We have had several questions lately about what happens if we connect a perfect short across an ideal voltage source.

This has been likened to the ancient "irresistible force meets immovable object" saw.

The difference is that Newton's Laws in mechanics provides a resolution to this issue in mechanics.

There are, however, no equivalent Laws in electrics so we must look elsewhere for resolution.

So consider these two questions side by side.

In mechanics acceleration is proportional to applied force, the constant of proportionality being mass.

In electrics current is proportional to applied electromotive force, the constant of proportionality being resistance.


A 9N force is applied to a body with a result of zero acceleration. Determine the mass. Suggest a realisation of this mechanism.

A 9 volt emf is applied to a circuit but that zero current flows. Determine the resistance. Suggest a realisation of this circuit.

 

Both are fault situations, where nothing can happen.

"Zero acceleration" can only occur if the mechanism is faulty/blocked etc, or if there is infinite mass (which is an impossibility).

And in the second situation; "zero current flows" again indicates a fault condition, something blocking the current flow through a real resistance, or a fault condition where there is no real resistance in the circuit (only an open-circuit fault).

It suits us in electronic calcs to say "infinite resistance" but what we are REALLY saying is there is ZERO current flow, which is possible in the real world, and we extrapolate that to equate to "infinite" resistance even though nothing is infinite in the real world other than extrapolated reciprocals of zero.

By your own reasoning in the other thread where you said E,I,R are all equally valid and transposable, if that was true and you allow "infinity ohms" in the real world you must also allow "infinity volts" and "infinity amps" of which it is obvious neither are possible.

Or if you are now saying "infinity ohms" is real and ok, but not amps or volts, then you are agreeing with my point from post #53 in that thread where I attributed some relationship of master/slave or cause/effect to those three items (where some conditions are valid and some are not, ie; the three items ARE different).

The argument for "infinity ohms" being a proof that infinity exists in the real world has been debunked over and over, there is no "infinity ohms" it's just an expression we use to describe the real condition (of zero current).

 

Good morning, RB.

The thing that suprises me is that despite the many readers of this thread and the other one where I commented that the mechanical situation has an easy resolution in Newton's Laws, no one has taken me up on it.

Rather folks prefer to heckle. I don't know why that is.

No, both situations can be realised in practise without faults being required. Even if there were to be a fault it should still be capable of analysis.

I don't believe I mentioned infinity, how did it creep into this thread?

It suits us in electronic calcs to say "infinite resistance" but what we are REALLY saying is there is ZERO current flow, which is possible in the real world, and we extrapolate that to equate to "infinite" resistance even though nothing is infinite in the real world other than extrapolated reciprocals of zero.

Yes I agree and that concords with my comments, edit : except that we should not 'extrapolate to infinity'.

By your own reasoning in the other thread where you said E,I,R are all equally valid and transposable, if that was true and you allow "infinity ohms" in the real world you must also allow "infinity volts" and "infinity amps" of which it is obvious neither are possible.

No I disagree. In Maxwell's Mesh Method of analysis currents are fictitious.

 

I've got nothing intelligent to offer towards solving these problems, but I am curious what you were referring to as to a resolution to the case where an "irresistible force meets immovable object".

Your problems state some parameters, but are they the whole configuration? For example, if along with the stated 9N force, there was another 9N force applied to the body opposing the first force, then the original condition is still met, but because the vector sum of the forces on the body is zero then the acceleration will be zero. But the mass will be unknown.

As far as the electrical case, I don't see why the resistance would not be either infinite or undefined, given Ohm's law.

 

Everyone:

Is there *really* such a thing a infinite resistance, and zero amps with a potential applied across that resistance?

I think not!

In the real world, everything "leaks", even if to an immeasurable degree. Two wires, with 9V across them, separated by air, will have a leakage current! Too small to measure, but it is there.

Most times, these leakage currents can be effectively assumed to be zero in practice (and, therefore "infinite" resistance.).

But try to build an long-time integrator across a 10 pF cap while ignoring leakage, and then tell me how that works out for you!

 

I'm glad one or two are taking up the challenge.

This is more like the good old times at AAC.

Suitable answers (there are more than one) do require a bit of lateral thinking and the realisatiion that you cannot apply one single physical law in isolation, you have to take the whole package.

Keep em rollin in.

 

...
Rather folks prefer to heckle. I don't know why that is.

Sorry if you thought my reply was "heckling", that was not my intent. I simply analysed the two situations you presented. To me, "heckling" is a type of harassment?

...
No, both situations can be realised in practise without faults being required.
...

I'm looking forward to seeing your realisations.

...Even if there were to be a fault it should still be capable of analysis.

Agreed, that is why I analysed it.

