A 4- pole DC motor is known to have an armature resistance of 0.5 Ω, and is operated as a separately excited motor.

(a)  When the motor is connected to a 250V DC supply with no external mechanical load and with rated field current, it runs at a speed of 1488 rpm with an armature current of 4A. Calculate the no load rotational losses under these conditions.

(b)  The motor is now mechanically loaded until the armature current reaches 40A, under which conditions the DC supply voltage sags to 245V. Calculate the motor speed if the field current is unchanged.

(c)  Assuming that the motor rotational losses vary proportionally with speed, calculate the motor efficiency under the load condition of (b).

(d)  The motor field current is now accidentally set to half rated value. Calculate the DC supply voltage that is required to return to the same no load operating conditions of part (a)

(HINT: remember that the rotational power losses must stay the same if the speed is unchanged).

(e)  Discuss the two possible ways of achieving variable speed operation for a DC machine. Show the torque speed characteristics of a DC motor operating under both these types of speed control strategies, and discuss how they relate to the concepts of the "constant torque" and "constant power" regions of variable speed operation. Discuss the advantages and disadvantages of each speed control strategy.