208 BELL SYSTEM TECHNICAL JOURNAL 



no chance for a lineman working on the wires to get in contact with 

 earth. Neither in power systems nor in telephone systems is it actually 

 necessary that the earth be used as part of an operating circuit but, as 

 the earth is a conductor, and power and telephone lines and apparatus 

 are located on its surface, it is essential in both systems that the earth 

 be taken into account in circuit problems and that paths to earth for 

 protective purposes be established at certain points. 



It must not be assumed, however, that the earth is a perfect conduc- 

 tor. For the most part the materials of which the earth's crust is 

 composed are of relatively low conductivity. From numerous meas- 

 urements in various places the average conductivity over considerable 

 volumes of earth has been found to range from 10"" to lO"'^ abmho per 

 cm. cube. The resistance of an earth path is therefore not zero but 

 may be many ohms or even in some cases many hundreds of ohms. 

 Most of this resistance is in the immediate vicinity of the electrodes and 

 can be reduced by increasing the surface area of contact between 

 electrcde and ground. 



In discussing the low-frequency induction problem, it is convenient 

 to consider the factors controlling: 



(1) The magnitude of induced voltages, (2) the frequency of occur- 

 rence of induced voltages, (3) the duration of induced voltages, and 

 (4) the effects produced by induced voltages. 



Factors Controlling the Magnitude of Induced Voltages 



The magnitude of voltages induced in telephone systems in specific 

 cases depends chiefly on the magnitude of residual currents and voltages 

 resulting from power circuit faults to ground and on the exposure 

 conditions. 



Residual Currents and Voltages. A balanced power circuit is one 

 in which the voltages from the various phase conductors to ground are 

 equal and sum up vectorially to zero and in which the phase currents 

 also are equal and sum up to zero. Under this condition all the cur- 

 rents in the circuit are balanced currents and all the voltages are 

 balanced voltages. If, however, one phase develops a fault to ground, 

 this relation becomes disturbed, the voltages to ground of the phases 

 become unequal, and their vector sum, which is the residual voltage 

 (3 times the so-called uniphase or zero phase sequence voltage) of the 

 power circuit, is no longer zero. The currents in the three phases like- 

 wise become unequal and when added vectorially their sum, which is 

 the residual current (uniphase or zero phase sequence current) of the 

 power circuit, is no longer zero. In most low-frequency induction 

 problems residual current is far more important than residual voltage. 



