448 ELECTRICAL MEASUREMENTS 



currents in the rotor, which on account of the inductances of the 

 eddy-current paths lag behind EI. The equivalent value of 

 these currents is /i, which lags behind EI by the angle 7. Like- 

 wise, the equivalent current Iz lags behind E 2 . The turning 

 moment is due to the reaction between $1 and 7 2 less that between 

 4> 2 and /i. The fluxes and currents are assumed to be sine func- 

 tions of the time. The instantaneous torque will be of the form 



r = Kiifa Ki^i 

 and the average torque will be 



T = (/fti</>2 - Kitfa) dt 



cos (7 + 90 + ft - a ) - 



cos (7 + 90 + 2 - 0,) 

 sin (7 - (02 - 00) + X'fci/a sin (7 + (0 2 - 0,)). 



At any given frequency the induced currents are 



and 



where Z is the impedance of the eddy-current paths. 

 Therefore, 



T = - -- { - sin (7 - (02 - 00) + sin (7 + (0 2 - 00! 



= - -^- - cos 7 sin (02 00. (1) 



The accelerating torque is proportional to the product of the 

 two fluxes, to the sine of the time-phase angle between them, 

 and to the frequency. 



If the armature is in motion, there will be a retarding effect 

 due to its movement through the two alternating fields. This 

 retarding effect will be proportional to the mean square values of 

 the fields and to the angular velocity of the armature a/, or to 



