What is the name of the device that sense low battery and automatically starts the charging system ?
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"What is the name of the device that sense low battery and automatically starts the charging system ?"

Outside a car : it is part of almost every professional battery charger.
Inside a car : it is part of the continuous charging system.
In both cases it is an electronic circuit that checks the status of the batteries (a regulator).

Have a look HERE , HERE and also HERE for more information...

:)

Way back it was separate and mechanical and was called a "voltage regulator". Today, it's solid state and internal to the alternator and basically turns on and off the rotor field current to regulate voltage.

In india, it is called as cut out system.