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A datasheet for a power connector I was looking at tonight has this warning:

Note:

Do not branch in parallel current which exceeds the rated current. If branched in parallel, current imbalance or other problems may develop. If it is absolutely necessary to branch such a large current in parallel, be sure to use contacts made of phosphor bronze. Design the circuits without causing imbalance and provide an extra margin for each circuit.

The connector has a current rating of 10A and has crimp pins that support 16AWG wire so presumably each pin of the connector can support 10A.

I read the language "do not branch in parallel current that exceeds the rated current" to mean that one should not draw more than 10A total across some number n of pins all hooked to the same power source.

I'm guessing it's a safety feature in case one wire of a parallel group were to break so that the remaining wires don't immediately have to take on a much higher current but I would like to check my understanding here.

Am I interpreting this correctly?

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Because of the variation in contact resistance between mated pin/socket sets, two sets in parallel carrying twice the current meant for one will divide the current in inverse proportion to their resistances, with the higher resistance set shedding current the low resistance one must carry.

For example, with a 20 ampere source feeding a 10 milliohm resistance in parallel with a 20 milliohm resistance, 1/3 of the current (6.7 amperes) will flow through the higher resistance, while the remaining 13.3 amperes will flow through the lower resistance, exceeding the 10 ampere current rating of the low-resistance contact set.

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