Equivalent Resistance 8ft. of Parallel Circuits. 275 

 With these substitutions equations (9) and (10) become 



1 ' Ba> 



€'« A 2 + BV 



(12) 



Here A and Bo> each stand for a summation, as expressed in 

 (6) and (7), and are calculated from the particular values of the 

 resistance, self-induction, and capacity of each branch. This 

 gives a definite value to the equivalent resistance, R/, accord- 

 ing to (11), and a definite value to -^ I/&>, according 



to (12). There may be an indefinite number of values 

 assigned to 1/ or 0' according to values assigned to the other. 

 If the right-hand member of (12) is positive, we may consider 

 that the equivalent circuit has no self-induction, i. e. L/ = 0, 

 and calculate the equivalent capacity. If this member is 

 negative, we may consider that the equivalent circuit has no 

 condenser, i. e. Q/ = co , and calculate accordingly the equi- 

 valent self-induction. The angle of advance or lag of the 

 main current is obtained from equation (8). 



If there is no condenser in any branch, the expressions for 

 A and Ba> are obtained by substituting C = oo in the summa- 

 tions in (6) and (7), thus 



and 



Equations (11) and (12) with these values for A and Boo give 

 the equivalent resistance and self-induction of parallel circuits 

 containing resistance and self-induction only. These expres- 

 sions are the same as those obtained by Lord Rayleigh. 



If there is no self-induction in any branch, the substitution 

 «f L = in (6) and (7) gives 



A= 2 - R 



and 



1{2+ <^ 



1 



r Ceo Cay 



Oar 



