Question

why voltage across armature is constant while field current control method

Answer 1

In the armature control method, the speed of the DC motor is directly proportional to the back emf (Eb) and Eb = V- IaRa. When supply voltage (V) and armature resistance Ra are kept constant, the Speed is directly proportional to armature current (Ia). If we add resistance in series with the armature, the armature current (Ia) decreases and hence speed decreases.

$hope \: helps$