Resistance and Resistivity

• Another way to find resistance

• The resistance varies directly with length and inversely with width (or cross-sectional area)​ of a wire

  • Kind of like trying to get a lot of water through a pipe

• Short, thick wire small resistance

• Long, skinny wire large resistance​

Resistivity

• ρ​ = resistivity

  • Unit: ​Ωm

• Resistivities of some materials:

  • Metals small resistivity (1 x10^-8 Ωm)

  • Insulators large resistivity (1 x10¹⁵ Ωm)

  • Semi-conductors​ medium resistivity (1 x10^-6 - 1x10³ Ωm)​

Resistivity and Temperature

• ρ = resistivity at temperature T

• ρ​₀ = resistivity at temperature T₀

• ​α = temperature coefficient of resistivity

  • Unit: 1/⁰C (or 1/K) ​

Materials and Resistivity

• Metals

  • Resistivity increases with temperature

  • ​α is positive

• Semiconductors

  • Resistivity decreases with ​temperature

  • α​ is negative

Resistance and Temperature

• R = resistance at temperature T

• R₀ = resistance at temperature T₀

• α = temperature coefficient of resistivity

  • Unit: 1/⁰C (or 1/K)​

Superconductors

• Materials whose resistivity is 0 Ω

• Metals become superconductors at extremely low temperatures

• Some materials using copper oxide can work at higher temperatures

• No current loss

• Used in:

  • Transmission of electricity

  • MRI

  • Maglev trains

  • Advanced computer chips

  • Powerful, small electric motors​

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