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.

Conditions:

  1. The cross section is uniform throughout the conductor.

  2. The current flows uniformly.

  3. The conductor is made of a single material.

  4. The electric field and current density are parallel and constant everywhere.

Links:

  1. Wikipedia, first formula.

resistance

electrical_resistance of the conductor.

Symbol:

R

Latex:

\(R\)

Dimension:

impedance

resistivity

electrical_resistivity of the material.

Symbol:

rho

Latex:

\(\rho\)

Dimension:

impedance*length

length

length of the conductor.

Symbol:

l

Latex:

\(l\)

Dimension:

length

area

Cross-sectional area of the conductor.

Symbol:

A

Latex:

\(A\)

Dimension:

area

law

R = rho * l / A

Latex:
\[R = \frac{\rho l}{A}\]