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To find the resistance of a material, we use the formula:
[ R = frac{L}{sigma A} ]
where ( R ) is the resistance in ohms (( Omega )), ( L ) is the length of the material in meters (m), ( sigma ) is the conductivity in siemens per meter (S/m), and ( A ) is the cross-sectional area in square meters (( m^2 )). Given that conductivity is provided in millimhos per square meter, we first need to convert it to siemens per meter (S/m). Note that 1 mho is equivalent to 1 siemens (S), and therefore 1 millimho = ( 1 times 10^{-3} ) S.
Given values:
– Conductivity (( sigma )) = 2 millimhos/m(^2) = ( 2 times 10^{-3} ) S/m(^2)
– Length (( L )) = 10 m
– Cross-sectional area (( A )) = 50 m(^2)
Substituting the values into the formula:
[ R = frac{10}{(2 times 10^{-3}) times 50} ]
[ R = frac{10}{0.1} ]
[ R = 100 , Omega ]
Therefore, the resistance of the material