Monday, April 8, 2013

Resistors or conductors with uniform cross-section

A piece of resistive material with electrical contacts on both ends.
Many resistors and conductors have a uniform cross section with a uniform flow of electric current and are made of one material. (See the diagram to the right.) In this case, the electrical resistivity ρ (Greek: rho) is defined as:
$\rho = R \frac{A}{\ell}, \,\!$
where
R is the electrical resistance of a uniform specimen of the material (measured in ohms, Ω)
$\ell$ is the length of the piece of material (measured in metres, m)
A is the cross-sectional area of the specimen (measured in square metres, m²).
The reason resistivity is defined this way is that it makes resistivity a material property, unlike resistance. All copper wires, irrespective of their shape and size, have approximately the same resistivity, but a long, thin copper wire has a much larger resistance than a thick, short copper wire. Every material has its own characteristic resistivity—for example rubber's resistivity is far larger than copper's.
In a hydraulic analogy, passing current through a high-resistivity material is like pushing water through a pipe full of sand, while passing current through a low-resistivity material is like pushing water through an empty pipe. If the pipes are the same size and shape, the pipe full of sand has higher resistance to flow. But resistance is not solely determined by the presence or absence of sand; it also depends on how wide the pipe is (it is harder to push water through a skinny pipe than a wide one) and how long it is (it is harder to push water through a long pipe than a short one.)
The above equation can be transposed to get Pouillet's law:
$R = \rho \frac{\ell}{A}. \,\!$
The resistance of a given material will increase with the length, but decrease with increasing cross-sectional area. From the above equations, resistivity has SI units of ohmmetre. Other units like ohm⋅cm or ohm⋅inch are also sometimes used.

* Quoted from Wikipedia