Zener Diode Current Source
With an 8.4 volt supply producing 1 amp to supply your load of 0.97232Ω you need to have a total resistance of 8.4 ohms (ohms law is still cool).

As you have only 0.97232Ω you need to put 7.42768 ohms in series.

That will produce 1 amp thru your load. It will also dissipate 7.42768 watts so choose a resistor that is rated for the power.

If, for whatever reason it must be a transistor current source and you need the accuracy of exactly 1 amp I wouldn't use the circuit in your question, I'd use an op-amp controlling the emitter voltage of a transistor like (7) in this below: -



The LM317 circuit I feel would also service your needs BUT, at the end of the day, with an 8.4 volt supply, something (usually the transistor) is going to be burning 7.42768 watts so get big components or a heatsink. It can be a BJT so don't worry too much about (7) showing a MOSFET.

Alternatively, use a switch mode current converter powered from the 8.4 volts and let the inductor and capacitor do what god made them for - taking energy in at one end (at higher voltage) and spitting it out at the other (but at lower voltage).

Smallprint - L and C can do the reverse too and I don't really believe in god, but it sounded cool to say that he invented L and C!