ELECTRIC CIRCUIT THEORY 



355 



Problem II. Our second illustrative problem may be stated as 

 follows: — A unit e.m.f. is impressed on a transmission line of length 5 

 and distributed constants L,R,C. At x^s the line is closed by a resist- 

 ance Ro in parallel with an inductance Lo. Required the current in 

 the terminal resistance. If V{t) denotes the terminal voltage, the 

 current at x = s is given by 



at Jo 



It is also equal to the current flowing into the terminal impedance; 

 that is 



Ko LoJq 



Equating and rearranging 



[^+522(0)] FW=5i2W-JV(r)[^ + 5'22(/-r)]^r. (279) 



Now the short circuit admittance ^22 and S12 are given by formula 

 (210-a) of a preceding chapter, and 522(0) ^\/C/L. In order to apply 

 numerical integration to (279), numerical values must be assigned to 

 the constants. We take 



Ro = \/l]C = 1935 ohms, 

 Lo = 0.4 henry, 



^=P = 292, 



v = 1/VlC=1.105X10\ 

 s = 100. 



