Well, you can make a very high speed flow of water in a straw. Realistically speaking, no matter how fast you make the water flow in a straw, it will take some time to fill a large tank.
The speed of electricity is not the issue, the question is how fast can a battery or capacity store ENERGY.
Chemical batteries can only accept a certain amount of charge per second (chemical reactions are not very fast in a battery). Therefore it is not relevant how fast electricity “moves” but how much charge can be accepted.
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