250 ALTERNATING CURRENTS 



enables us to obtain an expression for the mean value of the mean 

 square of the current in the coils included between two slip- 

 rings. Ee turning to expression (4), we notice that the first 

 two terms are constant, while the mean value of the last term 

 is given by 



-- II N x mean value of cos ( ~ >j) between < = and (j> = 



N 



= - - X COS ~ 



Hence the mean value of the mean square of the current in a 

 group of coils between two slip-rings is 



or, using (2) 



2 -- -1553\F 



Hence the mean rate of heat production in the armature is the 

 same as if each of its coils were traversed by a continuous current 

 of amount y/K . I, where 



K = - - -- 01553 ...... (5) 



N 2 sin 2 g 



or as if the armature were generating a continuous current of amount 



If we assume, as before, that the limit of output is fixed by the 

 permissible rise of temperature, and if VI = maximum output of 

 armature when acting as a converter, then its output as a continuous- 

 current generator is equal to 2y^K . VI, or 



converter output = , x continuous-current generator output (6) 



