Can a 6V rechargeable battery be charged to 5V after complete discharge?
No. As tomnexus has pointed out you need a voltage higher than that of the battery before it will charge properly.

An inverter is a circuit to convert DC to AC. These are most common in small UPS power supplies where a 12 V battery powers a circuit to convert to AC and step up the voltage using a transformer.

The circuit you have sketched is not an inverter but is a crude DC UPS. There are a couple of problems:


The diodes drop 0.6 to 0.7 V so the most you can possibly get out of your circuit will be 4.3 V.
You have the same problem with the 5 V rechargeable battery. You can only get 4.3 V at the battery and if it held any usable charge you would lose another 0.7 V on the way from D to C dropping you to 3.6 V.


Your best bet would be to use a 12 V battery (an old car battery would work and even if not much use for a car would run a Pi for a long time) and a car battery charger. Then use a 12 V to 5 V converter to power the Pi.







simulate this circuit &ndash; Schematic created using CircuitLab

Charge the battery while power is available. The Pi can run off the battery while it is charging. You could use a car cigarette lighter to USB adapter to power the Pi or use a voltage regulator, as shown. (If you're using the regulator you need to add some capacitors to the input and output terminals to prevent oscillation. There are lots of examples of this on the web.)