# Solution Exercise 1

Resistivity is an intrinsic property of a material and describes how difficult it is for electrical current to flow through that material. Electrical resistivity is the reciprocal of electrical conductivity. Electrical resistivity is therefore analogous to the reciprocal of hydraulic conductivity (*K*).

Resistance is also a measure of the difficulty with which electrical current can flow, but it is dependent on geometry. It is similar to transmissivity, which is dependent on hydraulic conductivity and layer thickness, but when resistance to current flow is measured, it depends on resistivity of the material, the distance between the measurement points, and the cross-sectional area through which current is flowing between those points. In 1-D current flow (e.g., in a wire, or column of uniform properties), resistance is directly proportional to length between the ends of the column and inversely proportional to the cross-sectional area of the column. The equivalent hydraulic parameter would be the hydraulic resistance, or *L*/(*KA*), where *L* is the length of the flow path and *A* is the cross-sectional area through which water flows. Consequently, because of this geometric dependence, resistance values can be small or large—even in a system with homogeneous resistivity.

Apparent resistivity applies a geometric factor to the measured resistance to estimate what the resistivity of the system would be, assuming a homogeneous Earth extends infinitely with depth and lateral distance. Only in the case of a homogeneous Earth will the apparent resistivity equal the true resistivity. The utility of apparent resistivity is that it allows a practitioner to look at their field data to see if the values are reasonable and to rapidly locate anomalies. Inversion of the data is required to obtain actual resistivity values.