Resistance via resistivity and dimensions¶
In the ideal conditions described below, the resistivity of a conductor is proportional to its length and the inverse of its cross-sectional area. The constant of proportionality is called resistivity of the material. Unlike resistance, resistivity is an intrinsic property of the material and does not depend on its geometry.
Notes:
This is a phenomenological equation.
Conditions:
The cross section is uniform throughout the conductor.
The current flows uniformly.
The conductor is made of a single material.
The electric field and current density are parallel and constant everywhere.
Links:
- resistance¶
electrical_resistanceof the conductor.
- Symbol:
R- Latex:
\(R\)
- Dimension:
impedance
- resistivity¶
electrical_resistivityof the material.
- Symbol:
rho- Latex:
\(\rho\)
- Dimension:
impedance*length
- Symbol:
l- Latex:
\(l\)
- Dimension:
length
- Symbol:
A- Latex:
\(A\)
- Dimension:
area
- law¶
R = rho * l / A- Latex:
- \[R = \frac{\rho l}{A}\]