So I got what, an 'A', 'B-'?

Sorry, someone that asks a question that they know the answer to, and then demands an answer, is trolling.

Uhm ... isn't that what we do all the time in the Homework Forum?

 

Can you really look back on this thread and conclude that those posts about 0/0 were about anything else other than algebra on the real or complex fields?

Even if we assume that folks were talking about something other than a field (I would have thought it have to be at least a ring to have a zero element, but I could be wrong), division by zero is always meaningless. I don't have your favourite text to hand, but I am always keen to learn, so please enlighten me as to where it is useful to assign a value (or values) to 0/0?

How much current is flowing in a superconducting magnet that has zero resistance and zero volts across it?

 

[studiot's questions were] meant to demonstrate (and your response did so quite ably) that we need infinity.

Taken together they can demonstrate that not only do we need infinity, but there is more than one infinity. [bold mine - dj]

As to zero/zero well isn't obvious in an electrical forum?

There are more than one infinities and mathematicians have counted them - or assigned a cardinality of infinite sets, such as the size of all natural numbers versus the size of the set of numbers between two rational numbers. The size or cardinality is called the Aleph number. This concept really struck me in college.

http://en.wikipedia.org/wiki/Aleph_number

 

Tesla, you noted that this was a question to do with voltages.

I am an applied mthematician, not a clairvoyant. So perhaps you or ernie would enlighten us all as to the origin of this question.
...

The origin was from this thread in the homework forum;
http://forum.allaboutcircuits.com/showthread.php?t=80545

Basically it was about a perfect 50v source driving a perfect short circuit.

 

Thank you, RB, for that useful information. Now I understand what is going on.

This is the maths forum and pure mathematicians work hard in the background to provide a sound, logically consistent framework for applied practitioners to use.

Now the algebra that tesla is referring to is proven for finite (or at least countable) sets. Ernie has correctly identified that different algebra is needed for transfinite sets.

This, of course is the reasoning behind limits and other statements about mathematical processes when we apply these rules.

Of course mathematics is another system and sometimes we can appeal to the physics of the real system to provide other answers or extra information that allows us to solve the system.

This is the case in my example of two nodes in a circuit at the same potential.

This leads to the question I posed "what is the current if we connect with an ideal wire?"

Mathematically this leads to a 0/0 situation.

However physically we can use the fundamental theorem that no current flows between two points at the same potential regardless of the resistance of the connection, or whether it floows a linear or other law.
This theorem underlies circuit theory.
So we can say that even with zero resistance no current flow, so in this case 0/0 is zero.

I note that others have shown an interest, eg metalmann, without really participating in the debate.

My intention was always to tease out the underlying maths if the interest is still there I will elaborate further.

 

But if no current flows through the short because the ends are at the same potential, then how much current flows out of the battery? What potential is the top terminal of the battery at? Here we violate KVL because the problem requires that the voltage at the top of the battery be both 50V and 0V simultaneously. The best we can do here is to declare that the system is non-conservative since KVL only applies to conservative electric fields. But to have a non-conservative electric field, we have to have electromagnetic induction going on, which we don't have. And even if we did, it doesn't result in a solution.

It is not sufficient to look at one portion of the circuit and find an answer that satisfy that one portion. Any answer is only valid if it is consistent with the entire circuit.

 

WBahn, my equipotential question was not directed at the 50 volt supply versus a short circuit question that prompted this thread.

Specifically I asked what is the current in an ideal conductor with zero volts applied?
If you prefer, what current would an ideal current meter read across a wheatstone bridge in perfect balance?

 

However physically we can use the fundamental theorem that no current flows between two points at the same potential regardless of the resistance of the connection, or whether it floows a linear or other law.
This theorem underlies circuit theory.
So we can say that even with zero resistance no current flow, so in this case 0/0 is zero.

Now on that point I disagree. Every real world physical super conductor has a resistance of zero. You seem to be defining these as super insulators rather than super conductors. Hint: current may be injected into a zero resistance path from an external source.

