In the schematic we have used a 12V lead acid battery. An adjustable power supply is essential to set the circuit for the first time. You can also use a LM317 adjustable power supply.

A 12V lead acid battery becomes weak when it shows 11.9V on the multimeter, so the starting point of the charging should be set on 11.9V. For setting the first VR1 to this point simply connect the power supply in the place of battery and set 11.9 volts in the power supply and adjust the VR1 to switch ON the relay and switch off the green LED.

When a 12V lead acid battery become fully charged with the charger or power supply connected it will show 14.4V.  So set the power supply to 14.4V and this time connect the positive lead of the power supply with the NC of the relay and adjust the VR2 until the red LED goes off. After this setting the circuit will be ready to charge any 12V lead acid battery. The circuit is using a 1A transformer therefore it is suitable for charging 12V 10AH to 12AH SLA batteries. But for charging higher AH batteries use 5A to 10A output current transformer.

The circuit can also be used to charge 6V SLA and other type of 6V, 9V and 12V batteries. For making the circuit to automatically charge 6V SLA batteries simply the change the 6.2V zener diode to 3.3V and 9.1V zener to 5.1V, and set the charging start point to 5.9V and stop point to 7.2V with the above procedure.

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This article describes a very easy circuit of 12, 9V, 6V automatic battery charger. The circuit can be set for charging different voltage batteries. There are two different set points are given in the circuit which are VR1 and VR2 with these points you can adjust circuit to charge different batteries from their desired voltage level.
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12V, 9V, 6V Automatic Battery Charger Circuit Diagram