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Since installing a 5000btu window ac in my TC I've been looking into getting a generator or more solar so I can do more dry camping and I'm curious if I upgraded from my single lead acid battery to a 300ah lithium and installed a dc/dc charger how long the truck would take to charge the 300ah battery with a 140a alternator while running at high idle?
This is very very rough math that you are asking about, so here goes:
Assuming the 300ah battery starts from dead, and also assuming that the truck has ~30A of responsibility just sitting there idling, with no lights or HVAC or anything else turned on, I'd guess that a 140a alternator would take 3-5 hours to charge a 300ah battery, depending on many variables.
It depends on the size of the DC-DC charger. They're rated on the output side, so a 10 amp unit will charge 10 amps. On the input side, that charger will pull as much as 15 amps, depending on what the input voltage is.
As far as how long to it takes to charge the house battery, using the 300 Ah battery proposed, a 10 amp charger would require 30 hours. 30 amp charger requires 10 hours. LiFePO₄ batteries are efficient enough at being charged that we tend to use a straight calculation. 10 amps of charge is 10 amps that goes into the battery. It's not 100% efficient but darn close.
The bigger the charger (more amps) the bigger the cables have to be to support those amps. My house battery doesn't get any charge from the tow vehicle because I have enough PV. If it did get a charge from the tow vehicle, I would probably limit the DC-DC charger to something like 8 amps so I could use the existing 7-pin wiring.
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