3/6 ELEMENTS OF ELECTRICAL ENGINEERING. 



to h cos /3, so that the total flux through this turn is equal to 

 2r/&cos/3, that 



= 2r//7cos $ sin 



but, dM* jdt(= AjirlH cos /3 cos 2irnt) is the electromotive force 

 which is induced in the turn of wire // by pulsation, so that the 

 electromotive force which is induced in one of the rods / is 



e n = 2irnrlH cos ft cos 2irnt. (iii) 



The above propositions are at once evident from equations (ii) 

 and (iii). 



A clear understanding of the theory of the single-phase induc- 

 tion motor as developed in Art. 139 of Chapter XIII depends on 

 a clear knowledge of the relationship between the two fluxes < 

 and < c in Fig. 253. The flux <E>, which is assumed to be 

 harmonically distributed, induces electromotive forces in the rotor 

 rods in the regions AA' because of the motion of the rotor, and 

 these electromotive forces due to the cutting of <I> are balanced 

 by the electromotive forces which are induced in the regions A A' 

 by the pulsation of the flux < c . A careful consideration of the 

 above propositions will show, therefore, that the flux <E> c is in 

 time quadrature with the flux <I>, that it pulsates at the same 

 frequency as <E>, and that its maximum value is equal to n' jn 

 times the maximum value of <I>. 



The clock diagram of the single-phase induction motor as 

 shown in Fig. 254 of Chapter XIII, involves a very interesting 

 consideration of the question as to positive directions around the 

 rotor (along a turn of the rotor winding) in the regions AA' 

 and BB 1 respectively. To ignore this question of proper choice 

 of positive directions makes it appear that the load current /' in 

 Fig. 254 should be opposite in phase to the impressed primary 

 voltage E f , which, of course, is incorrect. 



17. Rotor currents of the two-phase induction motor. The 

 discussion of equivalent resistance of the rotor per stator phase 

 which is given on page 287 is based on the assumption that the 



