# Power Loss from cable

1. Jul 28, 2011

### HelpFinch

Hi guys,

I am trying to calculate the power and temperature lost from a cable. So I can do some crude thermodynamic calculations on heat transfer.

I am assuming in this case that the object next to the cable is touching, and I am trying to calculate how much power and temperature is transferred from the cable to the neighbouring material.

I have presently been calculating it with the Power = VI and the temperature loss is equal to I^2 x R.

I am not that great at the electronics but I think I am actually calculating just the power in the cable and I am being stupid in assuming this is the actual power transmitted to the surroundings I would just like some clarrification or correction if I am misleading myself.

Thanks for any help in advance,
Finch

2. Jul 28, 2011

### Staff: Mentor

Welcome to the PF.

The power converted to heat in the cable is P = VI = V^2/R = I^2 R

Where V is the end-to-end voltage drop across the cable, R is the resistance of the cable, and I is the current flowing through the cable. This power goes into heating the cable materials. That heat will cause a temperature rise in the cable, until it reaches some equilibrium with the excess heat flowing out into the enviroment.

AFAIK, there are no simple equations for calculating what temperature the cable rises to, given the external environment's characteristics. You can determine it experimentally, or you can use simulation software to calculate what it will probably be.

Do you have a particular application in mind? What kind of cable are you thinking of? Is the power transmission down the cable at DC or 50/60Hz AC, or some other frequency?

3. Jul 29, 2011

### HelpFinch

Thanks for answering Berkeman I appreciate it.

I intend on using transmforming the UK AC current and use a transformer to reduce the standard to a low voltage input most likely below 40. I believe in the UK it is 220V and 50Hz.

The desired output here is the temperature and the purpose is to find a material that gives out high temperature while being low cost (a balance will obviously met).

I only need to do some crude calculations to prove concepts so that experimental data can be made. Thus I hope I do not have to go through long differential equations in order to find accurate data!

Thanks and Regards,
Finch

4. Aug 1, 2011

### es1

If all you need is an average temp of the wire this technique will work.

This will not find the peak temp in the wire. For that you need differential equations and information you can probably only get experimentally so you might as well just run the experiment.

http://en.wikipedia.org/wiki/Thermal_conductivity
http://en.wikipedia.org/wiki/Thermal_resistance_in_electronics

The trick is how you define the thermal resistance of the wire's insulation, assuming it has some, and the connection to ambient. Probably somebody already solved it for the geometry of a wire and some standard materials, with the assumption that the wire is suspended in air. I wouldn't be surprised to find out it was a typical physics homework question or something. Try googling with the keywords in the wikipedia article.