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UPSC-2015

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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 (ρa),

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


Potential of M and N is Vp1-p2 = 1.52+2.98

                                                             = 3.5 V

Current (i)= 1 amp


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


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


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


ρa = 2*π*(3.5) * [ 0.190-0.25 ]-1


ρa = 2*π*(3.5) * [ 0.44]-1


ρa = 49.95 Ωm


Therefore, apparent resistivity (ρa) = 49.95 Ωm




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