GENERAL THEORY OF THE TRANSFORMER. 



239 



to E 1 coPf. In this case the effect of magnetic leakage is to 

 cause the secondary voltage of the loaded transformer to fall con- 

 siderably below its ideal value. 



When the secondary receiving circuit is non-inductive, that is, 

 when the angle in Fig. 203 is zero, then a>PI' is at right 

 angles to Oa. In this case Oa is very nearly equal numerically to 

 E' , so that the secondary voltage is nearly equal to its ideal value. 



When the secondary receiving circuit is like a condenser, that 

 is, when the secondary current 1" is nearly 90 ahead of E 1 ' 

 in phase as shown in Fig. 204, then a>PI f is nearly parallel but 

 opposite in direction to Oa so that Oa is nearly equal numeri- 

 cally to E' -f (oPf. In this case the effect of magnetic leakage 

 is to cause the secondary voltage of the loaded transformer to 

 exceed its ideal value. 



118. Magnetic leakage is equivalent to an inductance in series 

 with the primary coil. To show that the magnetic leakage of a 

 transformer is equivalent to an inductance in series with the 

 primary coil (magnetizing current being ignored) it is necessary 

 to consider the relation between the alternating current i in any 

 coil of wire and the harmonically varying flux produced by i. 

 The flux is proportional to 



i, it is of course in phase / A \ / B 



with i, and it is the effects 

 of such a flux that consti- 

 tutes what is called the in- 

 ductance of the coil. If, 

 therefore, we can show that 

 the total flux through the 

 primary coil of a trans- 

 former can be resolved into 

 two parts, one of which 

 passes through the primary 

 coil only and is proportional to and in phase with the primary cur- 

 rent, and the other of which passes through both the primary and 

 the secondary coils, then our proposition will be established. 



C 



Fig. 205. 



