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You "could" run a 120V 5A window AC unit off a 12V deep cell battery but, assuming 100% efficiency (something you can never get), you would need an inverter or motor-generator set and 50A out of the battery to run, and maybe 5 or 10 times that to start.

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Q: Can you run a 120 volt 5 amp window ac unit off a 12 volt deep cell battery with a 12 volt dc to 120 volt ac power inverter installed on the deep cell battery?
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