generate electricty

Is 'generate' the correct word?
How do trains generate electricity? How come I can plug my phone in on the train and charge it?

Would you say that the socket isn't powerful if it doesn't supply as much electricity/ current? How would you say:
The socket on the train aren't very powerful. They don't supply as much electricity/current as my home socket. It took me 4 hours to charge my phone which usually takes 2 hours.

Thanks