Effective resistance and reactance of a rectangular conductor placed in a semi-closed slot

The paper has evolved from an earlier work by the present authors and develops the theory previously employed to determine the distribution of current over the cross-section of a rectangular conductor lying in a slot with a narrow opening. The analysis has been simplified by assuming that the thickness of insulation on the conductor is negligible, and that the effect of eddy currents in the slot walls may be ignored. It is found that the current density at any point can be expressed in the form of an infinite series of hyperbolic functions, from which the complex impedance per unit length of conductor has been determined. Graphs showing the variation of effective resistance and reactance with different bar configurations are given, together with the modifications necessary for different frequencies and conductor material. The results show that, at power frequencies, the effective resistance of the bar is unaffected by the width of the slot opening, and the appropriate formula agrees with that obtained by Field for the open slot; but the effective reactance is substantially increased as the slot opening is narrowed. A description of the conditions under which the effective resistance is affected by variation of the slot opening is included.