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How can I calculate the current carrying capacity of a DC copper bus bar with respect to temperature?

Bus bar specifications:
Width=40mm
Thickness=6mm

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  • \$\begingroup\$ could you define what you mean with "current carrying capacity"? That means different things to different people. \$\endgroup\$ – Marcus Müller Jan 16 '20 at 8:40
  • \$\begingroup\$ good amount of information can be found here: electronics.stackexchange.com/questions/22334/… \$\endgroup\$ – Hasan alattar Jan 16 '20 at 8:55
  • \$\begingroup\$ Given that the problem specifies only the cross-section area of the bus bar and little else, I'm pretty sure this boils down to a conductance/resistivity question. The longer the bar, the more it can dissipate. But the longer the bar, the more resistance and therefore more dissipation. Assuming the ratio between dissipation to ambient relative to dissipation is a constant (likely for this case), then it's just resistivity you need to worry about. How does the resistivity of copper vary with temperature? Do you remember this value? (Varies a little depending on purity and impurities added.) \$\endgroup\$ – jonk Jan 16 '20 at 9:43
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The permitted and the practical loading of busbars is a complex matter taking into account much more than just the resistivity of the material. I suggest reading the industry association's (free) comprehensive monograph on this topic:

  • Copper for Busbars – Guidance for Design and Installation, David Chapman and Prof. Toby Norris, The Copper Alliance Pub. 22, (2014 ed., 103 pp) Download page

Chapter 2 covers current carrying capacity and its calculation, which depends on many complex factors including the skin effect depth, bar shape and spacing, cooling mechanisms and so on.

There are two design limits; the maximum permitted temperature rise, as defined by switchgear standards, and the maximum temperature rise consistent with lowest lifetime costs - in the vast majority of cases, the maximum temperature dictated by economic considerations will be rather lower than that permitted by standard.
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Lowering the temperature by increasing the size of the conductor reduces energy losses and thereby reduces the cost of ownership over the whole lifetime of the installation. If the installation is designed for lowest lifetime cost, the working temperature will be far below the limit set by standards and the system will be much more reliable.

As you would expect, the exact kind of copper affects resistivity a lot, and there is good coverage in the book on the effects of different impurities and alloys. They say "normally, the purest copper is used for bulk conductors".

If you just want the basic effect of temperature on resistivity, the give a formula for basic resistivity of high conductivity copper for temperatures up to 200°C (section 1.2.2.1.1) as

R = R20(1 + α20ΔT)

  • R20 is the conductor resistance at a temperature of 20°C, in Ω
  • α20 is the temperature coefficient of resistance at 20°C, per K. α = 0.0039 for copper
  • ΔT = Tk-20 is the temperature difference, in degrees K
  • Tk is the final temperature, in K.
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