TRANSIENTS IN GROUNDED CIRCUITS 



765 



is given by ^ 



Zi2(co) = 2jco log -^ + 4a; [Va^^ + J - M]e-^*i+''^^''^ COS fxx^la d/x. (3) 

 P Jo 



where 



a 



= 47rXco 



p" = ^Vh + W^ 



X'^ 



Zii{<Ji) is limited by the neglect of displacement currents to frequencies 

 such that the propagation constant is a small quantity in c.g.s. units. 

 To obtain Z^it) it is necessary to integrate over all frequencies as 

 shown by (2) ; this introduces an approximation in all results for small 

 values of the time. 



100 

 90 

 80 

 70 

 60 

 50 



40 

 30 



20 



If) 



2 



o 100 

 m 9.0 



** 8.0 

 7.0 

 6.0 

 5.0 

 4 



3 



2.0 



10 



0.1 



02 



03 



0.4 

 SECONDS 



Q5 



Q6 



07 



08 



Fig. 4 — Plot of the voltage Zitif) on wire 2 as a function of / for two different 

 values of separation or conductivity as given by the product ttXa;-. 



7 Bell System Technical Journal, Vol. V, page 544, October, 1926. 



