Ohm's Law: Voltage Across Ideal Wire = 0

[cepheid]

Now, this question may be incredibly stupid, but it has been bothering me nonetheless. Say you have a basic circuit loop as shown in the picture.

Ohm's law:

$$V = RI$$

Now, according to a textbook I'm reading right now, "By Ohm's law, there is no voltage across an ideal (i.e. zero-resistance) wire regardless of the current flowing through it."

I'm just wondering what the meaning of that statement is. Yeah, sure, obviously:

$$V = 0I = 0$$

But when I look at that picture, here's how I see it: there is definitely a potential difference between points A and B, because they are at either end of the battery. But these points are also the two ends of the wire that makes up the loop! So how could there possibly not be a potential difference across the wire?! And if there weren't, why would there be any current at all? Aren't the electrons moving from a point of high potential to low potential, gaining KE along the way?

 

[krab]

There is no ideal voltage source. Meaning that for any realistic source, as current demanded is increased, you'll reach a point where voltage will start to drop. You can try this. put a voltmeter across a battery. Now short it out. I guarantee that if the shorting wire does not melt into a puddle, the voltage reading will drop to zero.

 

[cepheid]

Hmm...

I've seen someone (inadvertantly) short a battery in the lab, using one of those dinky jumper wires. The wire was toast...went up in an impressive display of pyrotechnics. Unfortunately, this explanation doesn't make the answer to my question clear to me. My fault. Maybe the problem is that my question is sillier than you were expecting. I'm asking about the idealised, perfectly conducting wire referred to in the textbook quote. You connect the ends of it to the terminals of a battery. So how could there be no voltage across the wire?

 

[krab]

So you are considering a case of an ideal wire and an ideal voltage source, and worrying that Ohm's law doesn't seem to apply? Do you realize that ideal means unreal? Are you the type of person who wastes time contemplating what happens when an irresistable force is applied to an immovable object?

 

[Chronos]

Krab is obviously on summer vacation. There is no such thing as an ideal wire or an ideal voltage source. See the Maxwell equation.

 

[Integral]

See this thread

Cross posting is a no-no!