Where is speed factored in the Amperes calculation?

[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

 

[dlgoff]

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

... to obey Ohm's law. A microscopic view suggests that this proportionality comes from the fact that an applied electric field superimposes a small drift velocity on the free electrons in a metal.

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

 

[Nugatory]

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.

 

[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.

 

[DrGreg]

Where is (are) the speed variable(s) in the equation A = Q/t?

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.

 

[Nugatory]

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.

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.

 

[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

 

[ptownbro]

In case someone later is interested. I asked same question on another forum and got interesting responses there as well:

http://forum.allaboutcircuits.com/threads/how-is-speed-factored-in-the-amperes-calculation.103271/#post-780163

 

[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.

 

[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.

 

[russ_watters]

I think the problem here is you want to combine two things that are already combined:

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.

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.

 

[Dale]

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.

 

[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).

 

[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
https://www.physicsforums.com/members/jerromyjon.528145/

 

[russ_watters]

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:

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!

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

Agreed. So perhaps you need to reread my post -- I even provided you an equation that describes the situation you just outlined.

 

[ptownbro]

Ok. My apologies. I misunderstood your post. Thanks

 

[sophiecentaur]

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

Yesterday at 8:10 PM#9
https://www.physicsforums.com/members/jerromyjon.528145/

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.

 

[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), what's the expanded equation where it is?

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

 

[A.T.]

whats the expanded equation where it is?

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

 

[russ_watters]

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), what's the expanded equation where it is?

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

 

[ptownbro]

I'm not. I was just re-explaining what I was asking. Thanks for your time, advice, and effort on this. Very appreciated.

 

[sophiecentaur]

It is possible to combine the equations which describe commonly used relationships in all sorts of ways. Some of the resulting equations prove to be more enlightening than others.

 

[Drakkith]

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), what's the expanded equation where it is?

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

I think you have a misunderstanding of just what exactly the electrons are doing in a conductor. Electrons aren't moving along neat little lines in set directions like cars on a road are. In a conductor the electrons are more like gas molecules bouncing around everywhere. They are free to move in any direction at any speed as long as they stay inside the conductor. If we apply a voltage to this conductor then the result is that when we add up all these velocities we find that there is a net flow of electrons in a particular direction, even though many of them are still moving in a direction opposite to the direction of current flow.

To simplify this into a single dimension, let's take your analogy of cars. Now, imagine that we are overlooking a section of the freeway with cars moving along both directions. At first, both directions have cars moving at many different speeds, some passing each other, some towing at a slow speed, etc. If we count the number of cars passing by a point over a particular unit of time, 1 minutes perhaps, we would find that they are equal for both directions.

Now let's say that a an accident occurs and the east-bound lane slows down a bit while everything gets cleaned up. We still have cars moving east, but the number has dropped slightly and the number of west-bound cars now outnumbers the east-bound cars. We now have a west-bound "current" flow.

Now, if you were to ask what the relationship between the speed of the cars and the current, I wouldn't be able to give you a single answer. Each car is moving at its own speed, and it is only when you add up all the different speeds and look at which direction they are going do we find that we have a current. So while you're correct in that the speed of the charges matters, the issue is that there is no single speed we can associate with the current because there is no single speed, direction, or even number that we can assign to the moving charges. If our east-bound lane suddenly had an extra lane opened, then we'd have more cars moving east at the same speed and thus a "current". If, instead, the speed limit was changed so that the the average speed of the east-bound cars increased, then we'd have more cars passing by our point per minute and we'd also have a "current". Or, the speed limit could be reduced at the same time as an extra lane is open, each one canceling the other out and leaving the number of cars moving east past our point every minute unchanged.

As complicated as calculating all this is with the different speeds and directions and such, we can make it easy and lay lines across both lanes that counts the number of cars passing by and subtracts the lower number from the higher number, giving us a value and a direction for our "current". The same thing applies in a conductor. We don't worry about what each individual charge is doing, we only worry about the net flow along the axis of our wire.

