INDUCTANCE AND CAPACITY 



393 







The bridge is arranged as shown in Fig. 230. All the resist- 

 ances are supposed to be non-inductive. The condensers to 

 be compared are at C x and C P . One or both may have an im- 

 perfect dielectric, and to duplicate their behaviors, it will be 

 assumed that perfect condensers having effective capacities C x 

 and C P are in series with resistances r x and r P respectively. 

 This is in accordance with the convention mentioned on page 359. 

 r x and r P are hypothetical resistances assumed simply as an aid 

 in the demonstration in order to introduce energy losses, their 

 values being such that the behavior of the combination of the 

 perfect condenser C x and the resistance r x will be the same as 

 that of the actual condenser at C x , and the behavior of C P 

 and r P the same as that of the 

 actual condenser at C P . The 

 balance arms RM and R N are 

 variable and R x and R P are 

 the adj ustable resistances used a 

 to bring the potential differ- 

 ences V c b and V cd into phase. 

 Two resistances are included 

 because it may not be known 

 at the start which of the con- 

 densers has the lower power 

 factor. Only one of the re- 

 sistances will be used. 



The balancing is effected as follows: with R x and R P both 



73 



zero, the ratio -~ is adjusted until the indication of the detector 



/LAT 



is a minimum. The balance is then improved by a'djusting R x 

 or R P as the case may require, and still further improved by 



E> 



readjusting -, - and so on, thus obtaining a perfect balance by 

 KN 



successive adjustments. When the balance is effected, 



r r RN 



^x ^P ~FT~ 



KM 



This may be proved as follows; in general by (26) 



FIG. 230. Diagram for the Wien im- 

 pedance bridge. 



In this case 



