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400 Ah battery means it will power max an appliance using 40A for 1 hour. 10A appliance will run 4 hours. I am sure that AC will need more than 10A. You can get consumption of an appliance from its sticker which shows power consumption in W (Wat). A = W / V. Example: consumption = 120 W, 12V battery A = 120W / 12V = 10A. Your battery capacity is 400 Ah. It will run h = Ah / A = 400Ah /10A = 40 hours
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