I have to assume the most low cost solder one can find. Lets assume the solder is 5x higher in resistance.
The copper is deposited on the board not etched off. It is thinner than anything you can get in the US.
Assume; the solder is 5x the thickness of the copper. (Probably much thicker)
The solder resistance is equal to the copper thickness.
The two resistors are in parallel. The total resistance is 1/2.
Most people are thinking 1oz copper and 1oz solder and the resistance changes very little. I agree with your thoughts.
Hi again,
Yes you are probably right, but not me
Actually common solder resistivity is about 9 times higher than copper. That means to *equal* the copper we need a layer of solder that is 9 times as thick as the copper, but that's not saying that much either because we might need 5 times that to get the required total resistance. Just twice as much might not be good enough, but if it is there are other considerations too. So for 0.00135 inch thick copper we need to put a layer of solder that is about 0.012 inches thick to *equal* the copper resistance. IF that's all we need that's great perhaps, but if we needed 5 times that we'd have to dump on a layer that is 0.06 inches thick, and that's not something we would want to do using wave soldering.
Another catch is that is at *room temperature*. As the temperature increases, the resistivity increases. And the third catch is that the total surface area only goes up a little with the volumetric increase (adding more material) so that means we loose part of the effect of surface area cooling meaning the temperature rises higher than if it was just a flat sheet (one layer of copper).
So the three to five factors that have to be considered are:
1. Resistivity 9 times higher than copper.
2. Total thickness requirement might be large requiring a large amount of solder.
3. Surface area to volumetric ratio does not increase much as we pile on solder.
4. #3 leads to adding more solder to make up for the temperature increase caused by lower surface area to volume ratio.
5. Reliability: how well does piled up solder hold up over vibration and years of use, and how hard is it to get right the first try.
Silver solder resistivity is somewhere around 7 times higher than copper so that's a little better but more expensive.
All of the above led me to do it with heavy gauge copper wire with end holes drilled in the board to accomadate the wire. This allows easy adjustment of the wire diameter for different current levels too. It's also easier to get right without having to do a perfect soldering "pile up" job.
On applications that only need a little less resistance it may be worthwhile, but a better design would use another method.
But there is yet more more consideration here. The THERMAL conductivity of solder vs copper. The thermal conductivity of solder is lower than copper, so in effect it can even prevent the proper cooling of the copper underneath because it can act as a pseudo thermal insulator compared to the copper. If the thermal conductivity was too much lower it would definitely not act like more copper on top because the copper on the bottom would get hotter than it would without the solder even with less current flow though it, and that would again make the resistance rise.
A test would be to measure the resistances and try to estimate the temperature rise with various current levels.
I reluctantly add still yet another effect to consider, when working with significant frequencies (we've only really talked about DC effects so far). That's the skin effect.
The skin effect is the effect where the current tends to distribute itself around the outside of the conductor. Simply put, the copper will get about 1/2 the current and the solder about 1/2 the current that would normally be present near the surface of the copper alone. That puts the resistance at just a little over half of what it would be with pure copper, effectively making the AC resistance actually higher than lower. I dont think solder is very magnetically active, so we dont have to worry much about an increase due to that unlike if we used nickle plating instead. This all gets a little complicated though as we also have the proximity effect which may alter the current distribution in a manner that could favor the solder coating slightly better than with just the skin effect alone, but probably not enough to make a huge difference.
For DC currents this wont be an issue though.