200 THE MAGNETIC CIRCUIT [ART. 72 



the synchronous speed. Therefore eq. (198) gives the torque of 

 an induction machine (including, as before, friction and hysteresis), 

 where the various quantities refer to the stator. However, these 

 quantities may equally well be taken in the secondary, but in 

 this case, since hysteresis occurs mainly in the stator, the torque 

 to overcome hysteresis is not included. 



Formula (198) is hardly ever used in practice, especially 

 for the computation of the starting torque, because it is difficult 

 to eliminate the large leakage flux which gives no torque. It 

 is much more convenient to determine the torque from the circle 

 diagram, or from the equivalent electric circuit. 



In case the torque is determined from the equivalent electric cir- 

 cuit, we can write from eqs. (195) and (197) the expressions for the 

 torque directly, by substituting for 6 its value 2ic -t- (R.P.M.) /GO. 

 For a direct-current machine, 



To* = 0.0325 p M Kg.-meters. . . . (199) 



Here the induced e.m.f. E = E t iR a , according to whether the 

 machine is a generator or a motor; E t is the terminal voltage 

 and R a the resistance of the armature, brushes, and series field. 

 For an alternating-current machine, 



. . . . (200) 



In a synchronous machine E is the induced e.m.f. and <f>' is 

 the internal phase angle. In an induction machine, iE cos 0' 

 is the power per phase delivered to the rotor, that is, the input 

 minus hysteresis and primary PR loss. The term (R.P.M.) is 

 in all cases the synchronous speed of the machine. 



Prob. 24. Two single-conductor cables from a direct-current machine 

 are installed parallel to each other at a distance of 16 cm. between their 

 centers, on transverse supports spaced 80 cm. apart. The rated current 

 through the cables is 850 amp. What is the force acting upon each 

 support under the normal conditions, and when the current rises to 

 twenty times its rated value during a short-circuit? 



Ans. 0.0737 and 29.5 kg. 



Prob. 26. A 4-pole, series direct-current motor must develop a 

 starting torque of 74 kg.-m. (including the losses). The largest possible 

 flux per pole is about 2.5 ml.; there are 240 turns in series between the 

 brushes. Calculate the starting current. Ans. 95 amp. 



