CHAP. VII] M.M.F. OF DISTRIBUTED WINDINGS 135 



Substituting the ratio of i 2 /i 2 from eq. (65) we find 



r 2 7r 2 =(m l /m 2 )(k bl n l /k b2 n 2 ).^ .... (68) 

 For a transformer this equation reduces to the familiar expression 





The ratio of the inductances is the same as that of the resist- 

 ances; this can be proved as follows : In order that the equivalent 

 winding may have the same effect on the power factor of the motor 

 as the actual winding, the equivalent winding must draw from the 

 line an equal amount of reactive volt-amperes, due to its leakage 

 inductance. The magnetic energies stored in the two rotor wind- 

 ings must therefore be equal, and we have, according to eq. (104) 

 in Art. 58, 



m l .fa'*L' 2 , ...... (69) 



where L 2 and Z/ 2 are the leakage inductances of the real and the 

 equivalent rotor windings, per pole per phase. The form of this 

 equation is the same as that of eq. (67) ; therefore, substituting 

 again the ratio of i' 2 /i 2 from eq. (65) an expression is obtained for 

 the ratio of L' 2 /L 2 identical with that given by eq. (68), namely 



L 2 '/L 2 =(m 1 /m 2 )(k bl n l /k b2 n 2 )* ..... (70) 



This result could also be foreseen from the fact that the reactances 

 and the resistances enter symmetrically in the equivalent diagram, 

 and relation (68) holds therefore for the reactances x 2 and x 2 . 

 But in the equivalent diagram the secondary and the primary fre- 

 quency is the same, so that the ratio of the inductances is equal to 

 that of the reactances; this gives eq. (70). 



It must be clearly understood that the expressions (68) and (70) 

 t o the resistances and inductances per pole per phase. \Yhen 

 the windings of a phase are all in series, both in the stator and in t he 

 rotor, the same ratio holds of course for the reaisUnoefl i>er phase; 

 otherwise the actual connections must be taken into consideration, 

 keeping in mind that the total i^r loss must be the same in the 

 equivalent winding as in the actual one. Having obtained the re- 

 sistance of the equivalent winding per pole, the turns are connected 

 in the same way as the stator turns. This fact must be remembered 

 in particular when dealing with individually short-circuited coils 



See the author's Experimental Eledrital Engineering, Vol. 2, p. 77. 



