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Battery draw on most inverters nowadays is more than 10 times the ac draw since they are roughly 90% efficient. So if the fridge draws 3 amps max of 120vac or 360 watts, what you will see off the dc side is 30 amps or 360 watts on 12vdc PLUS that extra 10% for a total of about 33 amps of 12vdc.
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2012 F350 6.7 L dually, 2013 3800RE with 6 pt leveling, Sumitomo 17.5" load range h tires, Samsung 18 cu ft residential fridge, 8k Morryde I.S. with disc brakes. Full timing since 2012.
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