As far as the problem goes, I can get any answer from it I want depending on how I choose to model an ideal voltage source shunted by an ideal wire. The actual "best" answer I can see is "none of the above" as that is the only way to avoid making assumptions not contained in the problem and the paper model items.

 

Now on that point I disagree. Every real world physical super conductor has a resistance of zero. You seem to be defining these as super insulators rather than super conductors. Hint: current may be injected into a zero resistance path from an external source

Not sure what you mean, I didn't mention superconductors, WBahn did.

 

WBahn, my equipotential question was not directed at the 50 volt supply versus a short circuit question that prompted this thread.

Specifically I asked what is the current in an ideal conductor with zero volts applied?
If you prefer, what current would an ideal current meter read across a wheatstone bridge in perfect balance?

Ah, I thought you were tying what you were asking back to that question.

 

Not sure what you mean, I didn't mention superconductors, WBahn did.

I don't think he's refering to what I mentioned. You talked about no current flowing in a conductor that has no difference in voltage potential across it. He's giving an example where this is not the case.

There is no physical prohibition against current flowing in a conductor that has no potential difference across it. This may be the case for ohmic materials having non-zero resistance, but that is not the case here.

But you don't have to even resort to superconductors -- consider the everyday case of ideal wires in a circuit. Say you have a 12V battery connected to a 2Ω resistor. What is the voltage drop across the wire connecting a battery to a resistor? 0V. What is the resistance of the wire? 0Ω. What is the current through the wire? 0V/0Ω = 6A.

And saying that there is no such thing as an ideal wire in the real world doesn't help any because (1) superconductors DO exist, and (2) we can certainly make conductors that have arbitrarily low resistance -- are we claiming that if we make them low enough that they will stop working?

 

WBahn,

I do not know a great deal about superconductors, (post#50), so I rather listen to those who do. One thing I do know is that it is an example of my point.

We need to apply different or extra physics to resolve the situation.

And yes, your example of the wire joining any two nodes in a circuit, (post#51), again exemplifies what I am saying about additional physics. In this case we have incorporated this comes from other parts of the circuit and we have incorporated it into standard circuit theory.

 

...
However physically we can use the fundamental theorem that no current flows between two points at the same potential regardless of the resistance of the connection, or whether it floows a linear or other law.
This theorem underlies circuit theory.
So we can say that even with zero resistance no current flow, so in this case 0/0 is zero.
...

I love it! So in the real world (where infinity does not exist) 0/anything = 0, and 0*anything = 0. No big surprises (to me) there.

But I think your model is wrong. Ohms law is properly not I = E/R, for the exact reason you (and WBahn) mentioned, the master is not E. Your argument gives the mastery to E which is why it fails. This is why I discussed the "credibility" of each component within the calc earlier (re credibility of "infinity" vs zero).

E in a load is actually a SYMPTOM, and that symptom occurs when I exists through something with R. I is the master, and can still exist even if E or R (or both!) are zero (or non-zero).

The correct "master" in the calc is I. I must be known and you can then calc E from R or R from E. This is backed up in ErnieM's and WBahn's examples, where there can be a real-world I, which then determines E or R based on the circuit the real-world I is passing through.

So the correct evaluation of the load would need I. To use WBahn's example, the 12v battery and 2 ohm load cause I to be 6A. The situation in a single wire will require I to be on the right to be evaluated correctly, so is E = I*R where the answer is 6*0 so the voltage E is 0 (as anything*0 = 0).

As for the original question (5v into perfect short circuit), the interesting part is that the master I is not given, leaving us with an imperfect calc where I cannot be calculated from the two lesser and mutually incompatible items.

In pure math you don't rank credibility or mastery of the items in the equation, but in the real world you need to do this or things can go very wrong. Not everything can be equally transposed, some things in reality are "causes" and some things are "symptoms".

 

There is no 'master'.

You can indeed have a voltage without a current or a current without a voltage.

