390 THE INDUCTION MOTOR. 



copper losses are neglected, the equation to the curve 

 would be 



. . watts output, 



efficiency = ? = - -TT 



watts output + constant losses. 



This would represent a hyperbola approaching its asymp- 

 tote t] = 1 more nearly as the load increases. Owing to 

 the copper losses the curve fails to reach this value and 

 begins to bend downwards at higher loads, thus departing 

 from the shape of the hyperbola. The curve should reach 

 its maximum value at normal load, and being very flat 

 near this point, the efficiency does not vary much be- 

 tween three-fourths and five-fourths of full load. 



The Power Factor. The power factor is very low at no- 

 load, which accounts for the fact that induction motors 

 take a relatively high no-load ciirrent, although absorbing 

 little power. 



The shape of the power-factor curve is similar to that 

 of the efficiency curve, but does not pass through zero. 

 It rises sharply at first, then becomes horizontal, and 

 finally falls slightly. The general shape of the curve 

 follows from the curves of power and stator current, 



alreadv discussed. Since cos = - - and 



amps x volts 



"\Vfl rro 



the voltage of supply is constant, the fraction ; 7 



is proportional to the power factor. Referring to Fig. 185, it 

 is seen that the watts rise rapidly from the first, whereas 



the current increases only slowly. The fraction ^LJ 



current 



must, consequently, rise rapidly at first. As the current 

 curve becomes steeper, the increase of the fraction 

 becomes slower. 



When the motor works at a low power factor the 

 current taken by it is chiefly magnetising or idle current. 

 The disadvantage of large idle currents in a supply 

 system is less due to its effect on the operation of the 

 motors than to the fact that considerable useless currents 

 flow in the supply circuit, producing losses in them and 

 in the generator armature, and tending to produce bad 

 regulation of the generator vqltage, through causes already 

 discussed, in connection with the characteristic curves of 

 alternators. 



