48 ALTERNATING CURRENTS 



Applying to the branched portion of the circuit of Fig. 33 the 

 rules established in 9 for parallel arrangements of impedances, we 

 find for the joint resistance of the branched portion 



and for the joint reactance 



From this we find the total resistance of the fine-wire circuit 

 to be 



, ____ 



h i + 



and its total reactance 



The current in the fine-wire circuit therefore lags behind the p.d. 

 by an angle 



-- 



tan 



or, approximately 



^ 



tan 1 p 



r 



where r = TO 4- r\. 



From this we see that the capacity of the non-inductive resistance, 

 if not excessive, is beneficial, as it tends to neutralize the effect of the 

 self-inductance of the fine -wire coil. 



The formulae established in 21 in connection with the effect 

 of self-inductance alone are immediately available for the combined 

 effect of self-inductance and capacity, provided that for we sub- 



, I - ?'! 2 C 

 stitute tan' 1 - - p. 



r f 



The capacity effect is greatly reduced by subdividing the non- 

 inductive resistance into a number of sections. Let there be n 

 sections, each wound non-inductively as before. If we imagine each 

 section bisected, we obtain n condensers in series, each of capacity 



- C, where C is the capacity of the resistance when wound in a single 



