The electrical impedance of a lossy conductor is a complicated function of time (or frequency) because of the skin effect. By solving the diffusion equation for magnetic fields in conductors of several prototypical shapes, the impedance can be calculated as a function of time for a step function of current. The solution suggests an electrical circuit representation that allows calculation of time-dependent voltages and currents of arbitrary waveforms. A technique using an operational amplifier to determine the current in such a conductor by measuring some external voltage is described. Useful analytical approximations to the results are derived.
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Kerst et al. (1986) studied this question.
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