SERIES MOTOR 



273 



vphoso current whoso r.m.s. value is i. In tho first case, how- 

 the torque is a steady one; in the second, a rapidly fluctuating 

 or pulsating one. 



As will bo seen presently, it is sulvisiible to have a relatively 

 small number of turns in the field winding of such a motor; this i 

 one (if tin- important differences between an ordinary continuous- 

 current and a single-phase series motor. 



The performance of such a motor is best studied by the aid of a 

 circle diagram. This we now proceed to establish, neglecting, for the 

 sake of simplicity, the iron or core losses in the motor. 



Let in Fig. 165 the horizontal direction be that of the current 

 vector. The p.d. impressed on the motor terminals may be regarded 

 as made up of the following compo- 

 nents : (1) the component OC = ri, 

 r being the total resistance of the 

 motor, and i the current ; this com- 

 ponent is clearly in phase with the 

 current; (2) the component OB 

 = CA, in quadrature with the cur- 

 rent, required to balance the induced 

 e.m.f. due to the self-inductance of 

 the field and armature windings ; 

 (3) the component AV, in phase 

 with the current, required to balance 

 the e.m.f. induced by the rotation 

 of the armature in the field. The 

 resultant OV of these three components gives the impressed p.d. 



Let us now suppose that the p.d. is maintained at a constant 

 value. The vector OV thus remains of constant length. Further, 

 since OA = current X impedance of windings, and since the im- 

 pedance on the assumption of constant permeability remains constant, 

 it follows that OA is proportional to the current, and may, therefore, 

 be taken to represent the current to a suitable scale. Again, since 



FIG. 165. Vector Diagram of Series 

 Motor. 



the angle BAO = angle AOC = tan" 1 



this anle will be 



, 

 resistance 



constant, and so will also the angle OAV = a, which is its supple- 

 ment. It is now evident that as the current (OA) changes, OV 

 remaining constant, A must move along the arc of a circle, in order 

 that the angle OAV may, as required, retain a constant value. Thus 

 the locus of the extremity of the current vector is a circle. 



The angle BVO = $ = angle VOC = angle of lag of current 

 behind p.d., so that cos <i> = power factor. 



We may now construct the diagram shown in Fig. 166, in which 

 the triangle OAV corresponds to the similarly lettered triangle of 

 Fig. 165. Lay off a line OV to represent, to any convenient scale, 



T 



