64 



BELL SYSTEM TECHNICAL JOURNAL 



The case is very much different when a higher frequency is ap- 

 pHed. Fig. 8 shows the building-up of the alternating current in the 

 cable when an e.m.f. sin wt is applied at time / = 0. The frequency 

 is so chosen that co' = a:a;/4 = IOtt. The outstanding features of this 

 curve are that the initial current surge is very large compared with 

 the final steady-state, and that the transient distortion is relatively 

 very large. It is evident that the frequency here shown could not be 



.028 

 .024 

 .020 

 .016 

 .012 

 .008 



.004 



-.004 



-.008 



1.0 2.0 3.0 4.0 



Fig. 8 — Non-inductive cable (G = 0). Building-up of alternating current. 



Applied e.m.f. sin ut; w = 107r ^pp 



employed for signaling purposes. This curve has been computed 

 from the steady-state formulas, and equations (160) and (161) for 

 the transient distortion. 



If the applied frequency aj/27r is very high, the steady-state becomes 

 negligibly small, and the complete current is obtained to a good 

 approximation by taking the leading terms of (160) and (161). Thus 

 if the applied e.m.f. is sin ut, and co is sufficiently large, the cable 

 current is 



2 1 d e-^l-" 



by (100) and (170) while, if the impressed e.m.f. is cos w/, it is 



2 /ly^/^e-v^ 



by (161) and (170). Here co' = aw/4 and r = U/a. 



