Why do rechargeable batteries (e.g., mobile phone batteries) need sometimes several hours to be fully charged? In other words, what are the physical constraints that don't allow me to charge my iPhone battery in 1 min, for instance?
I will give you an easy answer on the limit to charging rate, rather than the reasons for existing charging rates. If we assume a 2Ah battery capacity it means that it take (approximately) one hour at 2 amps to charge the battery. If, say, you wanted to charge it in a convenient 1 minute the battery would have to be fed with 120 Amps. That is far more than even domestic mains wiring is capable of taking, let alone the thing wire of existing wall wart chargers or the internal contacts in the phone electronics. The same kind of reasoning applies to electric car battery charging as well.