Alternate Current Transformer. 



This flux is produced by the auipere-turns 



w^Ci + WjC,, (a vector sura) 



so that Arnp.F or F = o-aiiip.(«,Ci + WoCg) 



where cr = ivr x permeance of the magnetic circuit. 



. Section of iron „ , , . . 



= '+7riu ; , tor a closed circuit, 



Mean Jength of iron 



and F is behind ;/jCi + WjCo in phase by an angle 8. (See >; 1). 



[It will be shown that, tliroughout the range of operation of a 

 transformer, when the primary volts and frequency are fixed, F 

 is very nearly constant, S(j that 8 and /x will be very nearly 

 constant. On referring tu Fig. 1, it will be seen that 8 is fairly 

 constant in any case in the neighbourhood of the flux densities 

 generally used in transformers, and though, at the same densities 

 /xis changing rapidly, we shall not, on account of the approximate 

 constancy of F, introduce much error by assuming both 8 and /x 

 constant during the operation of the transformer.] 



Hence from O draw OM, ahead of OR by the angle 8 = ROM, 

 and in length equal to F/o-. 



OM fully represents n-^G^ + n.^C^. 



In addition to the magnetic lines forming the main flux F and 

 looped on both circuits of a transformer, tliere are others, the 

 leakage lines, which are only partially looped on the circuits 

 and whose action must be taken account of. 



In Section III. of this paper it will be shown that, after the 

 transformer is somewhat loaded, the effect of these leakage lines 

 on its operation is the same as would be produced by two fluxes ; 

 one, the primary leakage flux, in phase with the primary current, 

 and supposed to consist of lines that are looped on the primary 

 circuit and miss the secondary, and the other, the secondary 

 leakage flux, in phase vvith the secondary current and supposed to 

 consist of lines that are looped on the secondary and that miss 

 the primary circuit. 



Let these two fluxes be specified by x^anS^^ and x^cthXj^ where 

 :Vi and x.^ are what we will call the leakage coefficients of the two 

 circuits, and cr = 47rX permeance of the magnetic circuit as before. 



3. The e.m.f. in the secondary coil being equal to 

 ^F 



