In electrical resistivity surveys for groundwater exploration using the Wenner electrode configuration, four collinear electrodes are spaced at equal distances $a$. The apparent resistivity $\rho_a$ is given by:
Options:
(A) $\rho_a = 2 \pi a \frac{\Delta V}{I}$
(B) $\rho_a = \pi a \frac{\Delta V}{I}$
(C) $\rho_a = 4 \pi a \frac{\Delta V}{I}$
(D) $\rho_a = \frac{2 \pi}{a} \frac{\Delta V}{I}$
Answer Key:
A
Step-by-Step Solution & Explanation
For the symmetrical Wenner arrangement with equal spacing $a$ between current electrodes $C_1, C_2$ and potential electrodes $P_1, P_2$:
Geometric factor $G = 2 \pi a$.
$\rho_a = 2 \pi a \frac{\Delta V}{I}$