9 6 



ELEMENTS OF ELECTRICAL ENGINEERING. 



Then 



and, since the current / is the vector sum of I I and 7 2 , we have : 



The problem is solved from these three equations in exactly the same way that the 

 problem of coils in series is solved from equations (i), (ii) and (iii) of Art. 44. 



47. The transformer. The use of complex quantity may be further illustrated 

 by a discussion of the problem of the transformer. The discussion here given of this 

 problem is unnecessarily complicated and it is therefore useless for practical purposes, 

 and it is all the more useless in that it takes no account of the effects of magnetic satura- 

 tion. One must not, however, conclude that the use of complex quantity is useless in 

 the development of the practical theory of the transformer. 



The difference between the practical theory of the transformer and the general 

 theory here outlined is that the practical theory is based on the assumption that the 

 magnetic flux which passes through one coil and does not pass through the other, that 

 is the leakage flux, is small in comparison with the flux which passes through both 

 coils. This assumption greatly simplifies the practical theory of the transformer, it 

 avoids any explicit use of the idea of the mutual inductance coefficient of the two coils, 

 and it gives rise to an idea of self-inductance depending upon leakage flux only. 



Two separate coils of wire A and ./?, Fig. 89, are wound on an iron core, or 



Fig. 89. 



merely placed near together. The coil A, called the pri mary coil, receives alternat- 

 ing current from supply mains, its resistance is r l and its inductance is L r The 

 coil J5, called the secondary coil, is connected to a receiving circuit. The total re- 

 sistance of the coil B and its receiving circuit is r 2 and the total inductance is Z 2 . 

 It is required to find the electromotive force, E v which must act on coil A to main- 

 tain in it a given harmonic current f r The coefficient of mutual inductance* of the 

 two coils is M. 



*See Nichols and Franklin's Elements of Physics, Vol. II, Chapter VII, for a 

 definition of mutual inductance. 



