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Assuming this could be done with no conversion loss a 20 watt load at 120 volts would require about 1/6 of an amp. A 7 ampere hour battery would run the load for 6 x 7 = 42 hours.

However, if you actually built a circuit to up convert 12 volts DC to 120 volts AC there would be significant conversion losses.

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Q: How long would a 12 volt 7 amp hour battery last if converted to 120 volts ac using 20 watts?
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