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)/(ne²τA)]. 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)/(ne²τA)]
=> R = [(m)/(ne²τ)] [L/A] ………………. (1)

R = ρ (L/A), where ρ =resistivity or specific resistance = (m)/(ne²τ) …………….. (2)

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

ρ = RA/L …………… (3)

formula of Resistivity or specific resistance

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 meter² 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 meter² 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 ] [ L²]/[L]

Dimension of resistivity = [dimension of resistance ] [ L²]/[L] = [ML² T ^-3A ^-2] [L] = [ML³ T ^-3A ^-2]

Dimension of resistivity or specific resistance = [ML³ T ^-3A ^-2]

Resistivity or specific resistance in terms of Material’s parameters

ρ =resistivity or specific resistance = (m)/(ne²τ)

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.