17 TRANSFORMERS. [Exp. 



desired, instead of per cent.) Lay off LJ = r and, JK x. Then 

 AK = E ot the secondary terminal voltage at no load. Per cent, regu- 

 lation = , = 2.585. 



As already stated, the graphical method can not be accurately 

 applied on account of the small values of r and x. From the 

 graphical method, an analytical method is derived as follows. 



40. Analytically, we have from Fig. 9, 



or, more simply (see 41), 



Transposing, we have 



Regulation =E -ioo = 

 41. Expressed more generally, let 



^ = per cent, in-phase voltage drop. 

 g = per cent, quadrature voltage drop. 



f 



E, = V(ioo + />)' + g" == zoo + p 



This practical identity* can be seen by squaring, or by solving a 

 numerical example. Transposing, we have 



Regulation = E, - 100 = p + 



or, for practical purposes, = p -f- (<? 2 -^-2oo). 



Regulation =( in-phase drop) -[-(effective quadrature drop). 

 It is the in-phase drop that chiefly determines the regulation of a 

 transformer; effective quadrature drop is small. 



42. Lagging Current. For a lagging current, with power factor 

 = cos 0, the resistance drop r makes an angle with the terminal 



* (4ia). Theorem. In a right triangle in which the height is small 

 compared with the base, the hypotenuse = base -f- [(height) 2 -r- 2(base)]. 

 This is convenient in solving many alternating current problems. 



For example, let base=ioo; when height = 5, hypotenuse = 100.125 

 (true valuer 100.124922) ; when height = 10, hypotenuse = 100.5 (true 

 value = 100.498756). 



