TL431 Constant current source
How to explain this circuit.?




Start from scratch imagining the transistor isn't conducting. Voltage across Rs is zero and therefore the TL431 is open circuit - but that's a problem because if it were open circuit (off) there would be decent base current into the transistor and Io would be large.

OK, look at it the other way, TL431 is conducting because Rs has enough voltage across it due to transistor being on - hey but this is wrong too because, if the TL431 were conducting there would be no voltage on the transistor base and therefore it isn't conducting and Rs has no voltage across it.

The goldilocks answer - the transistor is just conducting enough to allow 2.5 v to develop across Rs which in turn is just starting the turn the TL431 on and if it turned on too much, the current would reduce thru Rs and this would counteract the TL431 turning on too much.

It's called negative feedback.