202 



ELECTRICAL MACHINERY 



Use of a Rotating Vector. It is a familiar fact that a 

 sine curve may be properly represented by a rotating 

 vector, the length of which is equal to the maximum value 

 of the sine wave and the speed of rotation of which (mea- 

 sured in radians per second) is equal to 2x times the fre- 

 quency of the alternating current. 



In Fig. 121 the vector OA is supposed to rotate in the 

 counterclockwise direction with the angular velocity w, 

 where G> = 2-ju/. Time is reckoned as zero when the vector 

 OA coincides with the X axis so that at the end of the 



irectibn of 



fector rotation 

 A 



Line of reference 



FIG. 121. Vector Representation of Voltage and Current. 



time t the vector has swept through the angle <o. At 

 this time the instantaneous value of the current, which 

 the vector diagram is supposed to show, is OC OA cos tot 

 and as the length of OA has been chosen equal to the maxi- 

 mum value of the current it is evident that the projection 

 of the vector OA on the X axis represents, at any time, 

 the instantaneous value of the current expressed analytically 

 by the equation i=I m cos u>t, 



Projections on the X axis to the right of the Y axis 

 represent positive values of current while those to the left 

 represent negative values of current. 



