Capacitance measurements have been extensively used to measure the anchoring extrapolation length L at a nematic-substrate interface. These measurements are extremely delicate because the value found for L often critically depends on the sample thickness and the voltage range chosen to perform the measurements. Several reasons have been proposed to explain this observation, such as the presence of inhomogeneities in the director distribution on the bounding plates or the variation with the electric field of the dielectric constants. In this paper I propose a new method to measure Lp that takes into account this second effect. This method is more general than that proposed in Murauski et al. Phys. Rev. E 71, 061707 (2005) because it does not assume that the anchoring angle is small and that the anchoring energy is of the Rapini-Papoular form. This method is applied to a cell of 8CB treated for planar unidirectional anchoring by photoalignment with the azobenzene dye Brilliant Yellow. The role of flexoelectric effects and the shape of the anchoring potential are discussed.