Current density on a gold plated surface?

Question

I need to run 20 amps 3 volts along a ceramic with a gold plate. The length is only 0.5mm. What I am looking for is what is the minimum width that I can use. As I recall thickness of the gold plate won't matter only surface area. Any links to help calculate this would be greatly appreciated.

Thanks

Answer 1

No, thickness is important. The voltage is not.

So once you know the thickness, and the width and the length, you can calculate the resistance, and then the voltage drop (and you did not tell us the allowed voltage drop, or power, which is related).

If I assume a thickness of 0.02 mm, length of 0.5 mm, max voltage drop of 0.2 volt:

Max resistance is 0.2/20 = 0.01 Ω = 10 mΩ

resistivity gold = 0.022 µΩ-m

cross sectional area is 0.02 mm*w = 0.00002 m*W

10mΩ = 0.022 µΩ-m x L/A

10mΩ = 0.022 µΩ-m x 0.0005m/0.00002*W m²

10E-3 = 2.2E-8 x 5W-4 / 2E-5*W

W = 2.2E-8 x 5W-4 / 2E-5*10E-3

W = 5 E-4m = 0.0005 m = 0.5 mm

so it is possible.

power dissipated is 0.2v x 20 = 4 watts, which is a lot for that small area. without doing the calculations, I think 4 watts in that small an area will melt the gold. You may want to decrease this by a lot by making the plating thicker and the width higher.

For example if you made the width 1 mm and the plating 0.04mm, then the resistance would be 1/4, and the power would be 1 watt. Still high, but getting better.

Heat in that small area is going to be the limiting factor. You may have to plate a larger area just to provide a way for the heat to get out.