ARMATURE REACTION. 23 



induction. The value of the armature reaction at any instant is 

 therefore, by 13, Chap. II., equal to 



d(Li) 

 dt 



This is variable, since i is a function of the time, and the value 

 of L depends upon the variable position of the armature coils 

 relative to the field poles, and also upon the induction in the iron 

 of both armature and field magnets. 



There is also another source of variation of the magnetic field 

 which should be included under the head of armature reaction. 

 The variation of the flux produced by the armature currents will 

 induce a variable current in the field-magnet coils, and a conse- 

 quent variation of the flux due to the field coils themselves. This 

 variation is proportional to the mutual induction between the 

 armature coils and field coils. Under the same heading may be 

 included any variation in the strength of the field due to eddy 

 currents induced in the field magnets. 



We shall not, however, for the present, inquire further into 

 the effect of armature reaction upon the E.M.F. of an alternator, 

 but shall content ourselves with the assumption that both the 

 E.M.F. of the alternator and the potential difference between its 

 terminals are capable of representation by means of sine (or 

 cosine) functions of the time. 



19. We now proceed to obtain the relation between the 

 current, the E.M.F., and the constants of a circuit in which we 

 can treat the self-induction as constant. 



The product of the coefficient of self-induction and 2?r times the 

 number of complete cycles per second is called the Reactance 

 of a circuit. An extended definition of reactance is given in 45. 



The number of complete alternations per second is called the 

 Frequency, and is usually denoted by the letter n. 



The time taken for one complete cycle is called the Periodic 

 Time. 



We shall denote the whole electro-motive force round a circuit 

 by the letters E.M.F., and the potential difference between any 

 two points in a circuit by the letters P.D. 



