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:**

#. 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:**

#. `Wikipedia, first formula <https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance#Relation_to_resistivity_and_conductivity>`__.

.. py:currentmodule:: symplyphysics.laws.electricity.resistance_via_resistivity_and_dimensions

.. py:data:: resistance

    :attr:`~symplyphysics.symbols.electrodynamics.electrical_resistance` of the conductor.

Symbol:
    :code:`R`

Latex:
    :math:`R`

Dimension:
    :code:`impedance`


.. py:data:: resistivity

    :attr:`~symplyphysics.symbols.electrodynamics.electrical_resistivity` of the material.

Symbol:
    :code:`rho`

Latex:
    :math:`\rho`

Dimension:
    :code:`impedance*length`


.. py:data:: length

    :attr:`~symplyphysics.symbols.classical_mechanics.length` of the conductor.

Symbol:
    :code:`l`

Latex:
    :math:`l`

Dimension:
    :code:`length`


.. py:data:: area

    Cross-sectional :attr:`~symplyphysics.symbols.classical_mechanics.area` of the conductor.

Symbol:
    :code:`A`

Latex:
    :math:`A`

Dimension:
    :code:`area`


.. py:data:: law

    :code:`R = rho * l / A`


    Latex:
        .. math::
            R = \frac{\rho l}{A}