Question about current in an infinite circuit

[fluidistic]

I've asked myself the following question but couldn't think about an answer.
Imagine a hypothetical situation : you have a very large (more than 10^{10}m) circuit that contains only a wire (with no resistor) and an emf. Now you turn on the emf... will the current be the same in the whole circuit? Or will the current be null at very a large distance initially while close the emf the current would be theoretically infinite since there's no resistor?
So that you can't apply Kirchhoff's current law in very large circuits when the situation is not yet stationary.

Equivalently one can imagine a situation of a human size circuit but with very small time (less than say 10^{-12}s).

I'd like to know what really happens, just to understand better how the universe really work, it's not a homework question.
Thanks.

 

[platipo]

well, reality is a totally different animal. a REAL generator will have an internal resistance, no wire will have no resistance at all, though for a small circuit it could be negligible compared to that of resistors, so you will have no infinite currents. And since now your system does have a resistance the problem is quite easily solved.

 

[willem2]

look for "transmission line"

 

[Dale]

you can't apply Kirchhoff's current law in very large circuits

This is correct. Kirchoff's laws and the rest of the circuit theory are all approximations to Maxwell's laws. One of the assumptions is the so-called "small circuit approximation" which basically says that the circuit is small compared to the wavelengths involved so that all parts of a wire can be assumed to be at the same potential. Obviously the small circuit approximation is violated for very large circuits and then you have to use Maxwell's laws.

 

[fluidistic]

look for "transmission line"

Ok thanks I will look at it in details but I think they are not large enough.

This is correct. Kirchoff's laws and the rest of the circuit theory are all approximations to Maxwell's laws. One of the assumptions is the so-called "small circuit approximation" which basically says that the circuit is small compared to the wavelengths involved so that all parts of a wire can be assumed to be at the same potential. Obviously the small circuit approximation is violated for very large circuits and then you have to use Maxwell's laws.

Thank you very much, I'm done with this.

 

[Bob S]

Hi Fluidistic-
For a bare wire in vacuum (no dielectric) the signal velocity is the speed of light. The impedance of a coaxial transmission line with an air dielectric is

Z = (377/2 pi) Ln (b/a)

where b= radius of outer conductor and a is radius of inner conductor. When b/a becomes very large (like for a bare wire), the impedance gets very large logarithmically.
Bob S