Am I supposed to charge the battery with the camera on?

I recently upgraded from the Pocket. Having used a bunch of batteries for that one, I now have to deal with the Powerbase on the BMCC.

The camera I bought is used and didn't include the charger/adapter, but the Switronix PB, so I guess I have to charge it with the Powerbase directly. However, I left it charging for about 4 hours and the camera not only was still at 75% but also died in less than 20 minutes.

Is this normal? Should I be charging from the Powerbase while the camera is on? How long does it take for it to charge?

The camera will charge faster when turned off, more current is available to charge the battery.
Cheers

I'd just find out the voltage for charging and find a outlet charger that matches. Usually the wall will charge much quicker than a DC battery pack.

Try 12 VDC at 1.2 to 2 amps. That should do the trick.
Cheers

Will the wall charger charge the camera when the camera is turned off?
Thanks

Yes, and that is the preferred mode to charge the battery.