Resistance of Dielectric Configurations

The electrical resistance of most dielectric liquids and solids is a rather complex function of time, electrification, and in some cases of electric field intensity. The losses in a dielectric under alternating stresses are generally much greater than can be accounted for on the basis of d-c resistance. At least part of this difference is due to the polarization of the dielectric. In some kinds of dielectric a sudden application of d-c voltage is accompanied by a relatively large momentary current, which at first falls off rapidly and then decreases very slowly, sometimes still decreasing hours after the application of a constant potential.

However, if the resistivity of the dielectric is assumed constant, i.e., it is not affected by the electric field intensity or time of electrification, the resistance of the dielectric of a certain configuration is found by using the methods that were used for determining capacitance.

Consider two concentric spheres, the space between which is occupied by a dielectric that has an electrical resistivity of p ohms per meter cube. If Fig. 2-15 is applied to the case of concentric spheres instead of concentric cylinders, the resistance of the elemental spherical shell of thickness dx is expressed by

The resistance between spheres is therefore

[2-81]

It is interesting to compare Eq. 2-81 with Eq. 2-28 for the capacitance of concentric spheres. The product of these two quantities and of the relative dielectric constant k_r yields

[2-82]

This product is valid for any configuration of homogeneous dielectric.