TRANSIENT SOLUTIONS OF ELECTRICAL NETWORKS 115 

 B. Limiting Values with Open Circuited Line 



C. Solution for a Resistance and Inductance in Series 



As a first example of a transient solution obtained by this method 

 let us consider the case of an inductance and resistance in series with 

 a source of alternating voltage. To solve this problem, consider the 

 case of a voltage in series with a distortionless line, short circuited, 

 as shown on Fig. 1-A. The current immediately flowing on applica- 

 tion of the voltage will be io where 



to = 



Rn 



(20) 



This current is transmitted down the line and completely reflected 

 at the far end, returning to the near end. The first reflected current 

 entering the generator is then 



ii 



toe' 



(21) 



where P is the propagation constant of the line. Upon reaching the 

 near end, the current is completely reflected in the same phase and 

 again enters the line. At the end of the first reflection, the current 

 entering the line is 



i = ^(1 + 2e-'-P). (22) 



After (w — 1) reflections and passages through the line, the current is 



i = i^li -f 2e-'^P + 2e'^P + • • • + 2e--("-i)'P] 



1 - g-2«^\ . 1 (23) 



= to 



1 - e-''' 



- 1 



Now the time at which the wth reflection occurs will be 



/ = n{2D), 



