Cable charge and discharge

Conductivity determinations of insulating materials, and therefore the determinations of the leakage resistance of a cable, condenser or similar structure, have always been more or less unsatisfactory, due to a phenomenon often called “soaking in of the charges.” In general, if a constant direct voltage is impressed upon a circuit, in the first moment large transient currents flow, representing the energy storage and adjustment in the magnetic and dielectric fields of the circuit. These transient currents however vanish very quickly, usually in a very small fraction of a second, and all the currents in the circuit or circuits then become constant. If a constant direct voltage is impressed upon a cable or similar structure, large transient currents also flow momentarily; but after these currents of energy adjustment in the electromagnetic field of. the system have vanished, usually after a small fraction of a second, the remaining current is not constant, as in the usual electric circuit, but continues to decrease-slowly, for minutes or even hours. If then the cable is discharged by short-circuiting it, after the large initial transient discharge current has passed and the voltage on the cable has become zero — in a small fraction of a second — the current coming out of the cable does not entirely vanish, but a small discharge current continues to flow for many minutes or even hours. Or, if the cable has been discharged by short-circuiting it for a short time, until its terminal voltage has become zero, and the short circuit is taken off, a terminal voltage and an electrostatic charge gradually build up again at the cable, reach a maximum after some minutes, and then gradually decrease again. Various explanations have been proposed of this phenomenon as a hysteresis effect of the dielectric, etc. It is shown in the following, that this phenomenon of the “soaking in of the charges” or the “electrification of the- cable” is a true electric circuit transient, has nothing to do with hysteresis effects, but is the result of, and explained by the energy adjustment of a system with constant values of resistance, inductance and capacity, that is, is in no essential different from the usual rapid starting or stopping transient of the ordinary circuit, except that it is many thousands of times slower. This great slowness is due to the fact that the resistance in the transient circuit is the leakage resistance of the cable dielectric, and therefore extremely high, measured not in ohms but in hundreds of megohms. If the dielectric of the cable consists of two or more materials, having different resistivities, or different specific capacities, or both, then the distribution of voltage through the dielectric gradually changes. At the moment of voltage application, the voltage distributes between the component dielectrics in proportion to their specific capacities; gradually however this voltage distribution changes to a distribution proportional to the resistivities of the component dielectrics, and electrostatic charges build up in the interior of the dielectric, at the boundaries between the component dielectrics. The electric quantity has to be conducted through the dielectric, and due to the very high resistivity of the dielectric, this energy readjustment within the dielectric occurs with extreme slowness, giving a transient of a duration of many minutes, but a true electric transient nevertheless, like the usual transients of a duration of milliseconds. In the discharge of the cable, the reverse occurs, and the internal charges gradually disappear by conduction through the dielectric. This phenomenon is discussed in its various aspects, and the equations of the slow transient derived, in the following: It is shown that this slow transient always is impulsive or exponential, and consists of (n — 1) terms, if the insulation is composed of n materials. A number of con