Gate_2020
6)
Current and
potential electrode in resistivity survey over an inhomogeneous
ground is shown in the below figure. If 100mA current flow between C1
and C2
generates 50mV potential difference between P1
and P2
, then the apparent resistivity of the medium will be ________Ωm
(Thanks to Chandrasekhar, ANU)
Solution:
Given
that ΔV =50mV
I
= 100mA
Apparent
resistivity (ρa)
=?
Where
$
r_{1} =10 m$
$
r_{2} =50 m$
$
r_{3} =30 m$
The
apparent resistivity in of the array is given below (Wenner array)
$\rho_{a}
=( 2\pi)(\frac{\triangle
V}{I})\left\{(\frac{1}{r_{1}}-\frac{1}{r_{2}})-(\frac{1}{r_{3}}-\frac{1}{r_{4}})\right\}^{-1}$
$\rho_{a}
=(
2\pi)(\frac{50}{100})\left\{(\frac{1}{10}-\frac{1}{50})-(\frac{1}{30}-\frac{1}{30})\right\}^{-1}$
$\rho_{a}
=(
2\times3.14\times0.5)\left\{(\frac{1}{10}-\frac{1}{50})\right\}^{-1}$
$\rho_{a}=3.14\times
( \frac{40}{500})^{-1}$
$\rho_{a}=3.14\times
12.5$
$\rho_{a}=
39.25 Ωm $
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