136 TREATISE ON ALTERNATING CURRENTS. 



and weakened when the current lag's ; and that the field of 

 a motor is weakened when the current leads before its 

 counter E.M.F., and strengthened when the current lags. 



89. Referring to Fig. 44, we conclude that when the excita- 

 tion of the motor field is small, armature reaction weakens the 

 field of both generator and motor, and when the motor is over- 

 excited both machines have their fields strengthened. When work- 

 ing at minimum current, armature reaction strengthens the motor 

 field, and does not affect the field of the generator. When the 

 field of the motor is unaffected, the generator field is weakened. 



90. In ordinary working conditions, it is usual to excite the 

 field of the motor to a somewhat greater extent than is required 

 to obtain minimum armature current; for, though the fir losses 

 are a minimum and the efficiency a maximum when the current 

 is a minimum, it is advisable to increase the counter E.M.F. to 

 a certain extent in order to cope with accidental variations of the 

 load. Under ordinary working conditions, therefore, the effect of 

 armature reaction is to strengthen the field of the motor and also 

 of the generator, but to a less extent. 



91. We now proceed to obtain an expression for the alteration, 

 in ampere turns, of the field excitation due to armature reaction. 



Let be the displacement of phase of the current over the 

 E.M.F. of the machine; N the number of turns of wire in one 

 section of the armature; i the E.M.S. armature current; A the 

 mean value of the current through an angle on each 

 side of its maximum value ; and t sin pt the instantaneous value 

 of the current. 



The mean alteration of the field excitation in ampere turns is 

 then 



2AN+ 



7T 



(11) 



where $ is expressed in circular measure. 

 But- 



dt 



... (12) 



