A brain teaser

[BrownOut]

Brown, it is not like this hasn't been discussed or given so much thought. It is a very old problem. It has been beaten to death. The answer is just like I explained. It is like asking what is the largest number. You can't really answer that because you can always add 1 to it and it will just grow larger. You see my point? Here you should stop thinking math, and start thinking logic.

As for the circuit, you can go and try it. If you have an Ammeter, you can hook it in parallel with a 1.5v battery....it will just be like connecting the ammeter in series with a resistance of zero. Better yet, if you have a scope, you can do the same and make graphs for the voltage and current vs time. Do it and tell us what happens ^_^ ........The result can be predicted.

Too bad the ammeter has an internal resistance though.

I could not disagree more. The concepts are very important and have wide ranging applications. The discussion started as a theoritical electrical question, and was discussed from the standpoint of what is logical. But the math, while abstract, proves the point and is a foundation for thinking about these kinds of problems. And as someone has pointed out, there exists technology wherein the resistance becomes almost nothing, and these techniques are helpful for undertanding the technology.

You can't use an ammeter to measure the system, because per the OP, the system was assumed to be ideal. You ony have logic and the underlying math to count on.

As for being "beaten to death" this in nothing compared to other topics. I have the patience to go over this as much as needed so we understand it. Those who don't have the patience don't have to read.

 

[BrownOut]

Haha I love it!

So what is zero times infinity? Half way?

Hi MrRB, I was trying to show an apparent quandry. Zero times infinity can sometimes be solved, sometimes not. That's why I find this subject interesting. It also forced me to think about a rarely used math technique I studied about 30 years ago. I think it's good to dust off old learning from time to time.

 

[MrAl]

Hello guys,


We can't mix theory and reality by stating that I becomes very large while R becomes very small, and that when R equals zero V must be zero, because that's not the way it works. Either we choose to use pure theory or we choose to allow real life external quantities (like source series resistance) to enter the picture. Since back quite a few posts the OP stated that he knew that if you allow source resistance the problem becomes much easier, so he didnt want to do that. He wanted to look at the V^2/R and the I^2*R without any real life additions like that. This means he wants to stick to pure theory, so we use pure theory and dont worry about anything else.

What this means is that when we consider V^2/R that V is a theoretical voltage source, and a theoretical source (unlike a real life source) is capable of putting out an infinite current. Yes, that's an infinite current from a true theoretical voltage source. This should make the problem of V^2/R much simpler, because V is constant and only R is allowed to vary. Thus, when R goes to zero the power goes to infinity also, and it's quite obvious.

Now looking at I^2*R, it appears to be a different story, but it's not. The reason is that again we're working with pure theory and I and R are not independent, but I depends on R and V. This enables us to use the substitution V/R for I and thus we again come up with the same equation V^2/R and that's infinite power.
As a second more intuitive approach, we can consider the change in both variables. Since they are not independent, and they have a specific relationship, we can note that as R is halved, I is doubled, and this leads to a power increase of two times.
We can write this as a new equation:
P=(x*I)^2*(R/x)

and we will find the limit of P as x approaches infinity. First though, we can simplify this to:
x*I^2*R

where now I and R are constants, and take the limit as x approaches infinity. Obviously this also comes out to infinity.

So no matter how you look at it, with a theoretical voltage source and zero resistance we get an infinite current and because the voltage is constant we get an infinite power.

 

[BrownOut]

Be carful here,

This should make the problem of V^2/R much simpler, because V is constant and only R is allowed to vary. Thus, when R goes to zero the power goes to infinity also, and it's quite obvious.

Before making that statement, you need to consider who's law will hold at R=0. First you have an applied voltage which doesn't change. But you also have Ohm's law V=I*R, which gives the much discussed ∞*0. So, in order to use the simpler version, you are still up against a theoritical limit. That's why I calculated V at infinite current before using it in my calculations.

One might logically conclude that in this case, the result ∞*0 = 0 violates the applied voltage requirement. However, that would assume that the voltage law is valid as the discontinuity is approched. ( infinity ) I was not comfortable with that assumption until I proved it.

 

[MrAl]

Hello again,


Not really. Once we accept that we are using a theoretical voltage source we accept that it is possible to get an infinite current, and since the theo voltage source doesnt 'sag' in value, we have a constant times infinity, which is infinity.

It's not much different with V=I*R because I and R are NOT independent variables. They are functionally related because V is the aforementioned perfect voltage source. That's what makes it so simple.

