We cannot store AC in batteries because AC changes their polarity up to 50 (When frequency = 50 Hz) or 60 (When frequency = 60 Hz) times in a second. Therefore the battery terminals keep changing Positive (+ve) becomes Negative (-Ve) and vice versa, but the battery cannot change their terminals with the same speed so that’s why we can’t store AC in Batteries.
in addition, when we connect a battery with AC Supply, then It will charge during positive half cycle and discharge during negative half cycle, because the Positive (+ve) half cycle cancel the negative (-Ve) half cycle, so the average voltage or current in a complete cycle is Zero. So there is no chance to store AC in the Batteries.
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