Question

What is the unit of specific resistance?
A. Ohm$\times $second
B. Ohm$\times $cm
C. Ohm
D. Ohm/cm

Answer 1

Hint: Specific Resistance abbreviated as $\rho $. It is the property of the conductive materials, it helps to determine the end-to-end resistance of the conductor at a certain length and area in the formula.

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

Complete step by step solution:
First of all let us check what the specific resistance actually means. Specific Resistance abbreviated as $\rho $ which is the property of the conductive materials, it helps to determine the end-to-end resistance of the conductor at a certain length and area in the formula:
$R=\dfrac{\rho l}{A}$
Where R is the resistance of the material, l is the length of the material and A is the area of the cross-section of the material. Specific resistance is also known as the resistivity of the material. The resistivity is the resistance of a material having unit dimensions like one-meter length and one square meter area of cross-section. Specific resistance is directly proportional to the temperature. As the temperature increases, resistivity also increases.
When we look at the equation of resistivity,
$\rho =\dfrac{RA}{l}$
Here SI unit of R is the ohm, A is the square meter and l is in the meter.
Therefore the unit of resistivity will be,
$\rho =\dfrac{\Omega {{m}^{2}}}{m}$
As m is common in both numerator and denominator we can cancel one m from that
Therefore the final unit of specific resistance will be given as
$\rho =\Omega m$
Option B is similar to this as the meter is converted into centimeters. Therefore the correct answer from the options will be B.

Note: Specific resistance or resistivity is dependent on two factors. Firstly it depends on the temperature of the conductor and secondly the nature of the material of the conductor. As it is an intrinsic property so that it does not depend on the dimensions of the material.