We therefore have 



or 



CHOKING COILS. 



F 2 = v 2 -f vi* 



2 T7"2 2 



(1) 



If, therefore, L is the self- induction of the choking coil, and 

 # = 27rX where n is the frequency of supply, we have 



*> T- 



pLi = v 



Therefore, the self-induction of the choking coil necessary for 

 the purpose is given by 



pi 



(2) 



i being the E.M.S. value of the current in amperes. 

 CASE 2. Apparatus Inductive. 



Let the notation be the same as in Case 1. 



Let, in addition, the resistance of the apparatus be TI, and its 

 self-induction LI. 



Then the current i lags behind v\ by an angle 0, where (see 

 21)- 



Let OA (Fig. 34) represent vi, and 01 represent i, where the 

 angled 01 = 0. 



Then OL, which represents the E.M.F. 

 of self-induction of the choking coil, is 90 

 behind OL The P.D. V has to supply 

 a component equal to OA to work the 

 apparatus, and another equal to OL' to 

 balance the self-induction of the choking 

 coil, and is therefore given by OE. 



Now, the angle AOL' = *- - ; therefore 



whence 



Fio. 34. 



w! cos - 

 2 m?1 sin 



v = VV- - ^i 2 cos 2 - ?! sin . . . (3) 



