ok, I think I have this right; so here goes. Again, any EE dudes out there speak up! I am a novice here.
First we need to assume that the Power Factor in a single phase AC inverter is 1.0 Anything else makes the "figurin'" too hard.
So, Power (in Watts) = Amps (I) x Volts (E) for both AC (PF=1.0) and DC
400 watts of Inverter Output requires how many amps of 12 volt input?
400=12xI solve for I and you get 33.3 amps of battery draw to produce 400 watts assuming no loss in the inverter.
So what can I power with 400 watts of AC output?
400 watts = 120 volts (E) x I (amps) Solve for I and you get 3.3 amps.
This is why you never want to power your 1500 watt AC coffee maker from your 2000 watt inverter. To create 1500 watts of AC you need to pump in 1500 watts of DC plus inverter loss; that works out to about 125 amps of 12 volt DC.
You need BIG wires to your inverter to carry that load. In fact the instruction manual for my 2000 watt inverter suggests a 175 amp auto-resetting fuse inline with the battery. Since my battery bank is 150 amp hours (2x75 AH); making coffee eats up nearly all my capacity (dead batteries) in about 30 minutes. I use a percolator or french press for my morning fix.
This is why Thomas Edison's scheme to power the nation with many safe low voltage DC generators; lost out to Bell and his idea of using less power stations but more dangerous high voltage AC.
Oh, and don't get me started about how long you have to run your generator to put those AMPS BACK IN!
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