152 TREATISE ON ALTERNATING CURRENTS. 



di-phase and a tri-phase motor. This is probably due to the 

 influence of the rotor currents, which tend to diminish the varia- 

 tions of the induction. 



DIFFERENCE OF POTENTIAL BETWEEN TERMINALS OF 

 INDUCTION MOTORS. 



1O3. Di-phase Motor. If the coils are joined in the 

 star-grouping as in Fig. 55, with or without a common junction 

 at M, the potential difference between the line wires p and r, or 

 o and q, is the sum of the P.D.s between the terminals of the 

 coils I and &', and equals 2e sin pt, if c sin pt is the E.M.F. absorbed 

 in either coil. 



If the coils are star-grouped, and have a common junction M, 

 there is a P.D. between o and p given by 



v = e sin pt e sin (pi 



in (pt - *) ...... (2) 



= \ sn 



Which shows that the P.D. between the two line wires of 

 different phases is \/2 times the E.M.F. consumed in one of the 

 stator coils, and has a phase midway between the phases of the 

 E.M.F.s in the two corresponding coils. 



If the coils are mesh-grouped, as in Fig. 57, the P.D, between 

 o B.U&P is evidently the same as the E.M.F. consumed in a, and 

 equals e sin pt. 



1O4. Tri-phase Motor. Let the stator coils be A, B, C, 

 in Figs. 54 and 56, and p, q, r the line wires. Let the E.M.F.s 



consumed in A and 7>be e ii\pt and e sin (pt *} respectively. 



If the coils are connected in mesh-grouping, as in Fig. 56, the 

 P.D. between p and q is simply the E.M.F. consumed in A, or 

 e sin pt. 



If, however, the grouping is in the star method, as in Fig. 54, 

 the P.D. between p and q is given by 



v = c sin pt e sin (pt * 

 = \/3e sin (pt + ^) (3) 



