Electromagnetic induction in a system of straight parallel nonmagnetic conductors of equal circular cross-section

A method is described for calculating the alternating-current resistance of any member of a general system of straight parallel nonmagnetic conductors of equal uniform circular cross-section. The total current in each conductor is assumed to be known in magnitude and phase. The theory is a generalisation of that developed by Butterworth for two parallel conductors. The solution for two conductors carrying equal or opposite currents and the solution for three symmetrically arranged conductors carrying 3-phase balanced currents are derived from the general solution. These particular solutions agree with Butterworth´s solution for two conductors and with Costello´s solution for the 3-phase system. The present solutions have been evaluated numerically to high accuracy with the aid of a computer and the results are found to agree with available experimental results within the limits of experimental error. New solutions are derived for systems of four and six conductors and numerical results are compared with new experimental work, again yielding agreement within the limits of experimental error. The general solution may therefore be applied with some confidence to any system of parallel conductors.