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To find the resistance of a material, we can use the formula derived from Ohm’s Law, which relates resistance (R), resistivity (ρ), length (L), and cross-sectional area (A). However, in this context, we are given conductivity (σ) instead of resistivity (ρ). Conductivity is the inverse of resistivity, thus:
[ sigma = frac{1}{rho} ]
The given values are:
– Conductivity, ( sigma = 2 ) millimhos/m ( = 2 times 10^{-3} ) S/m (since 1 mho = 1 S (Siemens), and 1 millimho = ( 10^{-3} ) S)
– Length, ( L = 10 ) m
– Cross-sectional area, ( A = 50 ) m(^2)
The resistance (R) of a material is calculated from resistivity (( rho )), length (L), and area (A) using the formula:
[ R = frac{rho cdot L}{A} ]
Given that ( sigma = frac{1}{rho} ), we can rearrange this to find ( rho = frac{1}{sigma} ), then substitute ( rho ) in the resistance formula:
[ R = frac{L}{sigma cdot A} ]
Substituting the