//>/v7 i,( / ./A7/// ^ i\ III. Win 1 1 i.i.riioxE ciRcnrs 5w 



voltaic Ro=\ E iijK)n the seiuliiij; end of tlu- line L\ and causes a 

 current /,, to flow into it. Tlie voltage and current waves are propa- 

 gated rejiularly o\er the hne to the point B wliere lliey set up a poten- 

 tial dirt'erence R\ between the conductors and cause a current I\ to 

 How. fii anil I\ are smaller in magnitude and later in phase than 

 Ro and h l>ecause of the losses and finite velocity of transniissiiiir 

 of the line Li. Thcst' f|uantities ha\e the rcl.ition 



En Ex , . 



/„ /, ^'' ^^' 



since the line is regular. 



In the second line L; a different set of conditions exists. In this 

 case, the voltajje E- and the current h produced at B by the generator 

 have the relation 



f-=Z,. (2) 



When the e.m.f. of the generator G is zero, the conditions in the 

 third line Lj are the same as in La but by adjusting the phase and 

 magnitude of the e.m.f. of this generator the current in the terminal 

 impedance Zt can be made ecjual to I\ and the drop across this im- 

 pedance l)ecf)mes 



£3 = /.Z,. (3) 



Tnder these conditions the current /i flows at the end of the line 

 Li and the potential difference £i exists between the conductors at 

 this point. The line Lj is then in the same condition as the line L\ 

 between the points A and B. When the waves arrive at B over the 

 line Z-3 the generator boosts or depresses the voltage at the terminus 

 of the line by just the amount necessary to cause the terminal ap- 

 paratus to take the desired current. Then the e.m.f. of the generator 

 G is 



Ec = Ei-E,. (4) 



Removing the e.m.f. of the generator G makes the conditions in 

 line Lj identical with the conditions in Lj, but removing this e.m.f. 

 is the same thing as introducing another e.m.f. —Ec in series with the 

 generator which annuls its e.m.f. Ec.. This e.m.f. —Eg causes a 

 current /j to flow back into the line 



En 



^'^-z;+zr (^^ 



.Substituting from equations (1), (.3) and (4) abo%-e 



