Infinite Resistance
- Thread starter physis
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Re: Infinite Resistance
why didn't you say so! That's not Ohm's Law. It's hm's Law. (but even then, R is NOT equal to 1/zero)
oh, you mean you want to show the relationship between voltage, current and resistance, but without current?
why didn't you say so! That's not Ohm's Law. It's hm's Law. (but even then, R is NOT equal to 1/zero)
you've seen the proof. you just don't realize it yet.
physis
Senior Member
Re: Infinite Resistance
So you're saying if a field pushes on electrons but there's nowhere for the electrons to move that there is then no force on the electrons?
Edit: the closest to that I'm finding is that you may not be able to prevent the electrons from moving.
[ December 07, 2004, 02:04 AM: Message edited by: physis ]
So you're saying if a field pushes on electrons but there's nowhere for the electrons to move that there is then no force on the electrons?
Edit: the closest to that I'm finding is that you may not be able to prevent the electrons from moving.
[ December 07, 2004, 02:04 AM: Message edited by: physis ]
charlie
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Re: Infinite Resistance
Infinity . . . HMMM. If I have two parallel lines that go to infinity in one direction and one of them goes to infinity in the other direction but the first one is a ray (it starts where I am standing). Which line is longer, the line or ray?
Infinity . . . HMMM. If I have two parallel lines that go to infinity in one direction and one of them goes to infinity in the other direction but the first one is a ray (it starts where I am standing). Which line is longer, the line or ray?
Re: Infinite Resistance
This reminds me of the mathmatical "proof" that given A=1 and B=2, a series of equations proves that A=B. The flaw is a division by 0 in the middle of the proof.
If R= infinity (and this can be both a mathmatical and physical reality because current comes in discrete lumps - get the R high enough and no current will flow) then the correct equation for current is:
I = V/R which correctly gives 0 for I.
Changing this equation to I*R=V involves multiplying each side by 0, which no longer gives a valid formula.
Steve
This reminds me of the mathmatical "proof" that given A=1 and B=2, a series of equations proves that A=B. The flaw is a division by 0 in the middle of the proof.
If R= infinity (and this can be both a mathmatical and physical reality because current comes in discrete lumps - get the R high enough and no current will flow) then the correct equation for current is:
I = V/R which correctly gives 0 for I.
Changing this equation to I*R=V involves multiplying each side by 0, which no longer gives a valid formula.
Steve
charlie
Senior Member
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Re: Infinite Resistance
A? - A? = A? - A?
Factored two ways
A(A - A) = (A - A)(A + A)
Cancel the phrase (A - A) on both sides of the equation gives
A = (A + A)
Substituting 1 for A and completing the problem gives you 1 = 2
A? - A? = A? - A?
Factored two ways
A(A - A) = (A - A)(A + A)
Cancel the phrase (A - A) on both sides of the equation gives
A = (A + A)
Substituting 1 for A and completing the problem gives you 1 = 2
Re: Infinite Resistance
(A - A) = (A - A)(A + A)
Charlie divided it by 0 (A-A) to get
A = (A+A)
which is not true. Division by 0 is undefined.
No, this is trueOriginally posted by physis:
What you did was prove this Charlie
A(A - A) ≠ (A - A)(A + A)
My broken watch is right twice a day but as hard as it tries it can'tmake it always be 3:22.
(A - A) = (A - A)(A + A)
Charlie divided it by 0 (A-A) to get
A = (A+A)
which is not true. Division by 0 is undefined.
al hildenbrand
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- Electrical Contractor, Electrical Consultant, Electrical Engineer
Re: Infinite Resistance
Gentle Folks,
Let me interject a note of great appreciation for the whimsy and humor of this thread. I popped in for a quick scan, stumbled onto this thread, and enjoyed some of the best humor of my week.
The topics of infinities and zero is a source of great questioning to get to "where no one has gone before. . ."
Great Stuff.
Gotta go.
Gentle Folks,
Let me interject a note of great appreciation for the whimsy and humor of this thread.
I popped in for a quick scan, stumbled onto this thread, and enjoyed some of the best humor of my week.The topics of infinities and zero is a source of great questioning to get to "where no one has gone before. . ."
Great Stuff.
Gotta go.
al hildenbrand
Senior Member
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- Minnesota
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- Electrical Contractor, Electrical Consultant, Electrical Engineer
Re: Infinite Resistance
Priorities, priorities. . .It's off to meat space I go
Priorities, priorities. . .It's off to meat space I go
Re: Infinite Resistance
One of the rules is you cannot divide by zero. You CAN divide by almost-zero. But you CANNOT divide by zero. So, as you infinitely shrink your denominator, all is well. But when you get tired of all that shrinking, and make the giant leap from an infinitesimally small denominator to a zero denominator, the bubble bursts. All bets are off. You cheated. The math is no longer valid. Case closed! And you can refuse all you like, but the game is still over.
So, you can disgard your infinity=1/zero thinking and live happilly ever after, or you can remain attached to it and live in frustration for all eternity. It's your choice.
As for the practical application of all of this...rest assured that Ohm's Law holds true, at least until real (i.e non-ideal) obstacles enter into play. For example, for a constant voltage, as resistance moves toward zero, current moves toward infinity. At "short circuit" (which is really not zero resistance), current will move to it's maximum as limited by other non-ideal factors (likewise, not infinity). You cannot, for instance, have a *real* current source capable of supplying infinite amounts of current. Nor a real op-amp that will provide gain beyond the power supply rails, regardless of the fact that the amp's mathematical equation does NOT factor-in supply voltages.
So where do you go from here? Past arithmetic, through algebra, and onto calculus, which cuts through infinity like a hot knife through butter.
