KENNELLY, — OSCILLATING-CURRENT CIRCUITS. 381 



With respect to the potential difference as standard of phase, 

 I^= U^Y [90° = ^0*" [90°, maximum cyclic amperes 



P^ = ^ [90° = Ul\db° = -^^190° = U' F|90°, max. cyclic watts 



Wm=~\^° = ^T^ |yO° = ;^|90°. maximum cyclic joules 



With respect to the current as standard of phase : 



U^ = loZo [90° = Q^s |90°, maximum cyclic volts (10) 



P^ = Z£? [90°= ioJ??[90°=/c/ |90°=/2^^^°, max. eye. watts (1 1) 



W^ = 1^ [90° = ^' 1^° = ^ t^°- maximum cyclic joules (12) 



The vector- diagrams /, P, and W, of Figure 3, as well as U, P, and 

 W, of Figure 4, may also be treated as rotative vector-diagrams, for de- 

 ducing instantaneous values of their respective quantities projectively. 

 Thus in the case of /, Figure 3., we may rotate the vector I^ about the 

 point d, in the positive direction, with angular velocity w, commencing 

 at time ^ = 0, from the position shown. The instantaneous orthogonal 

 projections of the vector on the dotted line, or "real " axis, will then 

 give the corresponding instantaneous o. c. strengths. 



In the case of the P vector. Figure 3, the vector gk may be rotated 

 about the point g with positively directed angular velocity 2 w, com- 

 mencing from the position shown in Figure 3, at time ^ = 0. Instan- 

 taneous orthogonal projections on the dotted line, or " real " axis, will 

 then give the corresponding instantaneous oscillating-current power, as 

 indicated by the double-frequency sinusoid p in Figure 5. This is the 

 power of the condenser. The same rotating power-vector may also be 

 used to project the power of the inductance, if displaced in phase by 

 180°, that is, if it starts from rest in the diametrically opposite position 

 to that shown in Figure 3. 



In the case of the W vector, Figure 3, the vector bi may be rotated in 

 the positive direction about the point / with angular velocity 2w. If 

 the vector starts, at time ^ = 0, from the position indicated in Figure 3, 

 projections must be taken on the line In, or axis of imaginaries. In- 

 stantaneous projections of the vector on this axis will then mark off 

 instantaneous values of the energy in the condenser (u^c/2 joules). 



