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 or potential difference.
    • The terms electromotive force (abbreviated emf) and electric tension (as in the colloquial phrase "high tension lines") are sometimes used to mean voltage. Electromotive force still has some legitimate use, but electric tension is an archaic term that can only lead to confusion. Voltage and force are different concepts.
  • 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 SI base 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 =	(Ω m)(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.