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Resistivity Formula
Resistivity, denoted by the Greek letter rho(p), is defined as the resistance R of a specimen, such as a wire, multiplied by the cross-sectional area A and divided by the length l; ρ= RA/L. Its unit is the ohm(Ω).
Electrical resistivity refers to the resistance of a material’s current flow from one end to the other. Electrical resistivity is a straightforward and informative metric for describing a substance. It is the inverse of electrical conductivity.
The resistivity is denoted by and is proportional to both the material resistance and the length. The area of cross-section of a given material is inversely related to its resistivity.
The ratio of the area in square metres to length in metres is simplified to merely metres in the metre-kilogram-second (mks) method. The unit of resistivity in the metre-kilogram-second system is therefore ohm-metre. Resistivity can be stated in ohm-centimetre units if lengths are measured in centimetres.
The resistivities of electrical insulators range from 1012 to 1020 ohm-metres.
Formula:
The resistivity formula is as follows:
Formula for Resistivity : ρ = RA/l
Where ρ denotes resistivity, R denotes resistance, l denotes material length, and A denotes cross-sectional area.
Solved Examples
1. Calculate the resistivity of a material with a resistance of 3Ω and a cross-sectional area and length of 25 cm2 and 10 cm, respectively.
Solution:
Given
R = 3 Ω
l = 10 cm = 0.10 m
A = 25 cm2 = 0.25 m2
Resistivity is:
ρ = RA / l
ρ = (3 × 0.25) / 0.10
ρ = 7.5 Ωm
2. The wire’s length and area are 0.3 m and 1.0 m2, respectively. Calculate the resistivity of that wire if its resistance is 5Ω.
Solution:
Given
R = 5 Ω
l = 0.3 m and
A = 1.0 m2
Resistivity is:
ρ = RA / l
ρ = (5 × 1) / 0.3
ρ = 16.66 Ωm
