178 



ALTERNATING CURRENTS 



79. Leakage Reactance. In the preceding discussion it has 

 been assumed that all the flux which links the primary also links 

 the secondary. In practice it is impossible to realize this condi- 

 tion. All the flux produced by the primary does not link the 

 secondary, but a part completes its magnetic circuit by passing 

 through the air rather than around through the core, as shown 

 by <i, Fig. 173. That is, between planes a and b, Fig. 173, there 

 is a mmf. due to the primary ampere-turns, plane a being at a 

 higher magnetic potential than plane b at the instant shown. 

 This mmf. is proportional to the primary current and tends to 

 send flux from a to b both through the air and around through the 

 core. That part of the flux which passes from a to b through the 

 air follows a magnetic circuit which is acted upon by the primary 



FIG. 173. Mutual flux, primary leakage flux, and secondary leakage flux in a 



transformer. 



ampere-turns only. This flux </>i is called the primary leakage 

 flux. It is proportional to the total ampere-turns of the primary 

 alone as the secondary turns do not link the magnetic circuit of 

 </>i. Therefore c/>i induces an emf. in the primary but not in the 

 secondary. The flux <i is in time-phase with the total primary 

 current /i. The emf. induced by <i must lag <i and /i by 90. 

 (See page 27, Par. 14.) The emf. necessary to balance this 

 counter emf. is opposite and equal to it, and therefore leads the 

 current 7i by 90. As this counter emf. is proportional to the cur- 

 rent and lags it by 90, it is nothing more than a reactance volt- 

 age, and is denoted by IiXi. The component of line voltage 

 which balances this emf. is +IiXi. Therefore, a reactance 

 drop exists in a transformer primary in precisely the same manner 

 that a reactance drop exists in an alternator armature. The 



