Question

Which of the following is the S.I unit of resistivity?
$A.{\text{ V}}{\text{.m}} \\\ {\text{B}}{\text{. }}\Omega .{{\text{m}}^2} \\\ C.{\text{ }}\Omega .{\text{cm}} \\\ {\text{D}}{\text{. }}\Omega .{\text{m}} \\\$

Answer 1

A low resistivity indicates a material which readily allows the electric current. Resistivity is commonly represented by the Greek word $\rho$ (rho). Resistance is proportional to the resistivity and the length therefore it is inversely proportional to the cross - sectional area

** Complete step-by-step answer :**
We all know that,
$R = Resistivity \times \dfrac{{length}}{{area}}$
Where R have unit $\Omega$ and the length and area have units $Meters{\text{ and Meter}}{{\text{s}}^2}$ therefore,
From the above formula we can see that,
$Resistvity = \Omega \dfrac{{Mete{r^2}}}{{Meter}} \\\ therefore, \\\ Resistvity = \Omega - Meter \\\$
Therefore the S.I unit of electrical resistivity is the ohm-meter ($\Omega$.m)
So, the option (D) is the right answer.

Resistivity is an electrical resistance of a conductor of unit cross - sectional area and unit length. Higher resistivity designates the poor conductors. It is a property of the material and it depends on the nature of material. The electrical resistivity is used to delineate 3 dimensional structures with anomalous electrical conductivities. It is also useful for detecting simultaneously lateral as well as the vertical changes in subsurface electrical properties.
The resistivity increases with increasing temperature in conductor and decreases with increasing temperature in insulators. As the temperature rises the number of phonons increases. Moreover, when the temperature goes up, resistance goes up.

Note : The Ohm’s law states that the electrical current (I) which flows in a circuit is proportional to the voltage (V) and inversely proportional to the resistance (R). Therefore if the voltage is increased then the current will also increase which will provide the resistance of the circuit with no change.