KENNELLY. — BUILDING UP VOLTAGE AND CUHRENT. 705 



3. When the distant end of the line at B is grounded through a 

 receiving impedance Zr uhuis, 



1b = ^—r-, — ; vT^— amperes (23) 



Co Sinn La + Zr cosn La x v / 



Eb= laZr volts (24) 



All of the values of voltage and current in the steady-state formulas 

 (14) to (24) inclusive, may be regarded either as instantaneous vol- 

 tages and currents, in terms of instantaneous impressed voltage E and 

 current /; or they may be regarded as effective, or S(iuare-root-of-mean- 

 square values, in terms of etfective impressed voltage E and current 

 /, such as would be indicated by properly calibrated voltmeters and 

 ammeters. 



We may now proceed to show how formulas (19) to (24) inclusive 

 may be derived by taking into account the initial outgoing waves of 

 voltage and current, together with superposed reflected waves. The 

 only postulate needed is that when the line is first connected to the 

 alternator at A, the first outgoing current wave has the strength 



T E 



U — — amperes (2,)) 



~0 



and this current strength continues to be delivered to the line at A 

 until such time as current-waves reflected from the distant end modify 

 the current. This proposition is well known.* 



The outgoing voltage and current waves run along the wire hand in 

 hand, with the velocity : 



V — ~~ kilometers per second (2(5) 



a velocity which is soracAvhat less than the speed of long-wave light in 

 the dielectric. When the linear conductor resistance and leakage con- 

 ductance are very small, this velocity approximates to : 



v = —= kilometers per second (27) 



In the case of overhead aerial copper wires, v approaches 300,000 

 kilometers per second at high frequencies. At low frequencies the 

 effect of conductor resistance requires the use of formula (26), and 

 may bring down the velocity to 100,000 kilometers per second or less. 

 In paper-insulated, and especially in rubber-insulated cables, the veloc- 



* " On the Mechanism of Electric Power Transmission," by A. E. Kennelly. 

 Electrical World, 42, 673 (Oct. 24, 190-3). 



