Currents and Potentials along Leaky Ground- 

 Return Conductors * 



By E. D. SUNDE 



^ I ^HE problem of current and potential propagation for long 

 ^ conductors having large leakance to ground arises in connection 

 with certain railway electrification problems, such as inductive effects 

 in exposed communication lines, and voltages to ground of the tracks 

 and of nearby underground cables. Impressed voltages in exposed 

 lines are due partly to induction and partly to earth potential differ- 

 ences, and the latter in particular depend to a considerable extent on 

 the mode of propagation of the track current. Voltages to ground of 

 underground telephone cables depend on the mode of propagation 

 along the cables of current produced in these by nearby railway 

 electrification. These voltages may under certain conditions raise 

 questions as to the possibility of hazard or, in case of direct current, 

 give rise to electrolytic effects. 



In considering propagation along earth-return conductors of the 

 above kind, it is necessary to include certain effects which can be 

 neglected in circuits having small leakance. One of the quantities 

 involved in the differential equation for the current at a point of a 

 ground-return conductor is the axial electric force produced in the 

 ground adjacent to the conductor. For a given frequency and earth 

 resistivity, this electric force at the point under consideration depends 

 partly on the axial current distribution and partly on the leakage 

 current distribution along the entire length of the conductor. The 

 component depending on the axial current distribution is the vector 

 potential multiplied by — iw, co being the radian frequency, while the 

 other component is the negative gradient of the earth potential, 

 which depends on the leakage current distribution along the conductor. 

 In the customary treatment, applying to conductors of small leakance, 

 the axial current is assumed practically constant for great distances 

 along the conductor, so that the first component becomes the negative 

 product of axial conductor current at the point under consideration 

 and the external earth-return impedance of the conductor. Further- 

 more, the earth potential is neglected or assumed constant along the 

 conductor, so that the second component vanishes. 



* Digest of a paper to be presented at the Winter Convention of the American 

 Institute of Electrical Engineers, New York, January 25-29, 1937, and published in 

 full in Electrical Engineering, Vol. 55, No. 12, pp. 1338-1346, December, 1936. 



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