100 TEEATISE ON ALTERNATING CURRENTS. 



we see that the output is given by 



W = J&{a(arj - W) + b(br 2 ' + as,')} 



Again, the primary current is given by 

 (r a 





Jca 

 4- a2 4- 



Therefore the input, W 7 ", being the scalar product of e and ii, is given 

 by~ 



(6r 2 



~ 



the efficiency r) is thus given by 

 T) = ~W ^ ~ 



which, by the help of (14), may be written in the form 



Here n is the ohmic resistance of the primary coil, E its equiva- 

 lent resistance, given by equation (14), r 2 is the total secondary 

 resistance, and r% the resistance of the external secondary circuit. 

 The above expression for the efficiency does not take into 

 account the iron losses due to hysteresis and eddy currents, but 

 these can be allowed for in the following manner: 



