Re: Zero Ohms = Mathematically Incorrect


I tried to read all of the posts but it just became too wearisome so forgive me if I repeat something already said.

First things first ..... dividing by zero is not in itself wrong! The correct terminology, by the way, is 'undefined' not 'incorrect' and not 'error'. It is undefined because there are an infinite possibility of answers. It is only an error because we had no way to tell the calculator how to pick the correct answer. Simply put, your calculator bombs out trying to do it because the people who programmed your calculator had no way to know which answer to pick.

In actuality, division by zero can usually be solved as a limit. Forgive me, but I am not going to put the time into developing the limit equation. Though it should be simple enough it's been long enough that I would have to do some real head scratching and would probably botch it.

Suppose you had a 2 volt source across a 1 ohm conductor. As you know, the resulting current would be 2 Amps. Let's say, however, you measure the voltage across one half the conductor. By measurement, you would observe 1 volt across 1/2 ohm. This also calculates out to 2 amps since it is in fact the same current as would be measured through the whole 1 ohm conductor. If this process were repeated until the conductor section being measured was of zero length then the resistance of that section of conductor would be zero, the voltage across it would be zero, and yes it would still be carrying that same 2 amps as the whole conductor.

In this case: zero volts divided by zero ohms would be 2 amps.

Another way to think of this (without limits) is that if I had the original circuit described above and we ADDED a zero ohm conductor in series (be it an infinitely short conductor or a superconductor) we have done nothing that would change the current through the conductor nor change the voltage across the conductor.

The key to understanding this is that the zero ohms is not the entire circuit resistance ... it is an infinitely small piece of a larger circuit and by having zero ohms it has no effect on the ohms law equation because the overall resistance is not changed.





John Fields wrote:

On 16 Aug 2006 19:39:29 -0700, "Radium" <glucegen1@xxxxxxxxxx>
wrote:


Hi:

If a conductor has zero resistance, then what is the amperage of a
current flowing though it?


---
Strictly speaking, current doesn't flow through it, charge does.
Current, in amperes, is defined as the quantity of charge, in
coulombs, which moves past a fixed point in that conductor in one
second.
---


Amperage = voltage/resistance

If the resistance is zero, then the amperage is something that math
cannot explain. Anything divided by zero is an "error" when calculated.


---
No, it isn't.

Consider, in the case you've brought up, if the conductor has zero
resistance, there will also be no voltage dropped across the
conductor, and we'll be left with:

E 0V
I = --- = ---- = ?
R 0R

---


How to solve this puzzle?


---
Well, let's look at what's happening here.


1
If we say: --- = 1
1

-1
and ----- = 1
-1

it begins to look like if the divisor and the dividend are equal,
the quotient will always be 1 no matter what side of zero it's on,
so it would seem that at precisely zero:

0
--- also equals 1
0

After all, how many times can you fit nothing into nothing? Just
once, is my guess.

With that in mind then, the question becomes, IMO, "How much charge
_is_ there flowing around in there?


Let's look at the case of a superconducting ring in which one
coulomb's worth of electrons has been forced into motion around the
ring and that all of those charges pass by a fixed point on that
ring in one second. The current in the ring will be one ampere
because of the number of charges moving past the reference point in
one second.

But, note that that quantity of charge flows when both the voltage
across, and the resistance through, the ring are zero.

So, since:


E 0
--- = --- = 1
R 0

The induced charge flowing in the ring will be what it is times 1.

Which is to say that if 10 coulombs or ten microcoulombs were to be
induced into the ring, 10 coulombs or ten microcoulombs of charge
would be what flowed perpetually.

Unless you tried to measure it...


Thanks,


---
Any time...


.

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