Ls wtf ,!

[tasdex]

Hey folks ,,,
Have I got a good one for all ,,
2005 ls petrol 5 speed .
Miss arrived this arvo ,complaining that our loved focus was stalling , had a wiring noise , battery light illuminated, message on green led saying power steel failure ..
Great .
Lift bonnet and checked the battery connections , then fired up ..no warning lights , still a wirry ," is that a word ,?" Noise from round the p/s top pump .
Turn the wheel slightly and bang , idle drops and recovers , battery light illuminated ,,slight sort of hesitation on the throttle when revved noted ..
OK ...bung a simple multimeter on the battery when motor turned off ,,,,12.88 volt
Turn motor on ,,,volts drop to 11.33 ,,! Wtf ,,should be above that to charge battery ,,!
OK ....
Plug my OB2 scan tool in ...
No codes or faults ,,!
OK ..
Pull the right headlight out to check the brake reservoir fluid level ,,,stupid spot ,and a pain in the **** to read levels ,,,,,,checked out fine .
Noted a small smell out of the ordinary ..hmmmm ,,sort of electrical burn smell ..?!?.
OK ,,,
Bunged the battery on charge for a few hours and recheched with multimeter ,,,13.7 while on the carger,,,,12.88 when charger disconnected ,,
Why , would all symptoms " lights ,warning on led , stalling , wirry noise , non charging , etc ,etc ,,,be all connected ,,!?!?!?
Any help /answers gladly received