Question

If the area of the material is $4{m^2}$ and the length 20 m. What will be the resistivity of that material when its resistance is $10\Omega$.
A) 12 mho.
B) 20 mho.
C) 4 mho.
D) 2 mho.

Answer 1

Hint
Use the formula of resistivity i.e. $R = \dfrac{{\rho l}}{A}$ and compute the value of resistivity to find out the answer. Resistivity is property of a material. Resistance of a body depends upon its resistivity.

Complete step by step answer
Given that the area of the material is $4{m^2}$and the length 20 m. also given that resistance = $10\Omega$.
We know that resistivity is given by the formula,
$R = \dfrac{{\rho l}}{A}$
Where R is the resistance of the material.
$\rho$ is the resistivity of the material.
L is the length.
A is the cross section area of the material.
Putting the values in the above equation and simplifying we have,
$\Rightarrow 10 = \rho (\dfrac{{20}}{4})$
$\Rightarrow \rho = 2\,{\text{mho}}$
Hence the resistivity of the material is $2\,{\text{mho}}$ and the correct answer is option (D).

Note
Resistivity is the property of a material and it shows how much resistive a material is to electric current.
Just like resistivity, there is one more property named conductivity which shows how much conductive a material is. It is given by the reciprocal of resistivity. The formula for conductivity is $\sigma = \dfrac{1}{\rho }$.