The circuit is simple to construct. Regulator IC 7812 gives 12 volts regulated DC for powering the circuit as well as to charge the rechargeable battery. LED indicates the power on status. When the mains power is available, diode D1 forward biases and passes current into the battery through R2. Value of R2 is selected to give 90 mA current (12/100 = 0.1A) for slow charging.
When the mains power fails, D1 reverse biases and D2 forward biases and backup the circuit. The same circuit can be used in circuits having 6 volt 7.5Ah battery. For 12 volt battery, use 7812 regulator IC and 14 Volt input.