GATE-2018 (24) :Wyllie – Time average equation

UPSC-2015

1. Derive the generalized equation for determining the apparent resistivity from an array of current and potential electrodes . Use this expression to estimate the apparent resistivity for the above situation for the current of 1 ampere.

Solution:

Apparent resistivity (ρ_a),

(ρ_a) = 2*π*(V/I) * [ ( (1/AM) -(1/MB) ) - ((1/AN)-(1/NB) ) ]^-1 --(1)

Potential of M and N is V_p1-_p2 = 1.52+2.98

                                                             = 3.5 V

Current (i)= 1 amp

ρ_a= 2*π*(V/I) * [ ( (1/3) -(1/7) ) - ((1/8)-(1/2) ) ]^-1

ρ_a = 2*π*(3.5/1) * [ ( (7-3)/ 21 ) - ((2-8)/ 16) ]^-1

ρ_a = 2*π*(3.5/1) * [ (4/21 ) - (4/16) ]^-1

ρ_a = 2*π*(3.5) * [ 0.190-0.25 ]^-1

ρ_a = 2*π*(3.5) * [ 0.44]^-1

ρ_a = 49.95 Ωm

Therefore, apparent resistivity (ρ_a) = 49.95 Ωm