the battery lamp on the dashboard is mandatory to excite the alternator and hence start charging.

It is crucial that lamp be 3W only.

To test the alternator - get a 3W bulb and holder to test the alternator. The wiring on MB is usually junctioned in a heavy duty block near the firewall. the small dia alternator exciter wire is also there - undo it and use the bulb there. Key it on and you should see the bulb glow bright, start it and it should go out and the battery voltage should reach 14V.

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2012 BMW X5 (Beef + Granite suspension model)

1995 E300D - The original humming machine (consumed by Flood 2017)
2000 E320 - The evolution (consumed by flood 2017)