I assume you are talking about two RCD's in line ? One on the external power, i.e. an rcd outdoor socket and you have an rcd your consumer unit in the house, yes ? If they both have the same tripping current, 30ma is the 'norm' they will both trip if the external one is tested using the test button. If you have an rcd your main supply you don't actually require the second one.
They should not both trip if the RCD being tested has the usual test circuit is a resistor between Live on the output and Neutral in the input. There is no current to Earth during the test so the other RCD should not trip as a result of the test. ( There is no Earth terminal on a normal RCD so no route for current to Earth from the RCD )
The other RCD may trip as a result of a fault that has an effect when power is removed by the tested RCD tripping.
Indeed. If you recall, I did some experiments a while back, and all the (active) RCD sockets I tried worked like that. We had a lot of discussion about the reason, and I think we concluded that the reason might be that the test button would then test the adequacy of the earth/CPC at the socket, as well as the RCD functionality per se.
You will probably also recall that I found that some of them tripped if one removed the CPC, and could not be reset without an 'adequate' earth connected via the CPC. The explanation may be the same as the above (and more - i.e. the socket could not be used unless it had an adequate earth connection), but I still am not quite sure how they achieve that functionality!
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