# Length in relation to fusing current

Hi Guys and Girls

I have been given an investigation to do on "Fusing Factors of wires"

I have looked at the effect that increasing the length of a wire has on the fusing current. I know that it doesnt effect it but i do not know why!
I also have looked at diameter of the wire in relation to fusing current. I know that as you increase the diameter of the wire the fusing current increases but again do not know why!

Does anyone have any explainations to these?
Any views would be much appreciated!

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Integral
Staff Emeritus
Gold Member
Do you now the expression for the resistance of a wire?

A critical factor in fusing is the temperature of the wire. You must understand the factors which effect the generation and loss of heat in a wire. What do you know of this?

Well resistance is the opposition to the flow of current?
I have little knowledge of the generation and loss of heat in a wire.
Do you have any information that would help me?

Any information would be greatly appreciated!

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Integral
Staff Emeritus
Gold Member
The resistance of a wire is given by:
$$R = \frac {\rho L} A$$
Where $\rho$ is the resistivity if the material of the wire, A is the cross sectional area of the wire and R is resistance.

Power loss in a wire is given by

$$P = I^2 R$$
Where I is the current and R is resistance.

We can also say that the rate of heat loss from the wire is in part determined by the surface area. The hard part is arriving at a temperature given this information. It can certianlly be done theoritacally but requires an number of assumptions. These assumptions have to do with environmental condtions which can radically change the results.

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Like i said before, I need to know why the fusing current of a wire does not increase with an increase in length.
I also need to know why the fusing current increases with diameter of the wire.
I basically have done an experiment using different lengths and diameters of constantan wire and found various fusing currents for different lengths and diameters of the wire. I need to explain why what I have found out has happened!

I am doing A level physics, which is the level below a university degree in britain!

Hope This Helps.

berkeman
Mentor
As Integral hinted, ask yourself what effect the length of the wire has on the radiating surface area... and what effect the diameter of the wire has on the radiating surface area....

Well an increase in length will give an increase in radiating suface area?
As will an increase in diameter? So how does this explain the fact that the fusing current does not change for an incresed length?

Sorry if im being stupid! Is there sometihing that im missing?

Tom

berkeman
Mentor
When you double the length, you double the ability of the piece of metal to radiate away the heat that is being generated. So you generate twice as much heat, but it radiates away twice as fast compared to a single-length piece. So the temperature of a 2x long wire is the same as a 1x long wire, which means that the fusing/melting current is the same independent of length. When you change the diameter of the wire, you change the surface area a little, but you change the cross-sectional area a lot (which lowers the resistance), which means that the fusing/melting current will depend on the diameter.

Ah right I see, thanks for explaining it!

I am still unsure, what the two equations that integral gave me had to do with this. Obviously, the first enables me to calculate the resistance of the give length/diameter of the wire I have, but the second I am unsure how it will help me with the fusing of the wire?

berkeman
Mentor
Integral's second equation shows you how to calculate the power that is dissipated in a section of wire, given some voltage and current. That power is the amount of energy that goes into the wire segment versus time, and the heat energy that radiates away is the hard part to calculate. As Integral says, it depends on a lot of things, and doesn't lend itself to an easy equation.

Instead, I'd suggest that you look at some fuse datasheets, to get a feel for how they rate their fusing currents and how they use the concept of the "I^2 * t Melting Point". If you can come up with a controlled situation for the wire (like a known heat sink to a thermally conductive liquid or something), then you will be able to write the equations that show how the wire will heat up over time given some current. Otherwise, you'll need to use more of an approximation like the fuse folks do. Here's a page with some Littlefuse datasheets FYI:

http://www.littlefuse.com/cgi-bin/r.cgi/en/know_datasheet_results.html?TechnologyID=3&Family=156&LFSESSION=93GcTI7oFn

berkeman
Mentor
BTW, one other thought with respect to calculating how much heat radiates away. With explicit heat sinks or big power structures like transistor packages, the heat sink or package will be rated in its heat-dissipating capability in units of degrees/watt. Typical numbers might be 10C/W for a small sink, to 1C/W or less for bigger sinks with forced air cooling, etc. The number is used to anticipate what the delta-T temperature rise over the ambient air temperature will be, given a power level.

