Electrical resistance

A long and thin wire has more resistance than a short and thick one. A simple analogy is a road - the more lanes there are, the more cars can go through. The resistance ${\displaystyle R}$ of a wire with a constant width, therefore, can be calculated as:

${\displaystyle R=\rho {\frac {\ell }{A}},\,}$

where ${\displaystyle \ell }$ is the length of the conductor, measured in meters [m], ${\displaystyle A}$ is the cross-sectional area of the conductor measured in square meters [m²], and ${\displaystyle \rho }$ (Greek: rho) is the electrical resistivity (also called specific electrical resistance) of the material, measured in ohm-meters (Ω m).

Example: Calculate the resistance of copper wire with a radius of 2mm and a length of 5 meters.

Solution:

The resistivity (${\displaystyle \rho \,}$) of copper is ${\displaystyle 1.68*10^{-8}\,}$ Ω m.

The cross sectional area (${\displaystyle A\,}$) is ${\displaystyle \pi r^{2}=\pi *(2*10^{-3})^{2}=4\pi *10^{-6}\,}$ square meters

The length (${\displaystyle \ell \,}$) is ${\displaystyle 5\,}$ meters

Because: ${\displaystyle R=\rho {\frac {\ell }{A}},\,}$

${\displaystyle R=1.68*10^{-8}{\frac {5}{4\pi *10^{-6}}}\thickapprox 6.685*10^{-3}\Omega \,}$

Resistors are used in electrical circuits to provide electrical resistance.