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Mathematics for Physics

84 Resistance

A property of a conductor that is used to relate the potential difference across it to the current that flows through it.

The geometric formula for resistance. The resistance of a uniform conductor is set by its resistivity, length, and cross-sectional area. Resistivity is the material property that measures how strongly the material opposes current. This principle is used to compute \(R\) from the geometry of a wire.

The resistance of a uniform conductor is

\[ R = \dfrac{\rho L}{A} \]

where

  • \(R\) is the resistance.
  • \(\rho\) is the resistivity.
  • \(L\) is the length of the conductor.
  • \(A\) is the cross-sectional area.

Ohm’s law. Ohm’s law relates the current through a resistor to the potential difference across it. This principle is used to compute the current in a circuit element of known resistance.

Ohm’s law is

\[ I = \dfrac{\Delta V}{R} \]

where

  • \(I\) is the current.
  • \(\Delta V\) is the potential difference.
  • \(R\) is the resistance.