Alternate Current Transformer. 9 



The constants tj and t^ for a transformer of 1 K.W. capacity at 

 50 periods would in no case be less than 1200, and it will be 

 shown in Section III. (§ 55), that for similar transformers they 

 are proportional to the square root of the output, and to the 

 square root of the frequency. 



The greatest practical value of 6 or 6' for any transformer will 

 not be much above 



V 



^ where r is the mean of r, and t^ 



unless in case of excessive overload. 



The leakage coefficients Xi and x^ should each be less than 

 .002 ; and in transformers whose coils are wound in sections and 

 interleaved they become very much smaller. 



8, the angle of magnetic retardation, will lie between 40° and 

 55°, its value depending on the quality of the iron, thickness of 

 laminae, flux density and frequency ; hence SiuS will have a 

 value between .65 and .8. 



[The formulse given in this paper are only roughly approximate 

 when applied to open-circuit transformers, as will be explained 

 further on. 



For them the t constants are roughly .05 -.04 times the 

 constants of closed-circuit transformers of the same capacity 

 while SinS=.15— .08.] 



1 _ 1 tan^c^' 

 12. Since ^,2^^^^,^,-^,+ -^7^ 



1 tan0' 



we find on substituting for ^, and — ^7— from equations I. and II. 



of § 10 that 

 ^Cos<^ 



,=M 



6'Cos(/>' 



where M^ = 1 + 2 (x^Sincji + -^\ ^Cosc^ + ^.v/ + -,] ^^Cos ^ 



From § 4 we have 



A'!__i^2Sin(8+^) J^ 



6'^CosV'~ ^'Cos<^' ' r-'CosV 



2Sin8 ^ „tand)' 1 tan^' 

 =: 1 + —^ + 2CosS-^ + ^, + -^ 



substituting as before we find that 



A"^ _ A'' 



e'^Cos>'~^'-^Cos> 