...
I don't believe I mentioned infinity, how did it creep into this thread?

Huh? You said; A 9N force is applied to a body with a result of zero acceleration. Determine the mass. ...

f = m*a
therefore m = f/a
m = 9N / 0 accel
m = infinity mass

which is also an exact match for your second calc;
E = I*R
therefore R = E/I
R = 9v/0 amps
R = infinity ohms

If you were referring to something other than the most obvious of solutions please speak up!

 

I did something that was pretty close once, I dropped a wrench across a 48VDC 100A power supply. It was drawing a fair amount of current at the time for a burn in chamber, the wrench actually changed its trajectory a little (I'm guessing there was a magnetic field involved) just enough. When it hit the terminals the whole wrench glowed red, impressive and scary. I knocked it off the terminals with another tool I was holding in my other hand.

So what happens when a deep power supply meets a low resistance? Fire and smoke of course. I didn't bother using the wrench again, I figured its temper was shot.

 

No RB, I was not accusing you, you are actually discussing the issues.

I am trying out a simplified version of thoughts pertinent to several recent threads and the difference in the way that physics and mathematics treats infinities and the limitations of modelling action in one system by corresponding action in another.

I hope to show that it is best to find a form of analysis that avoids invoking infinities.

To the questions I posed.
I hope you will not all say "I wuz done guv!"

Firstly the 9N force.

Well there is nothing magic here. I have a pebble on my desk that weighs (conveniently) 9N.
It is not accelerating, despite the 9N that the desk applies to it constantly to prevent it falling to the ground.


So we have the concept of an object being held in place by a (finite) applied force.

So what about an immovable object? What holds it in place? How does it work.

Well it obeys Newton's Third Law. In short it applies an equal in magnitude, but opposite in direction, reaction to the source of any force, in accordance with N3.

So it will respond to any applied force, F, no matter how large, with an equal and opposite force.

So it will not move.

I have not needed to bring in infinity, all that is required is to allow F to be unbounded above in mathematical terms.

Borrowing from the words of the Good Book, "Get thee behind me, infinity!"

Oh and the electrical example?

Well we know that there is no equivalent of N3 in electrics (as I said at the beginning of the thread).

But we talking about circuit theory and ideal components.

An ideal insulator passes zero current.

Apply an ideal 9v source to an ideal insulator and zero current flows, by definition.

Infinities 0 ; Physics 3

It surely is a bad day for infinities.

 

...Well we know that there is no equivalent of N3 in electrics...

Why do you say this? Consider a simple resistor and battery:

The battery provides an electromotive force on the resistor, causing it to do work (i.e. dissipate power). The resistance interacts with the resulting current, causing an equivalent (but opposite) emf across the resistance, which opposes the emf of the battery. If this weren't the case, Kirchhoff's Voltage Law (the sum of all voltages in a loop must equal zero), wouldn't exist!

This is an exact parallel to N3: Apply a force to an object (whether or not it causes the object to move -- i.e. do work), and the object applies an equivalent but opposite force back. The net sum of all the forces must equal 0!

If this argument doesn't convince you, then consider the "back EMF" of an inductor as yet another example.

Edit: so there is no confusion, I recognize that it is actually the battery (and the source of the applied force in N3) that is technically "doing the work" -- not the other way around.

 

If this weren't the case, Kirchhoff's Voltage Law (the sum of all voltages in a loop must equal zero), wouldn't exist!

You must know a different Kirchoff from my classmate Gustav Robert. He was in the class ahead of me at school.

He said

"In any closed loop the sum of the emfs equals the sum of the products of the current and resistance"

We have discussed this before here. In the proper form, without zeros or infinities, it is not subject to the Lewin paradox.

Nor does it mention back emfs or other strange animals.

No back emf is applied to the battery, which would be the case if N3 had an electrical parallel.

 

I think the problem with this idea is that we are trying to define infinity. By definition, infinity cannot be defined, so that is one of the major issues with this situation.

Anyway, when you have a perfect short across an ideal voltage source, you have much more than electrics and mechanics to worry about. There are tons of other factors that come into play, making this an impossible situation. So let's assume that perfect voltage sources and 0 resistance shorts can exist in the real world. You would get an infinite amount of current through the short, which would cause it to heat up and break before you can really do any measuring or observing. With an infinite amount of current through the short, this would happen instantly. If you wanted to make it interesting, both the voltage source and shorting wire would have to be indestructible. Now what would happen if that were the case?

Just my $0.02. I know it's not much, but I thought I'd throw it out there.

 

You must know a different Kirchoff from my classmate Gustav Robert. He was in the class ahead of me at school.

