Alternate Current Transformer. 55 



where T=:|— + — =^- 



Tl To T 



Hence 7] is proportional to 1 — 2xs tan^SinS and the ratio 

 rj/rj' of the efficiencies of the same transformer, but differently 

 wound as above, is for loads of the same power factor, 



r) 1 — '2xg tani^SinS 



rj' 1 — '2x'g tan^SinS 

 =zl — 2{xs — x'g )tan(^Sin8, 

 = l + .OO328tan0Sin8, 

 as X, =—.00024, x's =.0014. 

 If Cos0, the power factor of the load, be .8, tan0:=.75, 



and "^ =1.0019 (taking 8=50°), 



V 

 and if Cos(^=.6, tan^ = 4/3, 



and 



^=1.0034. 

 V 



So that when the secondary coil occupies the two outside 

 positions the transformer will have for inductive loads, when 

 Cos0=.8, a greater efficiency by .19 per cent., and when 

 Cos0=:.6 a greater efficiency by .34 per cent, than when the 

 primary occupies the outside positions. 



For non-inductive loads the difference in efficiency will be very 

 small, as it then depends on the square of Xg, 



52. In § 41 it has been shown how, from the data for any 

 particular design, the dimensions of the carcass and approximate 

 values of the numeric t and of the efficiency can be quickly 

 obtained. 



Selecting from the series in § 41, transformer (c), of which the 

 the details are : — - 



Capacity 12.5 K.W. at 50 periods, 



2^'=3^, 2/3'=3/3, f3=lMU, t=6910, 



/*=2250, ^=12.9, Sin8=.766, ^^=.5, ^,=.7, 

 to which we will add E^=2200 volts=3111 . 10^ E, =311 . 10«. 

 let us determine its leakage coefficients and appi'oximate values 

 of its voltage drop for different kinds of loads if it be wound in 

 five sections, three secondary and two primary. 



