The most important point which the authors hope that a reader will take away from this discussion is that an intuitive understanding of how the world works in the context of DC systems (which includes any system with substantial relaxation toward a restively graded state) allows many properties of such a system to be predicted either from first principles, as in the case of a cable, or through a few simple finite element computations (of the AC and DC graded states) in the case of more complex systems. The greatest problem in engineering such systems is that the relevant material properties, especially the field and temperature-dependent conductivity, often are not well known. However the limited range of field over which the conductivity is needed eases measurement. For unfilled systems, the temperature dependence of the conductivity can be measured, the field dependence can be measured, and to first order, the two can be combined without an interaction term, as in (1).
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Qin et al. (2012) studied this question.
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