I am sure I didn't attend your school, and I've never met Mr. Robert. I've no basis for accepting any of his statements as authoritative. He was in the class ahead of you. Does that make him smarter?

He said

"In any closed loop the sum of the emfs equals the sum of the products of the current and resistance"

And he would be wrong (consider the forward voltage drop of a diode. This is definitely not due to a product of current and resistance! -- though it can be modeled as such for small signal analysis).

We have discussed this before here. In the proper form, without zeros or infinities, it is not subject to the Lewin paradox.

The only comment I made regarding zeros and infinity was that they simply don't exist in practice. But we can make valid assumptions that certain values can be large (or small) enough to be ignored on a case by case basis.

Nor does it mention back emfs or other strange animals.

No back emf is applied to the battery, which would be the case if N3 had an electrical parallel.

We shall agree to disagree on this point.

 

You must know a different Kirchoff from my classmate Gustav Robert.

Oh, I get it! Gustav Robert Kirchhoff!

Well, in that case you misquoted him. And you misrepresented your experience as a "classmate".

 

joey I can best suggest you read this thread here, in particular posts 39 and 44.

http://forum.allaboutcircuits.com/showthread.php?t=16150&highlight=kirchoff

As to N3.

It states more fully that when two bodies A and B come into contact the force applied by A upon B is equal and opposite to the force applied by B upon A.

It requires that the action and reaction are applied to different bodies.

There is no distinction between the bodies, they are fully interchangeable.

Are you trying to tell me that you consider a battery and a resistor interchangeable?

 

joey I can best suggest you read this thread here, in particular posts 39 and 44.

http://forum.allaboutcircuits.com/showthread.php?t=16150&highlight=kirchoff

I am well versed in Kirchhoff (and Maxwell -- I got an 'A' in Advanced University Physics I and II many, many years ago.). You may continue to apply the "sum of I*R" rule all you want -- as long as your circuits contain only resistive elements.

As to N3.

It states more fully that when two bodies A and B come into contact the force applied by A upon B is equal and opposite to the force applied by B upon A.

It requires that the action and reaction are applied to different bodies.

There is no distinction between the bodies, they are fully interchangeable.

Are you trying to tell me that you consider a battery and a resistor interchangeable?

It's simply a matter of who is working on whom. You can say that A is working on B. Or B is doing negative work on A.

Likewise, a battery can perform work on a resistor, or the resistor can perform negative work on the battery. It's all relative.

And, you didn't consider the case of a forward biased diode. Is the forward voltage drop simply a product of current & resistance? Or is the diode doing some work against the battery?

 

Joey, apart from your grades, which for which I congratulate you, you are talking absolute rubbish.

You read the pdf that Steve B, prepared and posted here, that contained an English translation of Kirchoff's original statement along with some explanation.

It was exactly as I said.

No, Kirchoff's law does not apply directly to diodes in circuit. Please demonstrate any version that successfully equates voltages for a negative pulse train applied to a circuit containing a positively biased diode.

Newton's third law says nothing whatsoever about work. There does not even need to be any work done whatsoever. It still applies to bodies in contact eg the previously mentioned pebble on my desk.

 

No, Kirchoff's law does not apply directly to diodes in circuit.

So I cannot use KVL to analyze a circuit with a diode??? Wow. Things have changed a lot since I was in school!

Newton's third law says nothing whatsoever about work. There does not even need to be any work done whatsoever.

Thus, my parenthetical:

(whether or not it causes the object to move -- i.e. do work)

It still applies to bodies in contact eg the previously mentioned pebble on my desk.

Consider two voltage sources, one independent, and the other dependent on the first with a magnitude equal to the first. Tie the negative terminals together. Attach a resistor between the positive terminals of each source.

Call the first voltage source "force due to gravity". Call the second voltage source "force due to desk". Call the resistor a pebble.

You now have exactly the equivalent of your exemplary mechanical system.

 

So it is possible to construct an electrical analog of a mechanical system.

So what?

It is not necessarily true the other way round. You still don't understand N3.

N3 requires a reaction force.

There is no such requirement in electrics.

That is I can construct an electric circuit comprising one voltage source and one resistor.

N3 makes it impossible to construct a mechanical system comprising one force and one object.

 

That is I can construct an electric circuit comprising one voltage source and one resistor.

N3 makes it impossible to construct a mechanical system comprising one force and one object.

The EMF generated across the resistor due to I*R is the opposing force! This goes back to my comment about diodes...is the forward voltage across a diode an EMF, or something else?

Further, consider an ideal current source in series with a resistor. The resistor generates an EMF of magnitude I*R, for which the source must compensate by providing it's own restoring EMF of equal magnitude but opposite polarity.