The correct answer is: A. Independent of armature current.
In a D.C. shunt motor, the speed is independent of the armature current. This is because the armature current is only responsible for the torque produced by the motor, while the speed is determined by the field current. The field current is the current that flows through the field windings, which are located around the stator of the motor. The field current creates a magnetic field that interacts with the current flowing through the armature windings, which produces the torque that drives the motor.
The speed of a D.C. shunt motor can be controlled by adjusting the field current. Increasing the field current will increase the magnetic field, which will increase the torque and decrease the speed. Decreasing the field current will decrease the magnetic field, which will decrease the torque and increase the speed.
Options B, C, and D are incorrect because the speed of a D.C. shunt motor is not directly proportional to, proportional to the square of, or inversely proportional to the armature current.