Resistance and Resistivity

Resistance and Resistivity

By Rachel Wampler

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)​

Multiple Choice

Why are long wires thick?

Wire thicknesses are measured in gauges. 20-gauge wire is thinner than 16-gauge wire. If 20-gauge wire has A = 5.2x10^-7 m² and 16-gauge wire has A = 13x10^-7 m². find the resistance per meter of each wire if they are copper wires.

Resistivity of copper is 1.72x10^-8Ωm

• 20 AWG - 0.0132 Ω/m

  16 AWG - 0.0331 Ω/m

• 20 AWG - 30.2 Ω/m

  16 AWG - 75.7 Ω/m

• 20 AWG - 0.0331 Ω/m

  16 AWG - 0.0132 Ω/m

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)​

Multiple Choice

A heating element is a wire with a cross-sectional area of 2x10^-7 m² and is 1.3 m long. The material has a resistivity of 4x10^-5 Ωm at 200 ⁰C and a temperature coefficient of 3x10^-2 1/⁰C. Find the resistance of the element at 350 ⁰C.

• 7.0 x10^-4 Ω

• 1430 Ω

• 2.2 x10^-4 Ω

• 1500 Ω

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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