The influence of frequency on the resistance and inductance of solenoidal coils

Abstract

The resistance and inductance of a conductor depend on the dis-tribution of the current within the conductor. When the current is continuous the distribution is uniform throughout the section of the conductor, and the problem of finding the resistance and induc-tance is a very simple one. If, however, the current is varying with respect to time, eddy currents with their accompanying magnetic fields will be generated within the conductor, which will alter the distribution of the current and consequently change the resistance and inductance of the conductor. The problem of finding the law of variation of resistance and inductance with the frequency is of consid-erable importance, and for the case of a straight cylindrical wire the problem has been satisfactorily worked out. The results, however, as obtained for the case of a straight wire, will not hold when the same wire is wound into a coil. It has been found experimentally that the change in resistance of a coil for any given frequency is much larger than if the winding of the coil were drawn out into a straight conductor. Dolezalek, 1 in his experiments with high-frequency currents, was the first to call attention to the fact that the change of resistance is larger than that calulated by the theory for straight conductors. Battelli and Maggi have also carried out a series of experiments along that line and found the same results. Owing to the importance of the problem in its application to wireless telegraphy, several investigators have sought to obtain solutions to this problem. Their efforts were not attended by any 1 Dolezalek, Annalen der Physik, 12; 1903.