Electrical resistance

2017-04-06T14:36:47Z

69.17.160.29: Fixed typo

{{Electromagnetism}}

The electrical resistance of an electrical conductor is a measure of the difficulty of passing an [[electric current]] through that conductor. It explains the relationship between [[voltage]] (amount of electrical pressure) and the [[Electric current|current]] (flow of electricity). With more resistance in a circuit, less electricity will flow through the circuit.

Resistance, discovered by [[Georg Ohm|Georg Simon Ohm]] in 1827, is the ratio between voltage and current. [[Ohm's law]] said that the voltage between any two points in a [[Electrical conductor|conductor]] changes directly as the current between the two points, given the temperature remains the same. He described it with the equation:

:<math>R = \frac{V}{I}</math>

which models the ratio, where:
:<math display="inline">R</math> is the resistance of the object, measured in [[ohm]]s (Ω)
:<math display="inline">V</math> is the voltage across the object, measured in [[volt]]s (V)
:<math display="inline">I</math> is the current going through the object, measured in [[ampere]]s (A)

== Calculating resistance ==
The resistance of a wire increases as it becomes longer and decreases as it becomes wider. (A simple analogy is a road - the more lanes there are, the less traffic there is.) The resistance {{math|R}} of a wire with a constant width, therefore, can be calculated as:

:<math>R = \rho\frac{\ell}{A}, \,</math>

where <math>\ell</math> is the length of the conductor, measured in [[meter]]s [m], <math display="inline">A</math> is the [[cross section (geometry)|cross-sectional]] area of the conductor measured in [[square meter]]s [m²], and {{math|ρ}} (Greek: [[Rho (letter)|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 (<math>\rho\,</math>) of copper is <math>1.68*10^{-8} \,</math> Ω m.
:The cross sectional area (<math>A\,</math>) is <math>\pi r^2=\pi *(2*10^{-3})^2=4\pi *10^{-6}\,</math> square meters
:The length (<math>\ell\,</math>) is <math>5\,</math> meters

Because: <math>R = \rho\frac{\ell}{A}, \,</math>

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

== Applications ==
[[File:6_different_resistors.jpg|thumb|upright]]
[[Resistor]]s are used in [[electrical circuit]]s to provide electrical resistance.

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[[Category:Electronics]]
[[Category:Electricity]]

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Electrical resistance