I believe the whole discussion went thru a wrong route. The 431 and R3 come in to picture only when battery is nearing full charge and current needs to be regulated. the 317 should pass current irrespective of the value of R3, rather R3 can even be short circuited nothing thru is passing except adjustment current which is .1ma. we need to analyze it again from the beginning.

Here is my reason behind my argument.

First of all the LM317 works on the principle that it merely tries to maintain the output terminal at 1.25volts above adjustment pin. In this circute this 1.25 volts is the sum of drop across R1 , R2 and R3. In the beginning therefore there is no current thru 431 therefore all drop is across R1, R2 only. . When the battery isn't near full charge . When battery nears full charge the 431 starts conducting and there is a voltage across R3. again the told drop across R1R2 and R3 should still be same 1.25 volts. To achieve this the 317 reduces current from out terminal which means less drop across R1R2 and more drop across R3.. With this in mind I ask why shouldn't the battery not charge when R3 is 1k? unless there is current leaking some where thru R3 which reduces current to battery. Did we check up the voltage drop across R3, when we see the charger not working?

I believe analysis should center about the voltage drop distribution acrossR1/R2 and R3( the total always should be 1.25v). Did we shorting R3?
In my opinion the min or max current ratings thru 431 shouldn't matter when the battery is not near full charge.

 

Note that you are responding to a thread that died three years ago and that the thread starter has not been seen for over a year. Don't be surprised if you don't get much in the way of response.