Zero Ohms = Mathematically Incorrect

No, the lack of Ohm's Law.

As I think I mentioned, Ohm's Law isn't a physical law. So E/0 is no different from 99/0; confusing perhaps, but not a physical singularity.

"R" is just a definition of E/I in some particular quasi-steady-state situation. As a definition, and not a physical reality, using it as a denominator creates no real-world difficulties.

I'm always an electrical engineer, and I don't let definitions get in my way. Real circuits never create mathematical singularities or physical absurdities.

John

On Thu, 17 Aug 2006 21:47:59 -0700, in message , John Larkin scribed:

No, you didn't mention that. You said that "Ohm's Law is not a law at all," and failed to explain yourself.

I am not confused by the concept of division by zero. I am confused by your style of writing, that seems to consist of stating claims and offering no examples or evidence. For instance:

"The simplest answer is that Ohm's Law is not a law at all. It's never true, and it's often wildly off."

I'd like some evidence that you know what Ohm's Law is, and some proof that it is never true, and some examples of when it is wildly off. Simple.

That's a statement that must be taken in context. "R" is also a very real phenomenon of electrical circuits, and your statement may be re-arranged to include all the iterations of the E=I*R representative equation. What do you mean by "quasi" steady-state? How do I plug "quasi" terms into a steady-state equation?

It presents no real-world difficulties, as long as the practitioner understands that the number being substituted for is a minute quantity. Thus using the term "zero" simplifies equations and is not meant as a precise representation of physical reality. (Bringing superconductivity into the matter is, IMO, a separate issue, because doing so introduces a basic shift in the underlying physics.)

I feel sorry for your cow orkers. It must be very difficult to work with someone who is so loose with standards and practices for which definitions exist. Are you familiar with ANSI and IEEE? Heaven forbid you ever get acquainted with MIL-STD! Your career path would be littered with piles and piles of discarded definitions. Come to think of it, I've know c programmers who, similarly, don't let definitions get in their way. Their products are predictably poor in quality and impossible to maintain.

So, is that akin to saying "there is no such thing as zero resistance in a conductor," in an extensively more complicated way?

On Thu, 17 Aug 2006 16:33:58 GMT, in message , "Bob Myers" scribed:

I applaud the simplicity of your eloquence.

How wonder how he can speak at all if he doesn't let any definitions get in the way?

A zero ohm conductor will have zero volts drops on it, amperage flows thru it is defined by other elements in the closed circuit.

Usually when you see a number devide by zero, one of these things might happen:

1) A mislead thinking 2) A careless mistake 3) Typos 4) Some one gave you a wrong direction 5) Beyond of this scope

Cheers

--- 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.

---

--- 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

---

--- 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...

--- Any time...

-- John Fields Professional Circuit Designer

WOW!

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:

Short circuit current would be limited by the power source internal resistance..wouldn't it???

No, it is wrong and the correct answer is error, not undefined.

Sure. I don't follow rules, I make rules.

Could be. I don't program in C; it's an abomination.

Oh, lighten up. Rigidity is no fun.

Definitions are merely things people agree to agree about. The R in "ohm's law" is a definition of "resistance" but ohm's law isn't a physical law because it isn't ever exactly followed, and sometimes it's not even closely followed. So we use it when it makes sense, namely when it produces usably close approximations and has some predictive value. But it ain't a law, and worrying about I=E/R going infinite is a waste of time.

I believe I noted in a couple of previous posts that some superconductors demonstrate unmeasurable resistance, specifically no measurable voltage drop or power loss with a finite circulating current. I had to leave my wallet on a table this morning so I could work right up against a superconductive magnet in a 140 GHz EPR system. The magnet was "charged" many months ago.

John

"Error" is what a $4 calculator will tell you that 0/0 is. "Indeterminate" is what an engineer will call it. "Undefined" is what a mathematician might say.

The reason is that you can spell ErrOr on a 8-digit, 7-segment display, but you can't spell UNDEFINED or INDETERMINATE.

John

0/0 is a "Undefined Result" according to my HP 28S calculator. Anything divided by zero is infinite, and 0 divided by anythiing is 0, so 0/0 must be something between 0 and infinity. Make it whatever you want.

-Bill

more precisely, can be _anything_ in between -infinity and infinity inclusive.

Mark

--- ISTM that it can only be 1.

That is, for any fraction where the numerator and the denominator are identical, the quotient is always 1, so if:

a --- = b = 1 a

and 'a' slides through zero, why should the value of 'b' be different from what it was infinitessimally before 'a' became zero?

-- John Fields Professional Circuit Designer

Well, don't do that! sin(x)/x, sin(2x)/x, sin(x)/x^2, and sin(x)/sqrt(x) are all 0/0 when x=0 but have different, and clearly defined, limits. Even x^2/x is 0/0 when x=0, but has a limit when you cancel a set of x's from the numerator and denominator. But the calculator doesn't know how you're getting to 0/0, that depends on what you're trying to model, so that's for the user to figure out.

Then why do they advertise Viagra?

--
To enhance turgidity.

Which is pretty much what I said.... as far as you go. Using limits, you can often, but not always, rewrite EQUATIONS that result in division by zero to indicate what the value for that EQUATION would be when the denominator approaches or (I think) passes through zero. Limits are taught as part of Calculus.

While, for instance, the statement "zero divided by zero" could have an infinite number of values it most likely has a finite number of correct values for the equation that caused the zero divided by zero condition.

You would use limits to find the appropriate value.

Unfortunately, too many of our high school teachers left of in teaching their students that it is carte blanche "incorrect".

BTW ... Personally, I'd have figured the other way around between an engineer and a mathematician. But then again, I'm an engineer with a minor in math.

Greg

Mark Fortune wrote: