276 ALTERNATING CURRENTS 



edges of the pole-pieces, instead of providing them with expanded 

 pole-shoes, as would be done in a continuous-current motor. 



Let the speed at which the motor is required to run when fully 

 loaded be specified. The speed being given, the full-load torque is 

 also known. Now, for a given gap induction, and a given number of 

 ampere-wires per cm. length of armature circumference at full load, 

 the torque is independent of the number of poles. The self-inductance 

 of the field is also independent of this number so long as the gap 



induction and the ratio ~ r r remain constant.* We may, there- 



pole-pitch 



fore, vary the number of poles without altering the reactance of the 

 field. If we assume the number of poles to be doubled, then for the 

 same speed, with a lap-wound armature, we shall require the same 



FIG. 167. Finzi's Design for Magnet of Series Motor. 



number of conductors per pole-pitch, but each conductor will now 

 carry only half as much current. The polar arc having been reduced 

 to half its original length, there will be only half the original number 

 of ampere-turns producing the cross-field, and only half the flux linked 

 with the conductors lying between two neighbouring sets of brushes. 

 The armature reactance e.m.f. will thus be reduced to half its original 

 value, and the power factor will be increased. 



This shows the advantage gained by increasing the number of 

 poles. There is another way of expressing the same result. Since 

 the speed of synchronism, for a given frequency, varies inversely as 

 the number of poles, increasing this number (for a given speed of the 



N . . , , . speed of motor . 



motor) is equivalent to making the ratio - -. larger. 



speed ol synchronism 



The result just established is, therefore, frequently stated in the form 

 that it is best to design the motor so that it will run at a high speed 



* If, e.g., we double the number of poles, the flux per field-turn will be halved, and 

 the number of field-turns doubled, the total flux linked with the field winding thereby 

 remaining unaltered. 



