I'm not an electrician or engineer, Soochu, but 'supply source' is the general term, and 'the mains' (as you said) is from the infrastructure, while a 'supply apparatus' would likely be something like a private generator or a windmill or a battery. Yes, you can say 'catch' instead of 'understand', but 'catching' is a more shallow process than 'understanding', so should be saved for brief bits of information input.
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