# SINUSOIDAL VOLTAGE APPLIED TO ZERO RESISTANCE CONDUCTOR

#### b.shahvir

Joined Jan 6, 2009
457
Hi Guys,

The following query would sound a bit ridiculous and abstract but it suddenly popped up in my head.

What would happen if I were to apply a purely sinusoidal AC voltage across a zero resistance conductor (theoretically, a super conductor) ? Zero resistance would mean the conductor is assumed to carry infinite current thru it (at least theoretically).

However, it would be interesting to note the behaviour of the AC current waveform since the current cannot be limited by way of 'frictional resistance' as the lattice structure inside the super conductor is considered to be absent.

Also the super conductor is assumed to possess zero inductance!

Kind Regards,
Shahvir

#### t_n_k

Joined Mar 6, 2009
5,455
Sounds a bit like that yet to be discovered material "unobtanium".

#### thingmaker3

Joined May 16, 2005
5,084
Also the super conductor is assumed to possess zero inductance!
Clarify, please. Are we to make such assumption for the thought experiment in question?

Real-world superconductors have both resistance (albeit very tiny) and inductance.

#### b.shahvir

Joined Jan 6, 2009
457
Clarify, please. Are we to make such assumption for the thought experiment in question?

Real-world superconductors have both resistance (albeit very tiny) and inductance.
Yes, but howsoever ridiculous it may sound, I would still humbly insist on assuming ideal conditions as that is where the fun lies.especially if one tries to plot the current vs. voltage waveform under such abnormal circuit conditions!
Thanx

#### thingmaker3

Joined May 16, 2005
5,084
With "zero" impedance and "zero" resistance, any voltage at all produces a current limited only by the source's internal resistance. If we're talking about the imaginary "ideal world," then the source would also be "ideal" and the current would increase without bound. I = E/R, and division by zero makes my head hurt.

Power dissipated would also be zero and simultaneously increase without bound: P = I^2*R = E^2/R = infinity times zero = minuscule divided by zero. Explain that one if you can.

#### b.shahvir

Joined Jan 6, 2009
457
With "zero" impedance and "zero" resistance, any voltage at all produces a current limited only by the source's internal resistance. If we're talking about the imaginary "ideal world," then the source would also be "ideal" and the current would increase without bound. I = E/R, and division by zero makes my head hurt.

Power dissipated would also be zero and simultaneously increase without bound: P = I^2*R = E^2/R = infinity times zero = minuscule divided by zero. Explain that one if you can.
Absolutely correct. I concur with you on this one. But imagine how the current waveform would turn out to be. I doubt it would be able retain it's sinusoidal nature especially in these extreme physical assumptions!

#### beenthere

Joined Apr 20, 2004
15,819
You can't establish a voltage under those conditions. E = IR is another infinity times zero situation. That should cross your mental eyes, as some minuscule voltage has to be present to supply the energy that moves all those electrons.

If current is infinite, how much energy must be present to move them? - an infinite amount, obviously.

#### BillO

Joined Nov 24, 2008
990
Ahhh, the old 'immovable object meets the irresistible force' problem.

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#### t_n_k

Joined Mar 6, 2009
5,455
Will there be a disturbance on the space-time continuum?

#### mik3

Joined Feb 4, 2008
4,843
Sounds a bit like that yet to be discovered material "unobtanium".
Did you see the movie "The core"?

#### t_n_k

Joined Mar 6, 2009
5,455
Hello mik3,

"The Core" - No I missed it - I'll see if I can get it on DVD from the video hire store. Perhaps I'll see my D.E.S.T.I.N.I all mapped out!

Thanks for the feedback.

#### b.shahvir

Joined Jan 6, 2009
457
You can't establish a voltage under those conditions. E = IR is another infinity times zero situation. That should cross your mental eyes, as some minuscule voltage has to be present to supply the energy that moves all those electrons.

The applied voltage across the abnormal conductor loop is present, which continuously drives the infinite current thru it. However, it just does not appear externally as there is no loop resistance (or impedance) for the applied voltage to drop itself across!....since, in my opinion, all of the applied voltage is completely used up in driving the infinite current thru the conductor.

If current is infinite, how much energy must be present to move them? - an infinite amount, obviously.

As the lattice structure in the zero resistance conductor is considered to be absent, there is no frictional opposition to the drift velocity of the electrons flowing thru it. As a result, even a negligibly small applied voltage causes the electrons in the conductor to accelerate to infinite speed. This infinite electron drift velocity gives rise to an infinite current flowing thru the said conductor. The case you have stated, in my opinion, could only be possible in a non-ideal scenario, i.e. in the presence of a conductor crystal lattice and if an infinite current is then assumed to flow thru such a set up under the influence of an externally applied voltage!

#### beenthere

Joined Apr 20, 2004
15,819
There is another interesting possibility here - what happens if your ideal voltage source has a limited quantity of electrons? If it has to supply an infinite current with only 1000 electrons, then those electrons must individually move fast enough to make up an infinite current. That means they will have to exceed the speed of light to do so. Might have some odd effects on the experiment when each electron's mass goes to infinity.

Actually, that also obtains in the first case. An infinite current can only be supplied by an infinite number of electrons moving with an infinite velocity. That should turn the entire universe into a black hole.

#### mik3

Joined Feb 4, 2008
4,843
Hello mik3,

"The Core" - No I missed it - I'll see if I can get it on DVD from the video hire store. Perhaps I'll see my D.E.S.T.I.N.I all mapped out!

Thanks for the feedback.
This is the movie:

http://www.imdb.com/title/tt0298814/

I find it interesting.

#### thingmaker3

Joined May 16, 2005
5,084
What if the letters d, o, and g really spelled "cat?"

#### b.shahvir

Joined Jan 6, 2009
457
There is another interesting possibility here - what happens if your ideal voltage source has a limited quantity of electrons? If it has to supply an infinite current with only 1000 electrons, then those electrons must individually move fast enough to make up an infinite current. That means they will have to exceed the speed of light to do so. Might have some odd effects on the experiment when each electron's mass goes to infinity.

Actually, that also obtains in the first case. An infinite current can only be supplied by an infinite number of electrons moving with an infinite velocity. That should turn the entire universe into a black hole.
An interesting observation I must say!

#### beenthere

Joined Apr 20, 2004
15,819
I would advise against the experiment. But that perfect current source might be useful in powering the world's power grid.

#### russ_hensel

Joined Jan 11, 2009
825
a large magnetic field woulb be created and that would quench the superconductivity

in pratice this is a major limitation of super conductors

#### beenthere

Joined Apr 20, 2004
15,819
When one deals with conceptual things such as "perfect" and "infinite", physical limitations become trivial.

#### BillO

Joined Nov 24, 2008
990
This is a typical division by 0 error. It warrants no discussion.