Resistivity

Resistivity (or volume resistivity) is the term used to describe the relationship between electric current and the applied electric field. It is a measure of the resistance to the flow of current from a microscopic level, that is, as explained in terms of the atoms, the basic building blocks of all solid materials. The resistivity, r (Greek letter rho), depends on the behavior and number of free, or conduction, electrons and not on the shape of the conductor, as does resistance. Like density, this inherent property of a material will change as the structure changes, as in the alloying of metals or the doping of semiconductor materials. It depends on the movement of charge carriers, electrons in metallic conductors, or ions in ionic materials. In fact, electrical resistivity is the reciprocal of electrical conductivity (s, the Greek letter sigma) (i.e., r = 1/s). This electrical property is discussed later in this module. Microstructure again plays a large role in these properties. Any imperfections in the crystalline structure, whether they are atoms out of their normal positions, dislocations, or grain boundaries, to mention but a few, increase the collisions between electrons. This, in turn, prevents the transfer of energy in the form of electron flow to some intended user.

Figure 9-3(a) and (b) shows a sketch of the effects of an increase in temperature on metallic conductors and semiconductors, respectively. With metallic conductors, the increased vibrational energies of the atoms as a result of an increase in energy make the passage of free electrons through the structure even more difficult. The mean free path, the average distance an electron can travel as a wave without hitting or deflecting off a positive-ion core (atom) in the lattice structure, is decreased. Consequently, the mobility of the electrons decreases, which produces an increase in the resistivity. For semiconductor materials, the resistivity decreases (conductivity increases) with an increase in temperature because more charge carriers become available to act as conduction electrons. Carbon's resistivity decreases with an increase in temperature. The doping of semiconductor materials also lowers the resistivity by increasing the number of charge carriers. In the discussion of resistance, we stated that resistance varies directly with the length L and indirectly with the uniform cross-sectional area A of a conductor. To write this as a mathematical statement, we need a constant to make the units agree on both sides of the equation. Thus, R = r l/A where r is the proportionality constant or resistivity in ohm-centimeters, assuming that L and A are expressed in centimeters. Note that a conductor, L cm in length with an area of 1 cm², has a resistance R equal to the resistivity r.

In selecting conducting materials for the express purpose of generating heat from the flow of electricity, such as Nichrome, a heat-resistant alloy of nickel and chromium, the material must have a carefully selected variety of properties, such as a moderate resistivity, excellent resistance to oxidation, and a capability to operate effectively at high temperatures without failure. Table 9-1 lists the electrical resistivities of some selected solids from three families of materials.

Illustrative Problem

           (a) A metallic wire 100 cm long has a diameter of 0.05 cm. If it has a resistance of 0.08 W when 10 A
           of current is running through the circuit at standard temperature, find the wire's resistivity in W * cm.
           (b) Using Table 9-1, identify the material from which the wire was fabricated.

           Solution

(a) R = r (L / A); therefore, r= R / (A / L).

A = p / d² = 0.7854 x (0.05)² = 1.96 X 10^-3 cm²

r = 0.08W X 1.96 x 10^-3 cm² /10² = 1.7 X 10^-6W * cm

(b) Either silver or copper would be adequate answers.

Note in our discussion that, where heat is involved in the flow of electric charge, efficiency is reduced. The incandescent light bulb is a good example. This bulb gets hot when used. A fluorescent bulb remains cool. Consequently, the fluorescent bulb is more efficient in the use of electricity (energy). As a matter of fact, the incandescent light is only about 3% efficient; that is, 97% of the energy needed to produce light is lost mainly to heat. Summarizing, the resistance R of an electrical circuit is a function of the shape, size, and nature of a solid material. Just like specific heat or density, resistivity p is a function of the intrinsic nature of the material itself Instead of thinking of resistivity, one can think in terms of conductivity, s. Low resistivity and high conductivity refer to a similar situation in different terms. To further reinforce the concept of resistivity, remember that 1lb of aluminum has the same resistivity as 1g of aluminum, whereas the resistance of 1lb of aluminum is very different from that offered by 1g.