Broken AC belts blows blower motor resistor?

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Here's a weird one. My blower motor resistor failed this spring. My AC failed sometime last winter but I didn't bother to fix it.

When I went to use the ac one day the fan stopped working, so I replaced the resistor and it worked until I turned on the ac and the resistor blew. So I started looking around and found the AC belt was broken and replaced that then replaced the resistor and it's been fine since. So that's twice that I powered up the AC with the broken belt and it blew the resistor. I know that the AC switch, at least, and the blower motor are on the same circuit but have no idea why those would be related.

Just thought I would post here for food for thought. Our Isuzu isn't a P'up as it's a 1995 but I think they have a lot in common.