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.

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