Problem:
When you're using the device with external monitor, you are probably doing things like watching a movie or browsing the net through wifi or 3G network, which drain the battery.

It would be great to be able to plug the device to the monitor, do what ever you want, and leave with a fully charged battery.

Solution #1:
HDMI supplies a minimum of 55mA current on the 5V line, but most source devices on the market today provide significantly more current on the 5V line than the HDMI specification requires. (http://www.hdmi.org/learningcenter/kb.aspx?c=13#42)

Use this current to charge the battery while the HDMI is connected.

Brainstorm proposal