1Which is the dimensional formula of resistivity?
Resistivity works out to [M L³ T⁻³ A⁻²].
Current electricityClass 12, Current Electricity
Dimensional formula of Resistivity
[M L3 T-3 A-2]
From R = ρl/A, a property of the material and not of the wire's size.
How to get the dimensional formula of resistivity
- Start from the definition: resistivity = resistance × area / length.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- energy = mass × velocity2, so energy is [M] × [L T-1]2 = [M L2 T-2].
- electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
- electric potential = energy / electric charge, so electric potential is [M L2 T-2] / [T A] = [M L2 T-3 A-1].
- electrical resistance = electric potential / electric current, so electrical resistance is [M L2 T-3 A-1] / [A] = [M L2 T-3 A-2].
- area = length × length, so area is [L] × [L] = [L2].
- Put in the dimension of each part: [M L2 T-3 A-2] × [L2] / [L].
- Add the powers of each base quantity: [M L3 T-3 A-2].
Three questions on resistivity
2What is the SI unit of resistivity?
The SI unit of resistivity is the ohm metre (Ω m).
3Do resistivity and conductivity have the same dimensions?
Resistivity is [M L³ T⁻³ A⁻²] but conductivity is [M⁻¹ L⁻³ T³ A²].
Resistivity: quick answers
What is the dimensional formula of resistivity?
The dimensional formula of resistivity is [M L³ T⁻³ A⁻²]. It comes from resistivity = resistance × area / length.
What is the SI unit of resistivity?
The SI unit of resistivity is the ohm metre (Ω m).
Is resistivity dimensionless?
No. Resistivity has the dimensions [M L³ T⁻³ A⁻²].