Transformer Indicator Diagrams. 477 



resistance was 76*52 ohms, and the inductance, measured 

 independently, was '212 henry. 



j^=54*13sin(^ — 10*5) — 536 sin 3(o)< — 12*5) -f 1*37 sin 5 (cot — 13'2). 



h =l-907sin(©^— 52-1)— *065 sin 3(«£-3"4-7)—-0l7sin5(®f— 63-1). 

 PiOi + n 2 Q, = 11-18 sin {cot -18-37) + 1*82 sin 3 {wt -42-14) + -31 sin o(cot—3o) t 

 = 154900 sin (cot - 99-9) -t-5200 sin Z(cot- 101-7) + 800 sin o(cot -98). 



2 =-299 sin(o>*-232-38)--015 sin 3(«rf— 215-4) -'002 sin 5(«t— 235). 



2 =312-9 sin (tot- 189*08) -31*8 sin 3(W— 189-5) -8'3 sin 5(®£- 223). 



(). The same wave-tracer deflexions were individually mul- 

 tiplied by their proper factors to reduce them to absoluts 

 measure, and the products plotted as wave ordinates against 

 the corresponding wave-tracer divided-circle readings (i. e. 

 against cot where &> = 27r/period) as abscissae. Fig. 2 (PI. XIII.) 

 represents correctly in amplitude and relative phase the differ- 

 ent periodic quantities for the transformer at no load ; fig. 3 

 (PI. XIII.) for the transformer at (q.p.) full non-inductive 

 load, and fig. 1 (PI. XIII.) for the transformer at (q.p.) full 

 inductive load. 



Obviously in figs. 2, 3, and 4 the same periodic quantities 

 are graphically represented as are analytically expressed in 

 series 1, 2, and 3 respectively of the preceding paragraph. 



In addition to the sets of related waves, there is, in each of 

 the three diagrams, an area very similar to the well-known 

 hysteresis indicator-diagram. In the present case these closed 

 curves were obtained by plotting the flux as ordinate against 

 the corresponding value of the magnetizing-current turns 

 (i. e., n 1 (J 1 + n 2 C 2 ) as abscissa for a complete period. 



Thus the area enclosed (A say) is 



t+ (n 1 C 1 + n,C 2 )dF, 



where T is the period, and this integral can be shown to be 

 equal to the total core loss per cycle due to both hysteresis 

 and eddy currents as follows : — 



Xeglecting rc~ losses, the energy entering the transformer 

 on the primary side in any element of time dt is eC\dt, where 

 e is the back E.M.F. due to variation of the flux ; and as 



^F 



i 



this energy is equal to 



e=ni m 



nfi^-dt. 



