Question

What is the SI unit of electrical resistivity of a material.
$\begin{align}
  & \text{A}\text{. }\Omega cm \\
 & \text{B}\text{. }\Omega \text{m} \\
 & \text{C}\text{. }\Omega \text{c}{{\text{m}}^{2}} \\
 & \text{D}\text{. }\Omega {{\text{m}}^{2}} \\
\end{align}$

Answer 1

Hint:Resistivity is the property of the material to oppose the flow of electric current through it. SI unit of electrical resistivity can be found from its basic formula. Resistance depends upon the resistivity, length and cross-sectional area of a material.

Complete step-by-step answer:
Resistance of a wire, whose length is L and cross-sectional area is A, can be defined as
$R=\rho \dfrac{L}{A}$
Where,
Proportionality constant $\rho $ is the resistivity of the material.
Resistivity of a material can be defined as resistance per unit length and per unit area. It is the characteristic of a material which varies for different kinds of materials.
Finding the SI unit of resistivity-
$\begin{align}
  & \rho =\dfrac{RA}{L} \\
 & \Rightarrow \rho =\Omega \dfrac{{{m}^{2}}}{m}=\Omega m \\
\end{align}$
Thus, the correct answer is B.

Note: Resistance of a wire is proportional to its length (L) and inversely proportional to its area (A), which means for thick and shorter wires will have less resistance than thin and longer wires.
Resistivity is a proportionality constant in the resistance formula, which varies with characteristics of material. It is based upon the atomic structure of the material. We can change the atomic structure of material by changing temperature.
In case of metals, where free electrons are easily available. If we increase the temperature, electrons will get more kinetic energy, and collide with each other. Thus, they will obstruct each other's motion. This will lead to increasing resistivity.
In case of non-metal, electrons are not free, they are tightly bound to the nucleus. If we increase the temperature, electrons will get kinetic energy and travel with ease. This will decrease resistivity.