GATE-2016
40. In resistivity logging using a 'Normal device' the distance between electrodes A and M is 0.40m . If 20mA current generates 10mV potential the apparent resistivity of the layer between the electrodes is ........ohm m
Solution:
MN
are the potential electorodes
AB
are the current electrodes
apparent
resistivity (ρa
) = 4*Π* (ΔV/I) *(AM) -------------(1)
Voltage
= 10 mV
current
I= 20mA
spacing
(AM) = 0.4m
substitute
above vaules in eq(1)
ρa
= 4*Π* (ΔV/I) *(AM)
ρa
= 4*3.14* (10/20) *(0.40)
ρa
= 2.512 Ωm
Extra information:
The factor is 4pi here rather than 2pi because the above equation (1) holds in the interior of the medium rather than at the surface of a semi-infinite medium
Reference: Applied Geophysics by W.M. Telford , L.P. Geldart and R.E.Sheriff.
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