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

CSIR NET – JUNE 2015

51) A 20cm Cube of a rock measures a resistance of 200ohm. The resistivity of the rock is

1) 4000 Ωm

2) 1000 Ωm

3) 800 Ωm

4) 40 Ωm

(Thanks to Neeraja, AU)

Solution:

Cube length(l)= 20cm

Resistance(R)=200Ω

Resistivity(ρ)=?

(Cube Area = a²)

$Area=length\times length=l^2=20\times20=400cm^2$

$\rho=R\frac{A}{l}$

$\rho=200\times\frac{400}{20}$

      $=10\times400ohm.cm$

     $=4000ohm.cm$

     $=40ohm.m$