Alternate Current Transformer. 33 



they are 



=2795.10=^^^(^+^). 



32. As we intend that the copper and iron losses shall be 

 equal at full load, 



2795^-(^ + g)^^ 3^ 



or J^ .5152 

 ?r(« + 2) 



where u^/3ji>, 



from which equation ?e (the positive root) can easily be determined 



by trial (using a slide rule) and is =1.151, 



hence y8=1.151^. 



33. The output P^, being 10 K.W., that is, 10" ergs, per second, 

 and (see § 13) as 



we find, using the approximate value for — given in § 31, that 



P'.j, the total power developed in the secondary is 

 = 1.01 . 10", 

 but P'.,=iE'2C,Cos0' 



=hzvfi.:^C.2Cos(f>' ; 

 hence, using the value of Cos(/>' given in i^ 31, and remembering 

 that w=2-nr . 50=1007r, 

 202 . 10'-' 

 "■2^2^=100^ . .808' 



=796 . 10". 

 Now C2 being the permissible current density = 12.91 (see § 30) 

 «A=^2^2-f.= 12.91 . 1.1 53<^-^ 

 = 14.9^^ 

 and y being the permissible flux density=4847, 

 F=4;^/5'-^y=3.6 . 4847 . ^\ 



= 17450/3'. 

 u- ,.,^, 796 . 10' 



«""" ^"^ - 14.9 . 17450 -="^«^ 

 and as ^==1-151^ 

 we find that /3=7.98 and ^=6.93, 

 which determine the carcass of the transformer. 



