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# current density of copper ?

## current density of copper ?

(OP)
We always say that copper is a better conductor than Al , this is because the temp coeff of copper is lower than that of Al. But can somebody tell me the connection between copper, temperature and area, or to put it straight how does one arrive at the fact  1 sq mm of copper while carrying 1 Amp of current for 1 hour heats upto what temperature, or to put it in the reverse, I will allow a temperature rise of 40 deg Cent (ie ambient + 40) and with this in mind I would like to choose the area of copper when I pass 1 amp of current for one hour.... is there a formula... hELP

### RE: current density of copper ?

The copper is a better conductor than Al, because your resistance specifie is smaller.
Cu=0,0176 ohm * cm.
Al=0,028  ohm * cm.
The resistance is :ohm*cm*L/S.
The Loose are:I*I*R and they become heat.
Coefficient of temperature for grade Celsius:
Al=0,0044
Cu=0,0043.
Regards.
Hugo.

### RE: current density of copper ?

If you have a specific temperature limit in mind, there are at least two ways to approach the calculation.

First, for short circuit withstand calculations, it is often assumed that no heat transfer outside of the conductor occurs.  In that case a given current for a given time equates to a given amount of energy which can be converted to a temperature rise based on the thermal capacitity of the conductor.  Times for this type of calculation are typically only a few cycles.

For steady-state ampacity calculations, the heating power given off from the conductor to it's environment (depends on temperature and thermal resistance) is equal to the heating power produced by I^2*R losses within the conductor (independent of temperature as a first-order approximation).  i.e. solve for I in the equation I^2Relec = Kthermal*(Tconductor-Tambient)  where Kthermal is equivalent watts per degrees C.... may be the product of an area and a watts/perC per meter^2 coefficient.

I realize that's pretty general.  More specific help may be available from the board if you give more specific description of your problem.

### RE: current density of copper ?

Suggestion: Reference:
1. Giacoletto L. J., "Electronics Designer's Handbook," Second Edition, McGraw-Hill Book Co., 1977
Reference 1 Table 3.14 "Bare Solid Copper Wire" on page 3-112 includes a general purpose operating current in Amps = 2 x 10**6 A/m**2
This means that AWG or B&S wire gage number 20 would carry 1.005Amps for wire at 20°C.

### RE: current density of copper ?

Suggestions:
1. Reference
IEEE Std 399-1900 or 1997 "IEEE Recommended Practice for Industrial and Commercial Power System Analysis"
Equation 35:
R2 = R1 x [1 + alpha x (t2 - t1)]
R2 = resistance at temperature t2
R1 = resistance at temperature t1
alpha = temperature coefficient per degree at temperature t1
At 20°C the coefficient alpha per degree Celsius is
Copper: 0.00393
Aluminum: 0.00403
2. Okonite Cables Bulletin EHB-81 page 14
"Allowable Short Circuit Currents for Insulated Copper Conductors"
(I/A)**2 x t = 0.0297 x logbase10 [(T2 + 234)/(T1 + 234)]
where
I = short circuit current in Amps\
A = conductor area in Circular Mils
t = Time of short circuit in seconds
T1 = Operating temperature 90°C
T2 = Maximum short circuit temperature 250°C

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