The work described in the paper is concerned with predicting the r.m.s. current which a simple harmonic voltage will drive through a non-ohmic resistor in series with an impedance, having either positive or negative phase angle. The non-ohmic resistor is supposed to be of the general character of those constructed from silicon carbide; i.e. its resistance is independent of the direction of the current, and the magnitude of the current varies approximately as the fifth power of the voltage. The paper is mainly experimental but there is an analytical Appendix in which it is shown that the observed experimental results can be predicted by simple algebraic methods.Experiments were made to discover the voltage which is needed in order to maintain a given r.m.s. current through a silicon-carbide resistor which is placed in series with (a) a variable ohmic resistor, (b) a variable condenser, and (c) a variable inductor. In all three cases it is found that the silicon-carbide resistor behaves substantially as though it were a constant ohmic resistance, at any assigned current. The magnitude of this constant resistance is a function of the given current and it can readily be deduced from the static characteristic of the given non-ohmic resistor. It is nearly accurate to say that the equivalent constant resistance, at any given current, is equal to the r.m.s. voltage divided by that current, in the circumstances when there is no impedance in series with the non-ohmic element.In the main, the experimental portion of the paper is concerned with r.m.s. values and not with waveforms, which are discussed in the Appendix. Taken as a whole, the paper should suffice to predict r. m. s. current, waveform and phase angle when a given non-ohmic resistor is connected in series with any general impedance.