The Physics
Hypertextbook
Opus in profectus

# Electric Resistance

## Summary

• Quantities in Ohm's law
• Current is the rate at which charge is transfered through a surface.
• The symbol for current is an uppercase italic I.
• The unit of current in the ampère (also spelled ampere or shortened to amp).
• The symbol for ampère is an uppercase roman A.
• Current is sometimes informally called amperage.
• Current is caused by a difference in voltage between two locations.
• The symbol for voltage is an uppercase italic V.
• The unit of voltage is the volt.
• The symbol for volt is an uppercase roman V.
• Voltage is more formally called electric potential difference.
• Resistance is a measure of the degree to which an object opposes the flow of charges through it.
• The symbol for resistance is an uppercase italic R.
• The unit of resistance is the ohm.
• The symbol for ohm is an uppercase Greek letter Ω (omega)
• Resistance is something like friction for electric current.
• Statements of Ohm's law
• Current is directly proportional to voltage.

I ∝ ∆V

• As an equation…  I = V R
or…

V = IR

• The ohm is a derived unit.
• In terms of other derived units (a useful bit of knowledge)…  R = V ⇒ ⎡⎣ Ω = V ⎤⎦ I A
• In terms of fundamental units (an exercise in dimensional analysis)…  ⎡⎣ Ω = V = J/C = J/A s = J = kg m2/s2 = kg m2 ⎤⎦ A A A A2s A2s A2s3
• Factors affecting resistance
• The resistance of a wire is…
• directly proportional to the length of the wire

R ∝ ℓ

• inversely proportional to the cross sectional area of the wire  R ∝ 1 A
• directly proportional to the resistivity of the material the wire is made of

R ∝ ρ

• The resistance of a wire is therefore…  R = ρℓ A
• The unit of resistivity is the ohm meter, since…  R = ρℓ ⇒ ⎡⎣ Ω = (Ωm)(m) ⎤⎦ A (m2)
• The resistivity of most metals increases with increasing temperature.
• Resistivity is approximately directly proportional to absolute temperature for many metals over some range of temperatures.
• Superconductivity is the complete and absolute loss of resistivity in some materials when cooled below a critical temperature.
• Resistance is a property of objects. Resistivity is a property of materials.