What is the relationship of the armature voltage and field current and how can this relationship affect the DC shunt Generator?
By &quot;shunt generator&quot; I am assuming you mean the field winding so connected directly or via a resistor onto the armature.  When you start spinning the generator here is what happens.
The little remaining magnetic field in the parts causes a little voltage to be produced.  This little voltage makes a little field current which make it produce more voltage which makes more field current and on an on and on.
The voltage doesn't rise to infinity because at some point the iron in the field coils starts to saturate so more current doesn't make much rise in the strength of the field.