576 BELL SYSTEM TECHNICAL JOURNAL 



Consider first that the inducing circuit carries direct current. In 

 such a case, as long as the magnitude of the direct current does not 

 change, the magnetic flux is constant and no voltage will be induced in 

 a paralleling telephone wire. However, if the current in the inducing 

 wire changes suddenly, the flux about it changes in the same proportion 

 and voltage is induced momentarily in the paralleling wire. The 

 magnitude of this impulse of voltage will be proportional to the rate 

 at which the flux changes and the voltage will last only as long as the 

 flux is changing. Rapid changes in the current in direct current 

 circuits, with consequent voltage impulses on paralleling telephone 

 circuits, may occur when power apparatus is turned off" or on. Also, 

 of course, if a short circuit occurs, the current may rise very rapidly 

 and then fall very rapidly as the circuit breaker operates. While the 

 consideration of these direct current phenomena are important in some 

 situations, they are not included in this demonstration and will not be 

 further considered. 



In the alternating current case, the current in the inducing wire is 

 continually alternating so that the flux about it is continually alter- 

 nating. Consequently, there will be induced in a paralleling wire, an 

 alternating voltage proportional to the inducing current. It should be 

 noted particularly that the induced voltage acts along the wire rather 

 than between the wire and ground. 



General Nature of Phenomena 

 In applying these principles of magnetic induction to the low- 

 frequency induction problem, only the conditions which exist when a 

 power circuit is faulted to ground and before the current is interrupted 

 (usually by the operation of circuit breakers) need be considered. 

 The current of interest during this time is that which flows out over the 

 power line wires and returns through the ground, called "residual" 

 current. The voltage induced is along the telephone wires in parallel. 

 Since the telephone circuits are metallic, the talking paths over them 

 are usually not seriously affected by the fundamental frequency voltage 

 unless this voltage causes the telephone protectors to operate. Service 

 over grounded telegraph circuits may, however, be impaired even if 

 the induced voltage does not reach values high enough to operate 

 protectors, and the telephone circuits under this condition may be 

 made noisier than usual. 



It can be seen that the electrical phenomcMia in which we are in- 

 terested will be affected by three basic factors. The first of these is 

 concerned with the "magnetic coupling" between the power and 

 telephone lines, considered with ground return for the reasons pointed 



