I=nAve?

how does I=nAve or v= I/ Ane make sense? i understand that they are all proportional so they are all timesed but is it that accurate because it misses out so many things that affects I such as resistance and what wire it is because the atoms in different metals are arranged differently and and one is arranged neatly then there isn't going to much collision between the electrons and the atoms so the current should increase and vice versa.
where am i tripping up?
also how do scientist come up with a formula like these.

Resistance is not involved in this, because the current is not actually dependant on the resistance. It's sort of like asking why Force is not a term in the equations of motion- it just isn't because it's not what we're talking about.

Finally, in terms of linking this to Ohm's law, the real statement of Ohm's law is simply that . I THINK that this is because when you increase the potential difference, you increase the drift velocity, thus increasing the net flow of charge.

well the the current does actually depend on the resistance I=V/R, but we are just taking about the current (the flow of electrons) in the wire and not the current thorough a component so the resistant does't come into play. you are right, i just realised that now.

however, doesn't resistivity come into play though? because different wires have different resistivity which affects the flow of electrons.



i don't understand where you are going with this. yes, i know increasing the p.d. increases the mean drift velocity and thus this increases the net flow of electrons, but since this is the case then why isn't the potential difference V, included in the equation.

thanks for the answer anyway :}

Here's an attempt at an analogy:

If you want to measure something's velocity you could try two things:

Measure displacement in a given time and use v=s/t
Measure force, mass and time it took to be accelerated and work out velocity using v=u+(F/m)t

In the case of current we can do the same thing:

It's the rate of flow of charge, so literally we can use the equation I=nAvq to add up the flow of charge contributed by each charge carrier.

OR

We can use Ohm's law I=V/R, which computes the same answer, but is looking at the situation in a different way.

You don't need to know resistance or voltage if using I=nAvq in the same way that you don't need Newton's 2nd law when you do kinematics. Yes in reality the forces are why there is motion, but we can describe motion perfectly well without ever introducing the concept of force.

i had to think about it for a second but ok i kind of get it what you are trying to say.
still,
i understand how you derive I = V/R because thats its definition.
but how is I=nAve derived, and how do we know its true apart from the fact that its written in the textbook. do you sub in different equations or do we guess an equation randomly, experiment then change the equation until you get it right or something else. do you know the thinking/ the concept / math behind the equation I = nAvq?

thanks!

Proof here - it's not about defining resistance or applying a pd.
It's just like asking how many cars pass a point on a road per second.
It depends on how wide the road is, how closely the cars are packed on the road, and how fast they are travelling. Substitute "number of cars per second" for "amount of charge per second" and you get the idea.

oh wow!this book makes the perfectest sense and was exactly what i was ****ing looking for.
can i ask you what textbook it is, because it is brilliant.
reps for you son!

It's an early (1st?) edition old A-Level text book by Tom Duncan from1982.
It's this one.
http://www.amazon.co.uk/Physics-Textbook-Advanced-Level-Students/dp/0719543363

this page looks all good and that because it explains things in a lot of detail and probably is better than my current textbook as well.
but this is 2014 now and the spec might've changed significantly since then. do you think its still useful for contemporary specification? i'm on OCR btw.
thanks.

also, if you took a picture of the content page, that would be very helpful.

Physics hasn't changed since 1982, but specifications and teaching strategies have.
The proof of the formula is exactly the same now as it was then. I have no idea if your spec. requires you to be able to prove it. (Unlikely) However, if it says you need to use and apply the formula (given on the formula sheet) then knowing the derivation is going to help you understand it.
When looking through older books you have to be aware that the book wasn't written for any particular exam board. It was just PHYSICS presented at a certain level. When you studied A-Level in those days you could have used any one of a number of different "A Level" text books. Your teacher would have picked the one best suited to the board he/she was following, and told you which topics in that book were not in the syllabus. You may have needed a second book if the 1st didn't cover everything. In 1982 some boards expected you to be able to derive the formula.
The emphasis was more on teaching physics as a subject than teaching how to pass an exam.

What does the n represent?