how to say recharging the battery and account

It's a Metaphor.

The information that flows from bank to bank electronically (and which we still call money) is in fact very similar to the electricity that flows from the wall socket to the phone.

  • they're both electrical in nature
  • they both raise the level of something fungible
    (money in the account, or battery charge)
  • they both fill a buffer to be depleted as needed.

So the metaphor is natural, though the technology may be too new to make the dictionaries yet.

But even electricity is a metaphor, since it uses concepts and words (flow, current, juice) borrowed in turn from water, another example of something with similar characteristics, as far as pumping is concerned.

In fact, Maxwell's equations, which describe the interaction of electricity and magnetism, are slightly modified versions of the hydrodynamic equations that describe the flow of a conserved fluid in a rigid container.

It's all Metaphor.