# Resistivity or specific resistance (ρ)

Last updated on June 9th, 2022 at 12:59 pm

Resistivity or specific resistance – While deriving Ohm’s Law with the help of drift velocity equations, we got the expression or formula of resistance as follows: R = [(mL)/(ne^{2}τA)]. Here, m = mass of an electron, L = length of the conducting wire, n = electron density or number of electrons per unit volume, e = charge of an electron, τ = relaxation time, and A = cross-sectional area of the wire. From this expression of R, we will get the concept and expression of resistivity or specific resistance.

## Resistivity or specific resistance – Formula

R = [(mL)/(ne^{2}τA)]

=> R = [(m)/(ne^{2}τ)] [L/A] ………………. (1)

R = ρ (L/A), where ρ =resistivity or specific resistance = (m)/(ne^{2}τ) …………….. (2)

ρ is the resistivity or specific resistance of the material that is used to make the wire through which the current is flowing.

formula of Resistivity or specific resistance

ρ = RA/L …………… (3)

When, A =1, and L=1 then ρ= R

We will define resistivity from this observation.

## Resistivity or specific resistance – definition

**Resistivity or specific resistance of the material is equal to the resistance of a wire of that material of 1 meter length and 1 meter ^{2} cross-sectional area.**

## Relationship between resistance and resistivity

Resistance **R = ρ (L/A)**, where ρ =resistivity or specific resistance. Similarly, **ρ = RA**/L. Resistivity or specific resistance of the material is equal to the resistance of a wire of that material of 1 meter length and 1 meter^{2} cross-sectional area.

**Related study**: Temperature dependence of resistivity

## Unit of resistivity or specific resistance

Unit of resistivity or specific resistance is ohm-meter.

## Dimension of resistivity or specific resistance

Following this equation **ρ = RA**/L, we can say that the Dimension of resistivity = [dimension of resistance ] [ L^{2}]/[L]

Dimension of resistivity = [dimension of resistance ] [ L^{2}]/[L] = [ML^{2} T ^{-3}A ^{-2}] [L] = [ML^{3} T ^{-3}A ^{-2}]

Dimension of resistivity or specific resistance = [ML^{3}T^{-3}A^{-2}]

## Resistivity or specific resistance in terms of Material’s parameters

ρ =resistivity or specific resistance = (m)/(ne^{2}τ)

m and e are universal constant, being the mass and charge of an electron respectively.

ρ (resistivity or specific resistance) depends on n of the material, where n is the number of electrons per unit volume (volume density).

**This means resistivity depends upon the nature of the material.** **Resistivity is the characteristic property of the material. It doesn’t depend on the size or dimensions of the conductor.**