a 6V battery a separate charger is required. The circuit shown here is able to charge both voltage batteries either it will be a 12V or 6V. It detects the voltage of the battery and auto selects the required input voltage to charge the battery connected. It can be used to charge Lead acid, sealed lead acid and other types of 6V and 12v batteries.

Setup
To setup the circuit few adjustments are required for the first time. For doing so remove the battery from the circuit and disconnect the 1K resistors from point 1 for temporary basis and connect it with positive rail of the 18V 2ampere power supply. Now connect 18V 2ampere power supply with the circuit and connect a DMM at the output of the LM317 and adjust the VR1 until the output voltage of LM317 shows 7.5V. After that reconnect that 1K resistor to its original place i.e. point1. Now disconnect 1K resistor from point 2 and connect it with the positive rail of the 18V 2ampere power supply and adjust the VR2 until the output of the LM317 shows 15V in the DMM. After that reconnect the point 2 to its original place.
Now remove the 18V 2ampere power supply from the circuit, take a separate  adjustable power supply set its output voltage to 7.2V  and connect it to the point3 (+) and ground / negative of the circuit, then slightly adjust 50K pot1 and stop on the point where relay gets deactivated. Now set 14.4V in the adjustable power supply and adjust pot2 and again stop on the point where relay gets deactivate. After these adjustment the circuit will be ready to use.  Remove the adjustable power supply from the circuit connect the input 18V 2ampere power supply and connect the desired battery.

Note: For charging high ampere batteries LM338 IC can also be used in the place of LM317 with 10 ampere didoes in the place of both 1N4007 diodes used with LM317.


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Here is the project of an automatic 12V & 6V battery charger with auto battery detection function. Normally  battery charger circuits or devices are built to charge single voltage battery for example to charge a 12V battery a 12V charger is used but it cannot be used to charge a 6V battery, for charging
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6V & 12V Battery Charger With Auto Battery Detect Function