236 



and 



ELEMENTS OF ELECTRICAL ENGINEERING. 



whence, using the values of M p and M w from equations (i) and 

 (ii) we have: 



P -4- P 



Si-r-' (') 



and 



41/2 ir WE 



(iv) 



116. Effect of coil resistances. The clock diagram, Fig. 202, 

 shows the general effect (greatly exaggerated) of the resistances 

 of the transformer coils. The line 0<& represents the harmon- 



ically varying flux in the trans- 

 former core ; the line Oa repre- 

 sents the useful part of E f , that is, 

 the part which balances the elec- 

 tromotive force which is induced 

 in the primary coil by the varying 

 core flux ; and the line Ob rep- 

 resents the total electromotive 

 force induced in the secondary 

 coil. The ratio of Oa to Ob is 

 equal to N'/N", the magnetic 

 leakage being zero. The line 

 OI" represents the secondary 

 current, the secondary receiving 

 circuit having a given power fac- 

 tor equal to cos 6, and the line 

 Or represents the primary cur- 

 rent. The total primary voltage 

 Fig - 202 ' E' is the vector sum of Oa and 



R f F , R f F being of course parallel to F ; and the electromo- 

 tive force E" at the terminals of the secondary coil is the vector 

 difference Ob - R"I", R" I" being of course parallel to I". 

 When the secondary receiving circuit has unity power factor, 



