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Dual power supply for a processor

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do not solder to a Ni-MH battery cell because there is plastic insulation inside that will melt.

You need a battery charger circuit, not just a simple resistor.

If the battery is completely discharged then your 160 ohm resistor will supply an average charging current of 65mA and it will take (2800/65) x 1.4= 60.3 hours for the battery to become fully charged. A battery charger circuit can safely charge a battery in 15 minutes, detects that the battery is fully charged, switch the charging current to a low trickle current or turn off.
 
Where would I obtain a device such as that which I could incorporate into my own circuits though? I already own a commercial AA NiMH battery charger, but unless I can disassemble it and be sure that I can connect it correctly to my own device, it won't be much use for this purpose.

Thanks for the warning about soldering NiMH batteries; I had already decided that getting a battery holder would be a better solution anyway.
 
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Most semiconductor manufacturers make battery charger ICs. You switch between different battery types with a jumper wire or a switch. Two resistors set how many cells are in your battery. Sometimes a thermistor senses over-temperature to shut down the charger if something causes the battery to get too hot.
 
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