Dimensional formula of Temperature coefficient of resistance

How to get the dimensional formula of temperature coefficient of resistance

1. Start from the definition: temperature coefficient of resistance = resistance / (resistance × temperature).
2. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
3. energy = mass × velocity², so energy is [M] × [L T^-1]² = [M L² T^-2].
4. electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
5. electric potential = energy / electric charge, so electric potential is [M L² T^-2] / [T A] = [M L² T^-3 A^-1].
6. electrical resistance = electric potential / electric current, so electrical resistance is [M L² T^-3 A^-1] / [A] = [M L² T^-3 A^-2].
7. Put in the dimension of each part: [M L² T^-3 A^-2] / ([M L² T^-3 A^-2] × [K]).
8. Add the powers of each base quantity: [K^-1].

Quantities with the dimensions [K⁻¹]

• Coefficient of linear expansion
• Coefficient of volume expansion

Equal dimensions do not make them the same quantity. Compare temperature coefficient of resistance with the others in the full grid.

Three questions on temperature coefficient of resistance

Related quantities

• J Current density [L⁻² A]
• R Electrical resistance [M L² T⁻³ A⁻²]
• G Conductance [M⁻¹ L⁻² T³ A²]
• ρ Resistivity [M L³ T⁻³ A⁻²]
• σ Conductivity [M⁻¹ L⁻³ T³ A²]
• μ Mobility [M⁻¹ T² A]