First off DO NOT plug I to dryer. Dryer is 220 volts camper is 110, it won't be pretty.
Yes you need a charged 12 volt battery. 12 volts controls a/c, (water heater, furnace and ref. also) but 110 operates a/c, water heater and ref. Even if using gas for water heater, furnace and ref you still need battery 12 volts to make them work. A/C will not work off 110 volt 15 amp extension cord need a dedicated 110 volt 30 amp service for the camper.
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