94 



TRANSMISSION LINE FORMULAS 



As when calculating the self-induction of an irregularly 



spaced line, consider a line three 

 miles long which is transposed 

 at the end of each mile. 



The work in carrying a unit 

 charge from C to B (Fig. 25) 

 assuming the charges concen- 

 trated at the centers of the 

 wires, is approximately 



a a c 



E a = q R 2 loge q r 2 loge - + q . 2 loge 7 



p P o 



Now q B is a periodic quantity, which alternates in value 

 at the same frequency as the voltage or current. 

 We have qs = CiE 



Fig. 25. 



where IB' is the charging current flowing into the capacity 

 Ci of the wire B. 

 Thus 



.' 2 lo ge - I c ' 2 k)ge + I A ' 2 log. 



2 TTJ \ p p 01 



In the second mile the conductors are transposed into 

 new positions. Let the currents in them remain the same. 

 Therefore, 



Ea = -lJ 2 log, --I C '2 loge ~ + I A ' 2 log, 



2irJ\ p p CI 



and in the third mile 



E.= =^(l B ' 2 log< - I c ' 2 log, + 1 A' 2 log, -) 

 27r/\ p p a/ 



