Final answer:
The speed of the motor can be calculated using the relationship between the back emf, armature resistance, and voltage, as well as the relationship between torque, back emf, and speed.
Step-by-step explanation:
The back emf constant of a PMDC motor is a measure of how much voltage is induced in the motor's coils per unit of angular velocity, while the armature resistance is the opposition to the flow of current through the motor's armature. In this case, the back emf constant is given as 40mVs/rad and the armature resistance is 10Ω.
To find the speed of the motor, we can use the relationship between the back emf, armature resistance, and voltage. The back emf can be calculated using the formula: Back emf = Voltage - (Current * Armature resistance). In this case, the voltage is 12V, the current is unknown, and the armature resistance is 10Ω.
If the motor produces an electromagnetic torque of 30mNm, we can use the relationship between torque, back emf, and speed to find the speed. Torque = Back emf constant * Current. In this case, the back emf constant is 40mVs/rad, the torque is 30mNm, and the current is unknown.