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Electricity/Wire transfer to Copper

Electricity/Wire transfer to Copper

Electricity/Wire transfer to Copper

(OP)
I have a wire to be soldered into a copper piece. The wire is rated at peak current of 1300 A (peak voltage is 880V). I am interested in how hot the copper piece will get from the current running through the wire, so I can determine the cross section I need to make the copper piece (it will be "T" shaped, with the wire going in one direction, and the other direction being a plug to transfer the current).

I have a few possible methods, though there are others I'm sure I haven't though of.

One I found in Mark's Handbook:

R1 = R2 (1+ alpha*T)

Where R1 is the resistance of the copper piece, R2 is the resistance of the wire, alpha is the temperature coefficient of copper, and T is the difference in temperature.

Resistance of the copper piecce is determined by rho*L/A, where rho is resistivity, L is length, A is cross-sectional area.


Another method I have though of is using conduction. Using the resistivity of the wire, and the current, I found power using i^2*R. Then using this as energy (W), I plugged into the equation

q = k*A*(delta T/L)

where q is Watts, k is thermal conductivity of copper, A is cross-sectional area, delta T is temp. difference, and L is length of the part.

Trying both, the delta T seems to be between 50-70 K, which when I convert to Celsius to check seems very high! Granted this could be due to using too small of a cross sectional area (say 8mm outside diameter and 3 mm inside diameter); however, I thought I would check with you all first.

Any input would be greatly appreciated. Thank you.

RE: Electricity/Wire transfer to Copper

(OP)
The problem I have with the first equation is the resistances are looked up at a predetermined temperature of 20 degrees C. I believe they should be dependent on the temperature rise (atleast one of them), yet how can I look that up without knowing the difference in temperature? I don't think that equation is made for this purpose.

RE: Electricity/Wire transfer to Copper

(OP)
Another formula suggested is

Delta T = J/(rho*V*Cu)

where J is Joules, rho is density, V is volume, and Cu is specific heat (J*K/kg).

I am not familiar with this equation, though. Is this one more reasonable?

RE: Electricity/Wire transfer to Copper

(OP)
Upon review, it appears the equation

R1 = R2 (1+ alpha*T)

Merely works for one material, and explains how the material's resistance differs depending on temperature gradient...so that one is out.

RE: Electricity/Wire transfer to Copper

I'm really confused.  Why wouldn't you make the copper cross-section at least as much as the wire cross-section?  Isn't your wire also copper?

TTFN

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RE: Electricity/Wire transfer to Copper

(OP)
That would work, I am just curious on how to calculate it.

RE: Electricity/Wire transfer to Copper

If you're dealing with alternating current, skin effect may become important and limit the effective cross sectional area.  Just a thought.

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