CHAP. XIII] TORQUE AND TRACTIVE EFFORT 261 



Prob. 26. Explain the reason for which the compensating winding 

 (Art. 54), while removing the armature reaction, does not affect appre- 

 ciably the useful torque of the motor. Hint: this can be shown by 

 applying the method of virtual displacements; also from the fact that 

 the local distortion of the flux in the teeth is not removed. 



Prob. 27. On the basis of Art. 15, explain the mechanism by which 

 the phenomenon of hysteresis in an armature core causes an opposing 

 torque. Explain the same for eddy currents. 



Prob. 28. Demonstrate that formula (193) may be used for slotted 

 armatures, provided that B stands for the average flux density per 

 tooth pitch. Hint: take a virtual displacement of one tooth pitch, 

 and express the induced voltage through the flux J<D=Btt per tooth 

 pitch. 



Prob. 29. Show that in a single-phase synchronous motor the 

 torque at the synchronous speed pulsates at double the frequency of 

 the supply; also that the torque is zero at any but the synchronous 

 speed. 



Prob. 30. Prove that in an induction machine the torque near syn- 

 chronism is approximately proportional to the square of the voltage 

 and to the per cent slip. Hint: t= Const. X Xslip. 



Prob. 31. Describe in detail how to calculate the maximum starting 

 torque of a given induction motor, and how to calculate the amount 

 of secondary resistance necessary for a prescribed torque. 



