CHAPTER XV. 

 THEORY OF CONVERGENT SERIES. 



THE well-known fundamental formulas for a transmis- 

 sion line without branches, in which the load is delivered 

 only at the end of the line, are as follows: 



E a = Ecosh VYZ + ^=7Zsinh VYZ, 

 and i s = I cosh VYZ + 7 sinh Wz, 



where E 8 and I a are the voltage and current at the 



supply end, 

 E and 7 are the voltage and current at the re- 



ceiver end, 



Y is the line admittance 

 and Z is the line impedance. 



The above equations have been published at various 

 times. They are obtained as follows: 



Let r = resistance of conductor per unit length, 



and x = reactance of conductor per unit length. 



Then z = r +jx 



= impedance of conductor per unit length. 

 Let g = leakage conductance from conductor per 



unit length, 

 and b = capacity susceptance of conductor per unit 



length. 

 Then y = g +jb 



= admittance of conductor per unit length. 

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