The effective conductivities of regular arrays of aligned long fibers possessive of superconducting interfaces are studied. Two most common two-dimensional arrays are investigated: square and hexagonal arrays. A dimensionless quantity, termed the dipole polarizability, which is a simple function of a dimensionless interfacial conductance parameter, C, and the normalized conductivity of the fiber, alpha and ranges from -1 to, 1, is identified to characterize the overall interfacial properties. The normalized effective conductivity of the composite can be viewed as a function of the dipole polarizability, and the volume fraction of the fiber. The dipole polarizability is found to be a unified parameter applying equally well to effective conductivity problems with the matrix-fiber interface in perfect contact or possessive of an interfacial resistance, only that the expression for the dipole polarizability is different for the different problem. A universal contour plot in the dipole polarizability, vs. fiber volume fraction domain is constructed for the normalized effective conductivity of the composite. A critical C (= 1-alpha) is identified, at which the overall conductivity effect of the fiber is neutral.