73^ INDUSTRIAL APPLICATIONS. 



For a machine, the factor to is the product of the angular velocity 

 by half the number of reversals of the current at each turn. 



The expression for the current, starting from the closing of the 

 circuit, contains first an exponential ; but, if the regime is permanent, 

 the current itself is sinusoidal, and of the form 



with the conditions 



OX 



. A 2 = 



K* + 



Lw 



tan 27r< = . 

 R 



The coefficient A represents the mean intensity of the current, and 

 27r< the difference of phase, being the fraction of the period which 

 elapses between the moment at which the electromotive force is null 

 and that in which the current passes through zero. 



The quantity \/R 2 + L 2 w 2 may be called the apparent resistance; 

 the effect is as if the square of a fictive resistance Lo> proportional 

 to the velocity, was added to the square of the real resistance. 



The mean square of the intensity 



A 2 QX 



2 2(R 2 + L 2 0> 2 ) 



is equal to the quotient of the mean square of the electromotive 

 force by the square of the apparent resistance. This value does 



not increase indefinitely with the velocity, it tends towards a limit 



O 2 



"r. independent of the resistance. 



2L, 



The difference of phase increases with the velocity, and at the 



7T I 



limit we have 27r<i> = , or </> = -. 



2 4 



1281. The energy expended in unit time is 



