Charging system problem light came on

[GasSavers_rGS]

The battery shaped indicator light came on last night. I was able to complete my errand and return home safely. Now I retested the electrical system using a DVM. With the engine off, the battery was reading 12.34 V. With the engine on, the battery was reading 11.xx V.

Questions:

1. What would cause an electrical system to be at a lower voltage when the car engine's on?
2. Would the OBD-II computer code help to diagnose the problem?
3. Are there any other tests I can do to diagnose the problem?

I would prefer to leave the option of taking my car to the mechanic/dealership as the last option. Thanks in advance for replying.