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# What is the physical relationship between the resistivity of a material and the material's length?

Question #101948. Asked by jonnowales. (Dec 27 08 6:14 PM)

Boycie75

The resistivity of a material is inversely proportional to the material's length.

The electrical resistivity ñ (rho) of a material is given by

ñ= R.A/l

where

ñ is the static resistivity (measured in ohm metres, Ùm);
R is the electrical resistance of a uniform specimen of the material (measured in ohms, Ù);
l 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).

http://en.wikipedia.org/wiki/Resistivity#Definitions

 Dec 27 08, 6:26 PM
zbeckabee

Aim -- I am going to be studying the resistance of wire. The purpose of this investigation is to see how length and thickness of wire affect the dependent variable, resistance.

Prediction -- I predict that, as the length of the wire doubles, the resistance will also double, but as the cross-sectional area of the wire doubles, the resistance halves. This means that the length will affect the resistance more than the thickness will.

The theory behind the conclusions are: As the length doubles the resistance doubles. Resistance is caused by electrons bumping into ions. If the length of the wire doubles, the electrons bump into the ions twice as much so the resistance will double.

More:

 Dec 27 08, 7:48 PM
looney_tunes

Resistance, a variable property, depends on the shape of the object being investigated. Resistivity is an intrinsic property of the material from which the object has been constructed.

For a wire, Resistance = resistivity x (length/cross-sectional area).

Most commonly, resistivity is calculated from measurements of resistance, length and area. However, once calculated, it is considered a fixed value for the material in question.

http://en.wikipedia.org/wiki/Resistivity

 Dec 27 08, 8:29 PM

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