The effectiveness of the two-dimensional electric potential method of damage sensing in a quasi-isotropic carbon fiber polymer-matrix composite depends on the electrical configuration, i.e., the current direction relative to the surface fibers and the electrical contact scheme. Oblique current application in any direction provides effective damage sensing, as shown by using electrical contacts on the opposite in-plane surfaces. In-plane current application through the cross section in any direction also provides effective damage sensing, as shown by using electrical contacts that are either on the edge surfaces or in holes through the composite. In-plane surface current application is effective when the current is perpendicular to the surface fibers (due to the low resistivity in the direction of the fibers) and is ineffective when the current is parallel to the surface fibers (due to the high resistivity in the direction perpendicular to the fibers). The oblique configuration is recommended for practical implementation. In general, the potential method is reliable when (i) the resistance between the electric current line and the nearly parallel electric potential gradient line is sufficiently low, as attained when these lines are sufficiently close, and (ii) the resistance between the current line and the damage location is sufficiently low, as attained when the distance of separation is sufficiently small.