The object of the thesis is to obtain the apparent- resistivity curves and induced-polarization (IP) effects that are utilized in geophysical exploration. Two different earth geometries, the thin horizontal conductive layer and vertical dike, were studied. The solution for both cases is identical. First, quasi- static electrical conditions were assumed, so that the problem could be solved using potential fields. The exact solution to the problem was obtained by using the Bessel integral formulation. Also, the image method was employed to find the potential fields. We noticed that the image -type series converges best when the dike or layer was thick (ratio of thickness to electrode spacing, b/a, is large) and the reflection coefficient was not near ±1. Otherwise, it is preferable to employ the thin conductive sheet model. The next step was to determine the dilution and distortion factors which are relevant to the induced polarization response. Finally, numerical results were obtained using a Fortran computer program. These calculations were compared with some results taken from the literature and good agreement is seen.