CHAPTER XII 



THE INDUCTANCE OF THE WINDINGS OF 

 ELECTRICAL MACHINERY. 



64. The Inductance of Transformer Windings. When a 

 transformer is operated at no load, i.e., with its secondary cir- 

 cuit open, practically the whole flux is concentrated within 

 the iron core. When, however, the transformer is loaded, so that 

 considerable currents flow in both windings, appreciable leakage 

 fluxes are formed (Fig. 50), which are linked partly with the 

 primary winding, and partly with the secondary winding. When 

 the load current is considerable, the primary and the secondary 

 ampere-turns are large as compared to the exciting ampere- 

 turns, so that at each instant the secondary ampere-turns are 

 practically equal and opposite to the primary ampere-turns. 

 An inspection of Fig. 50 will show that the m.m.f. acting upon 

 the useful path in the iron is equal to the difference between the 

 m.m.fs. of the primary and secondary windings, while the m.m.f. 

 acting upon leakage paths is equal to the sum of the m.m.fs. 

 of both windings. 



Take, for instance, the line of force fghk; with respect to the 

 part fg of its path, the secondary coil Si and the adjacent half 

 PI of the primary coil form together a fictitious annular coil 

 (leakage coil). The m.m.f. of this coil is equal to Jwiii, where 

 ii is the primary current, and nj is the number of turns in the 

 whole primary coil P. Similarly, the coil S 2 and the part P 2 

 of the primary coil may be said to form another fictitious coil 

 linking with the part hk of the path of the lines of force. 



It will be seen from the dots and crosses that the m.m.fs. 

 of the two fictitious coils assist each other, and that the paths 

 of the leakage flux are as indicated by the arrow-heads. Some 

 lines of force are linked with the total m.m.f. of the fictitious 

 coils, others are linked with only part of the turns. Although 



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