Unfortunately, knowing the current doesn't give us any clue as to what the individual charges are doing. If all we have is the amperage, we can't know the distribution of speeds for the charges. There simply isn't enough information. All we know is that we have a difference in the number of charges moving in the directions parallel to the axis of the wire, and that number is our amperage. Similarly, if we lay our wires across the freeway and go back to our office, we only know there is a difference in the number of cars moving in each direction every minute. We have no idea what the speeds of those cars are, or how many lanes there may be, etc. (Of course in real life we could easily modify our setup to find out, but this is just an analogy)

 

[sophiecentaur]

The OP seems to doubt that the speed factor is as irrelevant as we are all saying. Perhaps I could ask him of a situation in which it might be relevant.

Remember, heat is conducted through metals by the same electrons that conduct Electric current. How many seconds do you need to wait for one end of a copper rod to get too hot to hold when the other is in a Bunsen flame? Now use the thermal conductivity equations (or even some simple calculations based on cooking experience) to estimate the rate of heat transfer (power) through the bottom of a saucepan. How relevant was the electron speed there?

 

[ptownbro]

Drakkith: Thanks for you the response. First, I noticed that in my text that you quoted I had a typo. Instead of saying "though noted you may consider it relevant" it should have instead read "though noted you may consider it irrelevant"). Now to address your reply.

I understand exactly what electrons are doing in a conductor. Of course they don't move in neat little lines. My analogy was just that; an analogy. And as most analogies go (like for example the ones you used), they aren't meant to be literal or meant to be an exact representation of what really happens. Instead, analogies are meant to help in or assist in the conceptualizing of a topic. So yes, of course, you are correct. Electrons don't move in neat little lines... just like electrons don't have tires, or are on roads, or don't have little people in them driving them around, etc... =) It's an analogy.

Also, and this addresses sophiecentaur's comments as well, what you have essentially explained is why a good number of people are or may not be interested in speed in the context of electrical current or Amps. Let me note again as I attempted to do in an earlier post (despite the typo I mentioned earlier): I get and acknowledged that a lot of people may find the speed the electron irrelevant in the context of current and Amps (as well as maybe in other contexts as well).

However, the point of the question was, regardless of someone caring about it, speed does have an impact (along with other factors such as density, area, and other conditions of the conductive material). And as such, I was just curious as to what the equation that has speed (and those additional factors) in it was that illustrates that. Again, regardless of someone caring about it. That's all.

Anyway, below are some references I referenced earlier that addressed my question. All are in regards to drift velocity and illustrate what I'm getting at. Though not exactly the same as speed, it's close and addressed my curiosity and the root of my question.

Thanks again for the time and effort you took in your response. Much appreciated

References:

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

Also found these videos (among many others) which walks you through the equation:

 

[loquin]

https://www.physicsforums.com/javascript:void(null);

Assume two cases - over a 1 second period, you :

1. Have a million electrons that zip by a point at (near) the speed of light, or
   
2. Have a million electrons that creep by at a .001 meter per second.

In both cases, the number of electrons that passed by the measurement point is identical, and the current is therefore identical.

I think you've been getting hung up with the assumption that faster moving objects would be 'spaced' exactly the same distance apart as slow moving objects. There is no reason to assume this.

If they WERE spaced at the same physical distance, AND they were moving much faster, you would have a great deal more of them at high velocities and thus have increased current. BUT, the current would have nothing to do with how fast they are moving, but how many pass the measurement point.

 

[ptownbro]

https://www.physicsforums.com/javascript:void(null); ... edited ... In both cases, the number of electrons that passed by the measurement point is identical, and the current is therefore identical.

Good response and interesting points. I understand why many would agree with you, but, now that I have it :), let's look at the math. (I'll use "I" for Amps instead of "A" which is how I usually personally like it)

Standard equation for electrical current or amps is:

I = Q/t.

Now, the equation for drift velocity is "v = I / (n A q)", where "I" is same as above, and "n is number of charge carriers (electrons) per volume", "A is a cross sectional area", and "q is the charge of the electron" (see the links I provided above as source. also found on wikipedia).

If you do the algebra, for drift velocity then electrical current or amps can also be expressed as:

I = v n A q

Now answer this question: Holding "n", "A", and "q" constant, what happens to "I" if you have an increase in "v"?

Hopefully you'll see that any increase in drift velocity will have a proportional increase in the current.

Make sense?

 

[Dale]

I = v n A q

This is essentially what I told you in post 12. Current density is I/A, and charge carrier density is n q.

Anyway, it seems like the question has been well answered. Time to close it.