Infinite Resistance

Status
Not open for further replies.

physis

Senior Member
I don't know if anybody's particularly interested in this, but.

Another thread got me thinking about if V/R=0[zero]. When V is not zero.

In other words no current flows from a voltage source with nothing connected across it.

So to find the value of R, R=V/0[zero].

So the divide by zero illegal function comes up. I've always prefered to think division by zero to equal infinity. Which would satisfy this equation (as it would many others). 1/(10 to the -23) is a big number.

The smaller the divisor the larger the quotient. Until, reasonably, you reach X/0=infinity.

The only problem I see is that infinity times zero is not a rational argument. But if that's the case why not put the illegal function there instead of at divide by zero?

I know you're at least raising an eyebrow Charlie B. :)
 

rattus

Senior Member
Re: Infinite Resistance

physis,

I think the mathematicians say that division by zero is undefined, that is, it is meaningless. However, there is also the matter of a ratio approaching a limit of infinity as the divisor approaches zero. Having said that, I think most wire twisters would say, "Who cares?", or "What does the code say?"

The upshot of this is that you cannot compute the IR drop across an infinite resistance.

[ December 06, 2004, 05:41 PM: Message edited by: rattus ]
 

physis

Senior Member
Re: Infinite Resistance

Well rattus, hence line one.

I've tried to find an answer that I would be happy with more than a few times but have never been satisfied.

I think it's that the answer is always something like, the rules of convention dictate, blah blah. And it's been defined. Honestly I don't even remember the explainations anymore.

It just seems the closer the divsor to zero the closer the quotient to infinity.

The problem is that infinity is a concept that can't be given a rational value and therefore isn't math. But at the same time there's a similar situation with pi. It's an irrational number but we know it's real (not as an integer) because we understand the relationship it represents.

Edit: Divide by zero and infinity, to me, seem to be a similar relationship.

[ December 06, 2004, 06:00 PM: Message edited by: physis ]
 

physis

Senior Member
Re: Infinite Resistance

And how do we recocile no connection across a voltage source if we can't have infinite resitance?
 

rattus

Senior Member
Re: Infinite Resistance

Physis, how close can you get to infinity? I say close enough. And for practical purposes, there is such a thing as an infinite resistance. But how would you color code such a resistor?
 

physis

Senior Member
Re: Infinite Resistance

We use terms like infinite gain to describe an ideal OP amp and infinite impedence to describe radio circuits. It's almost common place in electrical engineering.

how would you color code such a resistor?
That's just it, it isn't a number. But I think you can say it's a value. So put that in your atom smasher. :)

Edit: I don't think you can even color code .0001Ω

[ December 07, 2004, 12:14 PM: Message edited by: physis ]
 

charlie

Senior Member
Location
Indianapolis
Re: Infinite Resistance

You know, this reminds me of the attempt to reach the speed of light in a collider. The faster they accelerate ions, the more energy is required to get them going faster. The mass continues to increase towards infinity and the amount of energy goes towards infinity as more speed is obtained. It is impossible to get to the speed of light because the faster an object goes, the more mass it gains and the more energy it takes to accelerate it. The bottom line is that sub-light is the only possibility and warp one or greater ain't a gonna happen. Sorry, impulse power only to visit the stars. :D
 

physis

Senior Member
Re: Infinite Resistance

The mass increases to infinity at C and you can't do it because it takes infinite energy to accelerate an infinite mass. Some genious must have assumed we don't have infinite energy.

You can acheive I=zero with V=zero/R :p
 

rattus

Senior Member
Re: Infinite Resistance

Infinity, for us practical types, is a number so large that we do not care anymore.
 

charlie

Senior Member
Location
Indianapolis
Re: Infinite Resistance

Sam, before you go to bed tonight, have a nice warm glass of milk. Think sweet thoughts and try not to have nightmares again tonight. :D
 

rattus

Senior Member
Re: Infinite Resistance

Hurk, even a resistor of infinite value has a voltage rating. You could wear a suit of chain mail tied to a code compliant ground rod to protect yourself from Thor and his thunderbolts.

