DETERMINATION OF DROP 155 



directions of 01 and OD as the fixed lines of reference in our diagram. 

 As the power factor varies, the point C moves along the circumference 

 of a circle having its centre at O. Now, the position of A is obtained 

 by displacing C through a distance CA equal and parallel to DO. 

 But since DO remains fixed in magnitude and direction, it follows 

 that the locus of A may be derived from that of C by displacing the 

 latter through a distance equal and parallel to DO. It is thus 

 evident that the locus of A is a circle whose centre is at D', as shown 

 in Fig. 114, where OD' = DO. The angle 10 A is the angle of lag. 

 The diagram shows very clearly the rapid increase in the drop with 

 increasing angle of lag, the drop being represented by the intercept 

 between the two circles of the radius vector drawn from to A.* If 

 the current is a leading one, i.e. if OA falls below 01, the drop 

 steadily decreases with increasing angle of lead, vanishes at the 

 intersection C of the two circles, and beyond this point changes sign, 

 becoming a rise instead of a drop. 



83. Algebraical Method of determining Drop 



Although the graphical methods explained above are useful in 

 exhibiting the relations connecting the various quantities in a manner 

 which enables them to be more easily remembered than would be 

 the case with a purely algebraical method, yet for the purpose of 

 actually determining the drop a purely algebraical method is pre- 

 ferable. Purely graphical methods are, in fact, incapable of giving 

 veiy accurate results, unless the diagrams are drawn to an incon- 

 veniently large scale, and with extreme care. It may be mentioned 



FIG. 115. To illustrate Algebraical Method of determining Drop. 



in this connection that the drop in Figs. 113 and 114 is greatly 

 exaggerated for the purpose of making the diagram clear, and that 

 in actual practice the angle AOC, in the case of transformers, may 



* When speaking of the drop in connection with voltage regulation, wo mean 

 simply the arithmetical difference between the open-circuit p.d. and the terminal p.d. 

 of the loaded apparatus ; we do not mean the rectorial drop AC, which represents the 

 voltage required to overcome the impedance of the apparatus. 



