Input voltage is only relevant as a reference.
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2.5v is where the protection circuit should trip. The battery will typically rebound back to 3.0v or 3.3v using a 2.75v protection, anything lower and you are damaging your batteries.
http://lygte-info.dk/info/BatteryLowVoltage UK.html
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I believe the LM117 has a built in voltage reference of 1.25v so:
R1 = Vref/Iout
Vref = 1.25V so for 500 mA
R1 = V/I = 1.25V / 0.5A = 2.5 Ohm
Power in R1 = I^2 R = 0.5^2 x 2.5 or 0.7 Watt
So you would want to use a 2-5 watt resistor.
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Some circuits can handle 1 amp which will decrease the test time.