Wire melts because of high current - help

[complications07]

Homework Statement

A wire melts in the middle when the current running through it reaches I(critical) (unless there is a kink in the wire). Discuss why the middle of the wire gets hotter than the ends.

The Attempt at a Solution

Is it because the 2 pastic posts to which the ends of the wire are connected absorb most of the heat generated by the current passing through the wire? As a result, the hottest part of the wire is the middle section because it is the furthest away from the plastic posts and the wire, therefore, melts and snaps in the middle due to the heat of the current passing through it.

Or does the answer have something more to do with potential and kinetic energy of the molecules?

Thx!

 

[xxkbxx]

Current is the same throughout the wire - so it being in the middle won't have anything to do with it. Remember what current is (by Ohm's law) and remember the formula for Resistance

 

[marcusl]

The Attempt at a Solution

Is it because the 2 pastic posts to which the ends of the wire are connected absorb most of the heat generated by the current passing through the wire? As a result, the hottest part of the wire is the middle section because it is the furthest away from the plastic posts and the wire, therefore, melts and snaps in the middle due to the heat of the current passing through it.

Thx!

I think you are on the right track. The posts may not "absorb most of the heat" but they may cool the wire a bit near the ends. If the ends of the wire are attached to heavier supply wires, they also will conduct some heat away.

 

[AndreJ]

I think you'll need to investigate something called "the skin effect".

 

[marcusl]

I assume the question refers to direct current or to common 60Hz alternating current, in which case the skin effect is absolutely negligible for ordinary wire.

 

[denverdoc]

I think that there might also be a positive feedback phenomenon present, that assuming this heat sink notion is right, the part that first warms, will have a local rise in temp, increasing resistance there, sort of a thermal runaway effect?

 

[AndreJ]

I assume the question refers to direct current or to common 60Hz alternating current, in which case the skin effect is absolutely negligible for ordinary wire.

True, but we are not given the frequency of current, diameter or gauge of wire or material of wire, so I can only suggest the skin effect without any other information.

Then again, there will be cooling effects of the posts and such.

 

[marcusl]

True, but we are not given the frequency of current, diameter or gauge of wire or material of wire, so I can only suggest the skin effect without any other information.

I can't see why the skin effect would have any bearing on this problem.

 

[Gokul43201]

This has nothing to do with the skin effect. The OP essentially was right, with the only correction being that it's not necessary (though it's possible) that the plastic posts conduct most of the heat generated.

PS: The real "ends" of the wire, must in fact be connected to something else (eg: a power supply) which is likely a better thermal short than the plastic posts.

 

[AndreJ]

I can't see why the skin effect would have any bearing on this problem.

It was merely a suggestion, rather than a definite answer. Since, I was just going to give an idea but not a solution.

I can see how it is irrelevant now, but my original post was just to give a suggestion which may help.

The OP's post has been solved, though. So this conversation is no longer needed.