The DC motor that will have the percentage increase in input current for the same percentage increase in torque is a Shunt motor.
In a shunt motor, the field winding is connected in parallel (shunt) with the armature winding. The input current in a shunt motor is primarily determined by the field winding, as it remains constant regardless of the load on the motor.
When the load or torque on a shunt motor increases, the armature current increases to provide the necessary torque. However, the field current remains relatively constant.
Therefore, in a shunt motor, the percentage increase in input current for the same percentage increase in torque is relatively low because the field current remains constant. The increase in torque is primarily achieved through an increase in armature current.
On the other hand, in series motors, cumulative compound motors, and differential compound motors, the field current is not constant, and it varies with the load. As a result, the percentage increase in input current for the same percentage increase in torque is higher compared to a shunt motor.
Therefore, the correct answer is B: Shunt motor. A shunt motor will have a lower percentage increase in input current for the same percentage increase in torque compared to the other options given.