Im not sure what you mean when you said you "calculated V at infinite current". There's nothing to calculate. It's a constant. He implied this when he declared that we cant use a series resistance with the voltage source. We either use a series resistance or we assume a perfect source...we cant have both.
Take a step back and see how simple this really is. There's no big paradox here. This is just too straightforward to make this big of a deal about. It's also written in good textbooks that a perfect voltage source can give rise to infinite current, with the added comments that it's not (of course) considered possible in real life, just in theory.

I dont want to start an argument about this if you still dont agree so if you would like to have the last word you're of course welcome to...

 

[BrownOut]

I wasn't the only one initially thrown by the fact that there is a zero in the equation V=I*R. For the sake of my sanity and other's I took a limit as R-> to verify consistancy with the applied voltage. The limit of the power equation agrees with the simplified method. Ofter if there are two different way to get a result, I'll try both and see if they agree. In this case, they do.

 

[magnatro]

considering the internal resistance of the cell, the resistance cannot be zero.

 

[carbonzit]

L'Hôpital's Rule

You know, Brownout, if you're going to harp on L'Hôpital's rule, you ought to get it right (note spelling, including circumflex "O").

Here's what my calculus textbook (Edwards and Penney) has to say about it:

Sometimes the limit of an indeterminate form can be found by a special algebraic manipulation or construction, as in our earlier computations of derivatives. Often, however, it is more convenient to apply a rule that appeared in the first calculus textbook ever published, in 1696, by the Marquis de l'Hôpital. L'Hôpital was a French nobleman who had hired the Swiss mathematician John Bernoulli as his calculus tutor, and "L'Hôpital's rule" is actually due to Bernoulli.

 

[BrownOut]

You know, Brownout, if you're going to harp on L'Hôpital's rule, you ought to get it right (note spelling, including circumflex "O").

First of all, carbonzit, I don't harp about anything. I've shown how it can be used to find limits and solve equations that are otherwise undefined, which is of more use than anything you ever posted. Secondly, I'm not the only one who has typos on here. I've always found those who are too uninformed to make any useful posts or ever have anything helpful to add to a discussion always cry about typos. I've never see you contribute anything useful to the discussions. Informed people have something to say. The uninformed have so say someting. That's you all the way my friend ( the latter ).

And screw your circumflex. I have no time for that silliness.

 

[carbonzit]

Whatever.

I guess it really doesn't matter if one writes "your" or "you're", "discreet" or "discrete", "lose" or "loose", "base" or "bass".

Cuz, like, man, you know what I mean, right?

Screw spelling. Screw punctuation. Screw grammar.

Screw everything except, apparently, your insistence on carrying on a theological discussion about how many electrons can dance on the head of a pin.

 

[vlad777]

Infinity times zero is any (undefined) finite number.
So pick one, that is closest to your likeing.

 

[BrownOut]

Screw everything except, apparently, your insistence on carrying on a theological discussion about how many electrons can dance on the head of a pin.

And screw vocabulary. Maybe you should look up the meaning of words before trying to use them.

theological

1 : of or realting to theology

theology

1: the study of a religious faith...

You don't have a clue about what the discussion is about. You're contributions are absolutely worthless. You're only good for finding a typo every once in awhile, and that evidently makes you feel much smarter than you are.

 

[carbonzit]

I should have written "electro-theological".

 

[BrownOut]

I should have written "electro-theological".

You should get a clue about the details of the discussion so you can make useful contributions.

 

[vlad777]

If you are talking about superconductor and somekind of ideal (voltage?? or Electric field) source, than it will be just transfering
energy from itself to superconductor and this energy will reach infinity only after infinite amount of time. No power.
P=0, I only gets to be infinite after eternity.

 

[Ratchit]

MrAl,

Take a step back and see how simple this really is. There's no big paradox here. This is just too straightforward to make this big of a deal about. It's also written in good textbooks that a perfect voltage source can give rise to infinite current, with the added comments that it's not (of course) considered possible in real life, just in theory.

I agree with you completely, MrAl. This discussion should be theoretical, not theological. The problem is too trivial to keep hammering and yammering about. Just a straight forward application of mathematical principles and understanding is all that is needed to quickly resolve it.

Ratch

 

[BrownOut]

hammering and yammering

We actually resolved this a couple days ago. The thread has been perpetuatled by those whining and crying because we had this discussion.

 

[Mr RB]

Hi MrRB, I was trying to show an apparent quandry. Zero times infinity can sometimes be solved, sometimes not. That's why I find this subject interesting.
...

Me too! Don't sweat it I was just messing with you.

Unfortunately these new forum smiley face icons are not very easy to see, I much preferred the old {wink} icon which was blue and you could actually see the eyes.