In general, nothing. Well, they’ll heat up like anything dark does under sunlight, but they won’t *do* anything, and the extra heat should be well within the panel’s ability to dissipate. There’s no completed circuit, so there’s either no flow of electrons, or extremely little flow. It isn’t wise to leave the thing disconnected for a *very* long time, like weeks, but a day or two would almost certainly not do anything meaningful to a typical solar panel.
Now, if it’s a relatively fragile type of panel, it’s possible that the extra heat could cause some damage. Further, in general, there’s really no *need* to leave it disconnected–it doesn’t cause any harm to let it run, after all, it’s not like you’re draining battery or the like. If you’re genuinely just not going to *use* the solar panel at all for an extended period (maybe it’s a cabin you visit only some of the time?), then it would be wise to cover it or store it away (if it isn’t fixed in place, that is) just to be very safe. But leaving it completely unplugged for a little while shouldn’t really do anything to it.
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