298 ELEMENTS OF ELECTRICAL ENGINEERING. 



When the rotor speed is below synchronism (n* less than n), 

 then A r =n'/n-J5'=A p , also 3> c =n' /n-3>, and B r =(n r jn) 2 B p 

 \=(n'lrif-E' since B p is always equal to E'~\. Therefore 

 /' = P' = (B p - B r )jR" = [i - (n'ln)*]E'IR", so that the in- 

 take of power E'l' is equal to [i - (n f j n)*\E'* j R" all of 

 which (in the ideal motor) is delivered to the rotor and of which 

 the portion R"f" 2 = R"F* = [i - (' /n) 2 ] 2 E' 2 /R" is developed 

 as electrical power in the rotor and the remainder is developed 

 as mechanical power. Therefore the mechanical power is equal 

 to (s l s 2 )E f2 /R /f , where s l is written for [i (n'/n) 2 ], and 

 the torque in synchronous watts is equal to njn' x (s l s l 2 )E f JR". 



The action of the ideal single-phase induction motor running 

 at speed n f would be reproduced as pure transformer action at 

 stand-still if the rotor resistance were increased to R lf js r This 

 is evident when we consider (a) that the net electromotive force 

 in the region BB' of the rotor (see Fig. 253) is equal to 

 B p B r or to [i (n f jnf^E' when the rotor is running at 

 speed n' y (&) that this net electromotive force becomes equal to 

 E r when n f o, that is, this net electromotive force is multi- 

 plied i/[i (n f jrif\ times by changing from speed n r to 

 zero, and (c) that this increased electromotive force in the region 

 BB' would produce an unchanged value of current in the rotor 

 if the rotor resistance were increased in the same ratio as the net 

 electromotive force. 



Now it may be shown (a) that the effect of magnetic leakage 

 in an actual single-phase induction motor is the same as an out- 

 side reactance X in the primary circuit of an ideal single-phase 

 induction motor, (b) that the effect of resistance of the stator wind- 

 ing is the same as an outside resistance R' in the primary cir- 

 cuit of an ideal single-phase induction motor, and (c) that the 

 effect of core reluctance (necessity of magnetizing current) in an 

 actual single-phase induction motor is the same as a shunt circuit 

 of proper resistance r^ and reactance x l connected across the 

 supply mains of an ideal motor. Therefore the combination of 



