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Notes -
Note that size only matters here if it's the size of a conductor (i.e. metal) attached to a semiconductor, not the size of the semiconductor itself (because the semiconductor's resistance also depends on size and that cancels out).
But that's kind of irrelevant; yes, photovoltaic solar cells are low-voltage semiconductor devices (specifically, they're giant diodes) and are thus likely toast if exposed to EMP. Solar-thermal can be EMP-proof, as there's no specific need for semiconductors and metals don't really care about EMP, but AIUI solar-thermal generators are more a thing for power stations than something remotely portable.
Metals do care about EMP but only by heating from the induced currents. This is why power delivery networks are going to be toast and can have problems even from major geomagnetic storms. For shortish length and reasonably large surface area (ie. most things you're likely to have at home), it of course won't be a problem.
So really two mechanisms: field strength induced overvoltage breakdown in semiconductors and heating from high currents induced to long wires.
It's specifically the transformers that are vulnerable to E3; the extra voltage/current buggers up the assumptions that go into their design, so they lose efficiency (efficiency at transmitting the normal power from power stations) and, yes, overheat. Of course, power grids don't work without the transformers, but the long wires themselves are in no danger (we know that one experimentally due to the Carrington event).
But yes, transformers are metal and they are vulnerable if not unplugged.
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