it's close enough I guess.

sophicentaur: Thanks, however, not sure how this applies to my question.

Yesterday at 8:10 PM#9
jerromyjon

15. Nov 9, 2014

### Staff: Mentor

Yes, speed is part of Amps, but that doesn't make them the same thing - I didn't say it was. Heck, that wouldn't even make sense: Tires are a part of a car, but that doesn't make a tire a car!
Agreed. So perhaps you need to reread my post -- I even provided you an equation that describes the situation you just outlined.

Last edited: Nov 9, 2014
16. Nov 9, 2014

### ptownbro

Ok. My apologies. I misunderstood your post. Thanks

17. Nov 9, 2014

### sophiecentaur

OK
I was trying to point out that the speed of the charges is not a relevant quantity when you are considering current - except in some very rare circumstances or experiments*.
If you put a thin wire, carrying 1A and a thick wire, also carrying 1A (with the appropriate metal to ensure that the resistances of the two wires are the same) and, electrically, the two wires can be treated as doing identical things, even though the charge carriers happen to be moving at a different mean velocity.
Are you forgetting that the drift speed (mean velocity) of electrons is only a few mm/s and the resulting Kinetic Energy is pretty much negligible? We are not talking about a substance flowing round a circuit and behaving like water with water wheels etc..

Bottom line is that you do not need to "factor in" the speed because it is of no relevance.

* Considering the movement of charged particles in a vacuum, perhaps, where the velocity will affect the path taken.

18. Nov 9, 2014

### ptownbro

Ah. Ok. Thanks. Makes sense.

Yes others indicated and explained why typically most are not concerned with speed. Yours was well explained and welcomed.

What I guess I was getting at was if you are concerned with speed, how would you express it in the or an Amps equation? Since it's not explicitly apparent in the simplified equation of A=Q/t (or even in A=V/R), whats the expanded equation where it is?

But you and others have confirmed it is a factor (though noted you may consider it relevant).

19. Nov 9, 2014

### A.T.

For example replace Q with v/d, as already explained in post #6.

20. Nov 9, 2014

### Staff: Mentor

Again, I already provided such an equation! (the expansion part) Why are you still ignoring it?