BMW suggests leaving the key inside the car in position 1 for 24hrs to wireless charge the key, but this isn't an option if you live in an apartment and don't have a garage. I'm trying to figure out how to charge the key from a home outlet and purchased an Adafruit Induction charging set to play around with. It's nice to have a fully charged key so you have a nice and long operating range. Sometimes after a while of not much driving you'll find the key range getting shorter and shorter. Some say they've had luck with certain toothbrush chargers but I wanted to do some more research.
So as I understand the receiving end usually handles all the voltage regulation and protection in this sort of setup. With stronger inductive coupling I should get more current draw from the transmitting end and faster charging.
I found that the circuit drew the most current when the key was placed with the roundel facing the inductive charging loop. (about 75mA over the idle current) I'd be interested to see how the coil is positioned within the inductive charging assembly in the vehicle itself to compare. Has anyone taken one apart to see the insides of one? Maybe I'll just buy an old one off of eBay to satisfy my curiosity.
The Panasonic VL-2020 battery used in these has a capacity of 20mAh and standard charge current of only 1.5mA, so you should be able to hit a full charge in well under 20hrs.