Since you have some experimental data, you might be able to come up with a number that is typical of the dissipative capability of wire (bare versus sheathed) in air, in units of degrees/W. Once you have that, and knowing the melting temperature of the wire, you will be able to have a pretty quantitative way to predict the fusing current for wire. If you have a thermocouple, you could even do more experiments to characterize the degree/W dissipative factor for the wires, without having to melt them first.

Ok thanks for that!!!

Just one more question. As I varied the length of the fuse wire, i found the fusing current constant untill I used a very short length (eg 10mm - 20mm). The fusing current increased by about 1A. Is there any explaination for this? Or is it just experimental error?

berkeman
Mentor
mrshoaib said:
Ok thanks for that!!!

Just one more question. As I varied the length of the fuse wire, i found the fusing current constant untill I used a very short length (eg 10mm - 20mm). The fusing current increased by about 1A. Is there any explaination for this? Or is it just experimental error?
Since the current went up, that means that the shorter piece of wire is cooling itself off more efficiently than the longer pieces for some reason. My guess would be the heat sinking effect of the clamps on the ends of the wire.

Ah right, what exactly is the heat sinking effect of the clamps and why wouldnt it happen with a longer length of wire?
I was using constantan wire and I found this to be farily constant with changes of lengths.
However, when i used copper wire the fusing current was no constant at all. Is this to do with the properties of copper cooling?

berkeman
Mentor
I'm no expert in calculating heat conduction. But heat can transfer by three mechanisms -- conduction, convection and radiation. The heat loss from the open areas of the wire would mainly be from the latter two, I think. But near the clamps, some heat from the wire can conduct out the clamp metal, which would tend to cool the wire near the clamps. If there were good clamps that were electrically conductive but not thermally conductive, then you could prove this to yourself. But good electrical conductivity usually implies good thermal conductivity anyway.

But that's a good thing to put into your experimental writeup. You should be able to plot the fusing current for different lengths of wire, and show where the end clamping effects start to change the results. It will depend on the pulse width of the fusing current, and the temperature of the clamps, but holding things constant should tell you about how long a piece of wire you should use for characterizing the melting/fusing current.

Ok thanks for that, sorry for the slow reply, I been skiing for a week!

Yep the graphs that I get get confirm this, the copper wire is still a mystery to me though!

Integral
Staff Emeritus
Gold Member
I would think that the heat loss due to your end clamps is pretty constant. With longer wires you produce more heat, so the loss is a small relative to the total. As the wire gets shorter the constant heat loss at the clamps becomes a larger fraction of the total, thus becomes more significant.

Copper is an execellent conductor of heat so its temperature may be more strongly influcened by the clamping heat loss.

Yes that would make sense regarding the results that I have for copper, thanks for that integral!

In terms of changing the diameter of a wire of constant length and material, is there any relationships that you can determine?

I have a graph of wire diameter (x axis) against av. fusing current (y axis) (see below)
I will need to add a line of best fit to this.
What relationships can i determine from this?

http://img522.imageshack.us/img522/6781/graph19qd.th.jpg [Broken]

Many Thanks

Tom

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Hootenanny
Staff Emeritus
Gold Member
Not much, I would say you need more points for any conclusions drawn to be meaningful.

Right ok, there were only 4 wires that could of used, although I can say this in my investigation. Would the line of best fit go though the origin, as where there is no diameter there is no fusing current?

Hootenanny
Staff Emeritus
Gold Member
Just looking at it, It doesn't look like it will intersect the origin. Regression calculations will give you can accurate equation for you line of best fit based on the data available, but really you need more data values.

Ok I have no idea what a regression calculation is? Is it a complicated process?

Hootenanny
Staff Emeritus
Gold Member
Not really, it takes a little bit of work, but i'm not sure if a linear regression calculation will be any more meaningful than a hand drawn line of best fit, under these circumstances.

Hootenanny
Staff Emeritus