Of course, the path followed by a thunderbolt has a rather low resistance. So just think big, like infinity squared or "e" to the infinite power!
 

physis

Senior Member
Re: Infinite Resistance

Rattus, I regretibly don't have them anymore and it's painful for me. :( And I don't recall indeterminate forms.

Good texts cost an actual fortune anymore.

by Charlie:

this reminds me of the attempt to reach the speed of light in a collider.
When I firt read this Charlie I thought you said colinder. The images I went through trying to figure that out. :D
 

rob123

Member
Re: Infinite Resistance

from post #1:

"Another thread got me thinking about if V/R=0[zero]. When V is not zero."

V/R=0[zero] has only one solution, V=0. For R=zero, the expression is undefined. (no arguments allowed :eek: )

"In other words no current flows from a voltage source with nothing connected across it."

yes, that's when R=infinity.

"So to find the value of R, R=V/0[zero]."

as stated, this expression is undefined, so stop searching for the solution. What is defined, however, is what happens as you approach infinity or zero (two different things entirely). For instance, for a fixed voltage, as resistance approaches infinity, current approaches zero. Similarly, if voltage is constant, as resistance approaches zero, current goes to infinity. So, all the laws hold for all cases, except the "undefined" cases.

"So the divide by zero illegal function comes up."

yes, because you're playing the game but breaking the rules.

"I've always prefered to think division by zero to equal infinity. Which would satisfy this equation (as it would many others). 1/(10 to the -23) is a big number."

there's your mistake! You should think of division by zero as undefined (illegal). Your example, stated in mathematically legal terms, is "the limit of 1/x as x approaches zero is infinity". But as we all agree, 1/zero is undefined.

"The smaller the divisor the larger the quotient. Until, reasonably, you reach X/0=infinity."

yes, but no. :roll:

"The only problem I see is that infinity times zero is not a rational argument. But if that's the case why not put the illegal function there instead of at divide by zero?"

Anything times zero is zero. zero/2 is rational.

from post #2:

"The upshot of this is that you cannot compute the IR drop across an infinite resistance."

Sure you can. For any positive current, as resistance goes to infinity, voltage goes to infinity (and possibly faster than the resistance). It doesn't get tricky until things start moving towards negative infinity.

from post #3:

"I've tried to find an answer that I would be happy with more than a few times but have never been satisfied."

you're very hard to satisfy, aren't you?

"The problem is that infinity is a concept that can't be given a rational value and therefore isn't math."

No, it IS math. It's just not arithmetic.

and from #7:

"The bottom line is that sub-light is the only possibility and warp one or greater ain't a gonna happen."

didn't you mean to say "warp one or greater ain't a gonna happen for objects with mass"?

:eek:
 

hurk27

Senior Member
Re: Infinite Resistance

didn't you mean to say "warp one or greater ain't a gonna happen for objects with mass"?
H'mmmmmm
So if we don't have mass, speed = infinity

Cool I got to have one of those. :p
f16.gif
 

rob123

Member
Re: Infinite Resistance

Cool I got to have one of those.
O.K., if you insist.

But we'll have to perform a bit of a transform on you first.

Sort of an Aiken's diet, taken to infinity.

Shouldn't hurt...much.


:cool:
 

physis

Senior Member
Re: Infinite Resistance

by Rob123:

there's your mistake! You should think of division by zero as undefined (illegal). Your example, stated in mathematically legal terms, is "the limit of 1/x as x approaches zero is infinity". But as we all agree, 1/zero is undefined.
That's the argument that I'm not satisfied with. I think I've been talked out of this before but it definately wasn't that way.

If I can prove you can have voltage with no current Ohm's law can only be satisfied with infinite resistance. Or the inverse of zero resistance or R=1/zero.

I'm not sure weather zero or infinity wins if you multiply them.

2 times infinity is infinity so is .5 times infinity. I don't think they can comprimise.

I'm looking for the proof! :)
 
Status
Not open for further replies.
Top