THE PROCESS OF BUILDING UP THE VOLTAGE AND CUR- 

 RENT IN A LONG ALTERNATING-CURRENT CIRCUIT. 



By a. E. Kennelly. 

 Presented March 13, 1907. Received March 5, 1907. 



Let us consider the simple alternating-current circuit indicated in 

 Figure 1 ; namely, a long single uniform wire AB, with a ground return 

 circuit. A single-phase sinusoidal alternator of negligible internal 

 impedance and generating an e. m. f. 



E=E^ sin lot ab volts (1) 



is connected to the end A at the instant ^ = 0, when E is starting 

 positively from zero at the uniform frequency w cycles per second, or 

 with angular velocity w = 2 tt w radians per second. At B, the distant 

 end of the line, there is connected an impedance Z to ground. If we 

 make Z = oo , we virtually free or disconnect the line at B. If we 

 make Z = 0, we virtually ground the line at B. If we make Z = Zr, 

 we virtually insert a receiving impedance at B. Any two-wire or 

 multiple-wire metallic circuit is capable of being reduced to an equiva- 

 lent simple single-wire circuit with ground return, such as is represented 

 in Figure 1. 



A B 



r 



Figure 1. — Simple alternating-current circuit. 



The current and voltage which exist at any point of the line in Fig- 

 ure 1 can be readily computed, whatever the given terminal impedance 

 at B, after the system has been allowed to operate for a sufficient length 

 of time, usually about one second, during which the initial unsteady 

 state may be regarded from a practical standpoint as developing into 

 the final steady state. It is proposed to discuss in this paper certain 

 formulas, that appear to be new in this application, by which the ac- 



