# Is there a limit on the charge that can flow in a wire?

I assume when I hook up a 12V battery to a wire, all the free electrons in the wire move. If I hook up 24V, they move faster so more charge passes a area cross section for i=C/s. But in AC, their movement is constrained. They move at 60Hz. So what happens if I increase the voltage? More electrons have to pass a cross section, so just some electrons move, and then more of them do if I increase the voltage? Maybe I am confusing myself :)

• The wire will vaporize long before you can reach any limit on the amount of charge you can transfer per second. – Ignacio Vazquez-Abrams Mar 25 '14 at 22:30
• Unless you want to take heat out of the equation. Have a look at this physics SE question on superconducting wires. physics.stackexchange.com/questions/1060/… – krb686 Mar 25 '14 at 23:50

## 1 Answer

But in AC, their movement is constrained. They move at 60Hz.

This shows a misconception. The AC frequency (60 Hz) tells you how often the current switches direction, not how fast the individual carriers are moving.

If I hook up 24V, they move faster so more charge passes a area cross section for i=C/s.

This is true to a point. But you have to remember that electrons are moving around randomly in all directions, and a reasonable current in an ordinary wire just "biases" the direction of this motion slightly in one direction or the other. If you have a higher current, the bias is even a bit more in the direction of that current, but not every electron is moving with the current and the effect on the speed of each electron is fairly small.

I assume when I hook up a 12V battery to a wire, all the free electrons in the wire move.

This is not really true. All of the electrons were already moving. Applying a voltage just made the average of that motion slightly to one direction or the other.

Is there a limit on the charge that can flow in a wire?

Practically, the maximum current in a wire is limited by the resistive self-heating of the wire. If too much current is carried, the wire will get hot enough to melt itself or cause a fire hazard. Typically we choose a wire large enough to limit its temperature rise to 20 or 30 degrees C under expected loads. On this basis, you can find tables online giving the ampacity of round wires depending on diameter or pcb traces depending on width and copper thickness.

• I think he's really just saying as a general rule, the electrons don't move (aren't long-term biased) in any particular direction with AC, so I don't think he has a misconception there, assuming he meant to say "they cycle at 60Hz". Also, I think this answer has some good clarity on some points, but have you really answered his original question? – krb686 Mar 26 '14 at 2:00
• @krb686, good point. Edited. – The Photon Mar 26 '14 at 2:55