Electrical resistance

Theelectrical resistanceof an electrical conductor is a measure of the difficulty of passing anelectric currentthrough a substance. It explains the relationship betweenvoltageand thecurrent.With more resistance in a circuit, less electricity will flow through the circuit. The inverse of resistance is conductance, a measure not much used. All objects have some resistance, exceptsuperconductors.

Resistance, discovered byGeorg Simon Ohmin 1827, is the ratio between voltage and current.Ohm's lawsaid that the voltage between any two points in aconductorchanges directly as the current between the two points, given the temperature remains the same. He described it with the equation:

$R={\frac {V}{I}}$

which models the ratio, where:

$R$is the resistance of the object, measured inohms(Ω)

$V$is the voltage across the object, measured involts(V)

$I$is the current going through the object, measured inamperes(A)

Calculating 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$R$of a wire with a constant width, therefore, can be calculated as:

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

where$\ell$is the length of the conductor, measured inmeters[m],$A$is thecross-sectionalarea of the conductor measured insquare meters[m²], and$\rho$(Greek:rho) is the electricalresistivity(also calledspecific 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 ($\rho \,$) of copper is$1.68*10^{-8}\,$Ω m.

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

The length ($\ell \,$) is$5\,$meters

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

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

Applications

Resistorsare used inelectrical circuitsto provide electrical resistance.