It's your call, but I must warn you...
1/zero resistance is futile!
did I say that? What I did say is if you don't follow the rules of math, you can't expect the math to work.
One of the rules is you cannot divide by zero. You CAN divide by almost-zero. But you CANNOT divide by zero. So, as you infinitely shrink your denominator, all is well. But when you get tired of all that shrinking, and make the giant leap from an infinitesimally small denominator to a zero denominator, the bubble bursts. All bets are off. You cheated. The math is no longer valid. Case closed! And you can refuse all you like, but the game is still over.
So, you can disgard your infinity=1/zero thinking and live happilly ever after, or you can remain attached to it and live in frustration for all eternity. It's your choice.
As for the practical application of all of this...rest assured that Ohm's Law holds true, at least until real (i.e non-ideal) obstacles enter into play. For example, for a constant voltage, as resistance moves toward zero, current moves toward infinity. At "short circuit" (which is really not zero resistance), current will move to it's maximum as limited by other non-ideal factors (likewise, not infinity). You cannot, for instance, have a *real* current source capable of supplying infinite amounts of current. Nor a real op-amp that will provide gain beyond the power supply rails, regardless of the fact that the amp's mathematical equation does NOT factor-in supply voltages.
So where do you go from here? Past arithmetic, through algebra, and onto calculus, which cuts through infinity like a hot knife through butter.
It's your call, but I must warn you...
1/zero resistance is futile!
Re: Infinite Resistance
Physis:
Resistance has an inverse called conductance. I think it usually uses the symbol G. So G = 1/R. So if R= infinity, G=0. More correctly, we should start with G. That gives us R=1/G. So it is actually R that is undefined for G=0. In other words, R= infinity is more of a concept implying G=0, than a real number for R.
Now ohms law becomes I=V*G. And I=0 for G = 0. In this form all the inifinites are gone, and the equation makes sense. (The equation has to make sense. Like someone else said, this is really the equaiton for an open switch).
In order to get any infinities out of this equation, you would have to divide both sides by G, and G=0. So the resulting equation with the infinities may not be valid.
Steve
Physis:
Resistance has an inverse called conductance. I think it usually uses the symbol G. So G = 1/R. So if R= infinity, G=0. More correctly, we should start with G. That gives us R=1/G. So it is actually R that is undefined for G=0. In other words, R= infinity is more of a concept implying G=0, than a real number for R.
Now ohms law becomes I=V*G. And I=0 for G = 0. In this form all the inifinites are gone, and the equation makes sense. (The equation has to make sense. Like someone else said, this is really the equaiton for an open switch).
In order to get any infinities out of this equation, you would have to divide both sides by G, and G=0. So the resulting equation with the infinities may not be valid.
Steve
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- Retired Electrical Engineer
Re: Infinite Resistance
What?s with you guys? I step aside for half a day, and the world falls down around me.
What?s with you guys? I step aside for half a day, and the world falls down around me.
Re: Infinite Resistance
you could similarly argue that you don't even have a circuit.
but that would be infinately less fun, so lets just think of the open circuit as being closed by a humungous resistance...say maybe 1000 feet of dry air?
someone get Mr. Ohm, quick! (or Mr. Tesla & Mr. Franklin?)
exactly! Like I said earlier, it's not Ohm's Law, it's hm's Law (something's missing)
you could similarly argue that you don't even have a circuit.
but that would be infinately less fun, so lets just think of the open circuit as being closed by a humungous resistance...say maybe 1000 feet of dry air?
someone get Mr. Ohm, quick! (or Mr. Tesla & Mr. Franklin?)
- Location
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- Retired Electrical Engineer
Re: Infinite Resistance
It is not a true statement.
I will even set aside the ?proper? mathematical response, that the concept is not defined. Let us instead start with a big number, and let it start getting much bigger. Let us also start with a small number (less than one, but still positive), and let is start getting smaller. If we multiply the two at any given point, we will have a number times a number, and the result will be a number.
But if we were to let the big number increase without bound, and let the small number decrease without bound (other than that it is not allowed to reach exactly zero), what will happed to the product of the two? Chose from the following four possible answers?
(A) Will the product keep getting bigger, or
(B) Will it approach zero, or
(C) Will it approach some other value, or
(D) Will it appear to vary randomly?
The answer that I quote at the top of this post is that the correct answer is (B). Not true. The correct answer is ?any of the above.? The answer will depend on the way we chose to make the first number increase, and the way we chose to make the second number decrease.
The mathematics of infinity and of zero is fascinating, but it is not simple. More importantly, however, it is not self-evident, and our instincts as to the result will often fail us.
In this thread, I have seen several inaccurate statements, regarding the rules of mathematics. Not to pick on physis, but this one is a good example for me to discuss.
It is not a true statement.
I will even set aside the ?proper? mathematical response, that the concept is not defined. Let us instead start with a big number, and let it start getting much bigger. Let us also start with a small number (less than one, but still positive), and let is start getting smaller. If we multiply the two at any given point, we will have a number times a number, and the result will be a number.
But if we were to let the big number increase without bound, and let the small number decrease without bound (other than that it is not allowed to reach exactly zero), what will happed to the product of the two? Chose from the following four possible answers?
(A) Will the product keep getting bigger, or
(B) Will it approach zero, or
(C) Will it approach some other value, or
(D) Will it appear to vary randomly?
The answer that I quote at the top of this post is that the correct answer is (B). Not true. The correct answer is ?any of the above.? The answer will depend on the way we chose to make the first number increase, and the way we chose to make the second number decrease.
The mathematics of infinity and of zero is fascinating, but it is not simple. More importantly, however, it is not self-evident, and our instincts as to the result will often fail us.
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