You will find the former between the terminals of a fresh disconnected battery.

You will find the latter in the drift current in a vacuum tube, edit unpowered (disconnected) except for the heater.

But yes the point is that pure maths is only a model of the physical world and like all models is not a perfect match.

 

I think that this thread has made something quite simple seem really complex. I don't think you need any complicated maths.

Consider the ohmic resistor where V = I*R.

If R is not zero, then the voltage is proportional to the current and the current may be determined by measuring the voltage and dividing by R: I = V/R - easy.

If R is zero (for a superconductor, or the idealised perfect electric conductor), then the voltage across the resistor is zero - independent of the current, and so its value contains absolutely no information about I. So when you try to determine the current from this voltage you get 0/0 which is indeterminate, meaning that it is giving you no information. So you have to determine I by some other means (e.g. by magnetic fields or making the same current flow through an non-zero resistor).

Say you use a hall sensor and determine I=3 (in some units that make WBahn happy), then you have simply found the value of I, NOT the value of 0/0.

I=3 and 0 = I*0 are not inconsistent.

Neither are the same equations written as
I=3 and I=0/0.

It is meaningless to try to deduce that this tells you something about 0/0.

As far as the original problem of a short circuit across a voltage source, this is simply one of those arrangements that violates the rules of circuit theory. A voltage source sets the voltage between two nodes to a particular value. If you connect it to another one with a different value, you violate the rules.

We do have superconductors, and we can make approximately perfect voltage sources and we can connect the two together. Neither of these though is truly perfect, at high enough current levels they both misbehave, and this is what will limit the current in practice.

However physically we can use the fundamental theorem that no current flows between two points at the same potential regardless of the resistance of the connection, or whether it floows a linear or other law.
This theorem underlies circuit theory.
So we can say that even with zero resistance no current flow, so in this case 0/0 is zero.

I think this is wrong, it is easy to set up currents in superconductors where it flows between equipotential points, after all that is why they are useful. Simply connect a superconductor to a current source and current will flow without any voltage being developed. Similarly you can induce currents, google magnetic levitation and you can see magnets levitating above superconductors, what is keeping them up is the magnetic field from the circulating currents in the superconductor. Again there will be no measurable voltage.

Now the algebra that tesla is referring to is proven for finite (or at least countable) sets. Ernie has correctly identified that different algebra is needed for transfinite sets.

The algebra of fields that I referred to applies to finite and infinite fields. The real numbers are an infinite field:
http://mathworld.wolfram.com/RealNumber.html
Division by zero in a field is undefined: http://mathworld.wolfram.com/DivisionbyZero.html

You don't need anything more complicated than that.

 

This is the case in my example of two nodes in a circuit at the same potential.

This leads to the question I posed "what is the current if we connect with an ideal wire?"

Mathematically this leads to a 0/0 situation.

However physically we can use the fundamental theorem that no current flows between two points at the same potential regardless of the resistance of the connection, or whether it floows a linear or other law.
This theorem underlies circuit theory.
So we can say that even with zero resistance no current flow, so in this case 0/0 is zero.

WBahn,

I do not know a great deal about superconductors, (post#50), so I rather listen to those who do. One thing I do know is that it is an example of my point.

We need to apply different or extra physics to resolve the situation.

And yes, your example of the wire joining any two nodes in a circuit, (post#51), again exemplifies what I am saying about additional physics. In this case we have incorporated this comes from other parts of the circuit and we have incorporated it into standard circuit theory.

So which is it. In some posts you assert that some fundamental theorem that underlies circuit theory states that no current can flow between two points if there is no voltage difference between them, and in others you say that the fact that it can has been incorporated into standard circuit theory?

Can a current flow between two points at the same potential or not?

 

I love it! So in the real world (where infinity does not exist) 0/anything = 0, and 0*anything = 0. No big surprises (to me) there.

