By using spherical Cu powders as the conducting sintering material, the microstructures of sintered powder particles at different stages in the process of spark plasma sintering (SPS) have been investigated. Theoretical analyses are proposed to quantify the effects of the pulsed direct current on the neck formation and the neck growth of conducting powders. It is found that there is a considerable inhomogeneous distribution of the temperature increase from the particle-contacting surface to the center of the particle when the pulsed current passes through. The temperature at the particle-contacting surface may reach the boiling point of the material, which results in neck formation at relatively low-sintering temperatures through a process of local melting and rapid solidification. The neck growth depends on the local distribution of the current intensity, which is determined by the competition between the neck cross-sectional area and the electrical resistivity increasing with the temperature. Accordingly, we propose that the coarsening of necks follows a "self-adjusting" mechanism, which is likely to be the essential reason for the homogeneous distributions of neck sizes and sizes of fine grains formed in the neck zones during the SPS process.