Resistance and resistivity / Résistance et de la résistivité

Génie May 02, 2011

The resistance of an electrical conductor depends on four factors, these being: (a) the length of the conductor, (b) the cross-sectional area of the conductor, (c) the
type of material and (d) the temperature of the material. Resistance, R, is directly proportional to length, l, of a conductor, i.e. R∝l. Thus, for example, if the length of a piece of wire is doubled, then the resistance is doubled. Resistance, R, is inversely proportional to crosssectional area, a, of a conductor, i.e. R∝1/a. Thus, for example, if the cross-sectional area of a piece of wire is doubled then the resistance is halved. Since R∝l and R∝1/a then R∝l/a. By inserting a constant of proportionality into this relationship the type of material used may be taken into account. The constant of proportionality is known as the resistivity of the material and is given the symbol ρ (Greek rho). Thus,

ρ is measured in ohm metres (Ωm). The value of the resistivity is that resistance of a unit cube of the material measured between opposite faces of the cube.
Resistivity varies with temperature and some typical values of resistivities measured at about room temperature are given below: