VARIABLE ELECTROMOTIVE FORCE. 511 



535. VARIABLE ELECTROMOTIVE FORCE. Suppose that the 

 electromotive force, instead of being constant as with ordinary 

 batteries, undergoes periodical variations, and is represented by an 

 expression of the form 



(n) E = E sin 27T . 



When the steady condition is obtained, the intensity of the 

 current evidently follows the same period, and may be represented 

 by the expression 



(12) 



/ -- (j>\ 



Substituting this value in equation (i), and determining the 

 constants A and <f>, by the condition that it shall be satisfied for 

 any given time, we find 



(13) 



^2 



and 



277-L 



(14) tan 27Td> = . 



TR 



It will be seen from this that the effect of the coefficient of 

 self-induction is to increase the apparent resistance of the circuit. 



T 



The strength of the current is zero whenever /-<T = # . The 



2 



value <T expresses the time which elapses from the time at which 

 the electromotive force is zero, and that when the current itself 

 passes zero. It is a kind of retardation to the transmission of 

 the electromotive force, which arises solely from the effects of 

 induction. 



Whatever be the values of L, of R, and T, the maximum 



value of 27T(f> is - , that is to say, that the difference of phase <f> 



is equal to -. The maximum retardation of the induced current 



4 



is therefore equal to a quarter of the whole period, or to half 

 the semi-period. 



