Question

Unit of specific resistance
$\eqalign{
  & {\text{A}}{\text{. }}ohm \cr
  & {\text{B}}{\text{. }}oh{m^{ - 1}} \cr
  & {\text{C}}{\text{. }}ohm{\text{ }}metre \cr
  & {\text{D}}{\text{. oh}}{{\text{m}}^{ - 1}}metr{e^{ - 1}} \cr} $

Answer 1

Hint: Specific resistance or resistivity is the resistance offered by a unit length of material having unit area. The unit of resistance is ohm, the unit of area is $metr{e^2}$ and the unit of length is metre. So to find the required solution, just form mathematical expressions of the given definitions and solve those expressions.

Formula used:
$R = \dfrac{{\rho l}}{A}$

Complete step by step answer:
Specific resistance or resistivity of a material is defined as the resistance offered by a unit length of the same material having unit area. It is a material constant. And is independent of the electric field existing in the material. Additionally, it can also be defined as the reciprocal of conductivity.
The mathematical relation between resistance, resistivity, length of the material, and area of the material is given by:
$R = \dfrac{{\rho l}}{A} \cdots \cdots \cdots \cdots \left( 1 \right)$
where ‘R’ represents the resistance offered by the material,
‘l’ represents the length of the material,
‘A’ represents the area of the material
and $\rho $ represents the specific resistance of the material.

We know that the unit of resistance is ohm, the unit of area is $metr{e^2}$ and the unit of length is metre. So, substituting these values in the formula equation (1) we have:
$\eqalign{
  & \rho = \dfrac{{RA}}{l} \cr
  & \Rightarrow \rho = \dfrac{{ohm \times metr{e^2}}}{{metre}} \cr
  & \therefore \rho = ohm{\text{ }}metre \cr} $
Therefore, the correct option is C. i.e. the unit of specific resistance is ohm metre.

Note:
Resistance is a property of each and every conductor to oppose the flow of charge through it. The higher the value of resistance, the lower is the amount of current passing through. It depends on the length, area of cross-section, and nature of the material. The nature of the material decides the resistivity of the system. Thus, the resistance is directly proportional to the resistivity of a material.