Electricity

Resistance of a conductor - formula in LaTeX

Resistance grows with the length of the wire and falls with its cross-section. The Greek letter is \rho. A lowercase l is easy to mistake for the digit one, so if the formula must read clearly in print, use \ell instead.

R = \rho\dfrac{l}{S}

LaTeX code

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$$
R = \rho\dfrac{l}{S}
$$

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What the symbols mean

$R$: resistance (Ω)
$\rho$: resistivity of the material (Ω·m)
$l$: length of the wire (m)
$S$: cross-sectional area (m²)

An electricity and magnetism formula - the basis of circuit problems and electrical lab reports.

Worked example

A copper wire 100 m long with a 1 mm² cross-section, that is 10⁻⁶ m²: convert the area to square metres before substituting. The unit product Ω·m is separated by a thin space, \Omega\,\mathrm{m}.

R = 1.7\cdot 10^{-8}\,\Omega\,\mathrm{m} \cdot \dfrac{100\,\mathrm{m}}{10^{-6}\,\mathrm{m^2}} = 1.7\,\Omega

LaTeX commands in this formula

\rho: Greek letter rho
\dfrac: fraction (display)

How to use this formula in LaTeX?

Copy the code with the button above - $$…$$ is centered display math.
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Inside a sentence, use single $…$ instead of double.
The formula needs the amsmath package - CamteX templates include it in the preamble.

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