The relationship between the region 1 field-aligned current (FAC) intensity and the ionospheric conductivity in geomagnetically quiet conditions has been believed to be useful to determine whether the FAC is driven by a voltage generator or a current generator. This paper, however, shows that at least for daytime (0800--1600 MLT) FACs, the current generator has the same characteristic of linear relationship between the current intensity and the conductivity as the voltage generator. This conclusion is obtained due to the fact that the sum of Pedersen conductivities, maintained by solar EUV ionization, at two conjugate points on the northern and southern ionospheres is approximately independent of the solar zenith angle at either of these points. Notably, the pressure-gradient-driven model for the generation of the region 1 FAC from the low-latitude boundary layer is then consistent with observations that the current intensity increases linearly with the height-integrated Pedersen conductivity.