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Your refer uses heat to make cold. There are 2 ways of doing that, LP flame or AC heating element. If the fridge isn’t working on shore power you need to check a couple of things:
First is the obvious, is there power at the outlet on the backside of the fridge and is it plugged in. If it is then you need to verify the glass fuse on the control board is good. After that you need to check for AC voltage at the element connections on the board.
If it passes all those tests then it’s time to test the resistance of the heating element.
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2012 Copper Canyon 273FWRET being towed by a 1994 Ford F350 CC,LB,Dually diesel.
Airlift 5000 bags, Prodigy brake control, 5 gauges on the pillar.Used to tow a '97 Jayco 323RKS.
Now an RVIA registered tech. Retired from Law enforcement in 2008 after 25+ yrs.