But I think your model is wrong. Ohms law is properly not I = E/R, for the exact reason you (and WBahn) mentioned, the master is not E. Your argument gives the mastery to E which is why it fails. This is why I discussed the "credibility" of each component within the calc earlier (re credibility of "infinity" vs zero).

E in a load is actually a SYMPTOM, and that symptom occurs when I exists through something with R. I is the master, and can still exist even if E or R (or both!) are zero (or non-zero).

The correct "master" in the calc is I. I must be known and you can then calc E from R or R from E. This is backed up in ErnieM's and WBahn's examples, where there can be a real-world I, which then determines E or R based on the circuit the real-world I is passing through.

So the correct evaluation of the load would need I. To use WBahn's example, the 12v battery and 2 ohm load cause I to be 6A. The situation in a single wire will require I to be on the right to be evaluated correctly, so is E = I*R where the answer is 6*0 so the voltage E is 0 (as anything*0 = 0).

As for the original question (5v into perfect short circuit), the interesting part is that the master I is not given, leaving us with an imperfect calc where I cannot be calculated from the two lesser and mutually incompatible items.

In pure math you don't rank credibility or mastery of the items in the equation, but in the real world you need to do this or things can go very wrong. Not everything can be equally transposed, some things in reality are "causes" and some things are "symptoms".

You contradict yourself in this very post. You say that I is somehow "the master" and E is merely "the sympton", yet you use E and R to find the I and even use the phrase that the 12v battery and 2 ohm resistor "cause" I to be 6A.

By your same reasoning, the voltage across an open circuit would have to be 0V since E = IR and therefore, if I is 0, the E must be zero regardless of what R is. After all, I=0A is somehow more "credible" than R=∞. Thus 0*∞ must be 0 and no voltage can ever appear across an open circuit. A direct consequence of this, of course, is that the entire universe is an equipotential surface.

The notion that one is the cause and the other is the effect is silly. They are two parameters that have an imposed relationship based on the nature of the connection between them. Interaction with other parts of the circuit are always needed to determine either I or E (or a second relationship between them, as in the case of a diode) and then the imposed relationship can be used to find the other.

 

I love it! So in the real world (where infinity does not exist) 0/anything = 0, and 0*anything = 0. No big surprises (to me) there.

blah..blah..blah

Another classic RB post, speaking ex cathedra from his belly button.

 

There is no 'master'.

You can indeed have a voltage without a current or a current without a voltage.
...

I clearly stated "in a load".

The current I is "master" in a load, in that is can exist regardless of other factors;

I=6A,  R=0 (possible)
I=6A,  R>0 (possible)
I=6A,  E=0 (possible)
I=6A,  E>0 (possible)
I=6A,  R=0 AND E=0 (possible)
I=6A,  R>0 AND E>0 (possible)

So I can be 6A for all realistic combinations of zero and nonzero in the other two items. It has a very definite "mastery" or control of the electrical situation.

Now check that for E in a load;

E=6v,  R=0 (fail)
E=6v,  R>0 (possible)
E=6v,  I=0 (possible)
E=6v,  I>0 (possible)
E=6v,  R=0 AND I=0 (fail)
E=6v,  R>0 AND I>0 (possible)

Regarding electrical activity through a load (or some type of conductor) I is the master, which is the actual real-world stimulus that can cause E as a symptom.

Let's not forget the original source of this problem; 50v into a short circuit. The problems asks about conditions in the load. The 50v supply can only win if it can source "infinity" amps.

Another classic RB post, speaking ex cathedra from his belly button.

And if you were just a BIT smarter, you would have understood my point.

 

I am posting this in an effort to prevent this thread becoming ill tempered, instead of a discussion which pushes forward with contributions from all to the benefit of all.

All have contributed and searching questions have been asked. That is good as important points in theory and practice are being aired.

I have to plead guilty to some of this myself, and in particular thank you WBahn and RB for making me stop and think about the current in circuit connecting wires. I was too glib.

I will post a more considered answer in my next post, as the basic idea is correct, just my poor wording as usual.