Why battery can’t store AC supply?

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.

We cannot store AC in batteries because AC changes their polarity upto 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.
Also 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.
Also note that Average Voltage x Average Current ≠ Average Power.
 

Battery is a static charge accumulator device. That is, the charge stored on the plates in form of chemical reaction is in static in nature. As a result, the power stored in the battery is static is nature thats direct current (DC).