Resistivity is a measure of the ability of an electric conductor to resist the flow of an current. Also known as specific resistance, it is given by the formula ρ = AR/l, where ρ (rho) is the resistivity, A is the cross-sectional area of the conductor, l is its length, and R is its resistance in ohms. resistivity usually increases with rising temperature. Its SI unit is the ohm-meter.
Ohm's law states that the ratio of the voltage between the ends of an electrical conductor to the current flowing through it is a constant. For a given conductor this constant is called the resistance. In other words, voltage / current = resistance. The resistance is an indication of how much opposition the flow of electrons meets in its attempt to pass through the conductor.
Materials which conduct electricity may be classified as good conductors if they offer a low resistance, and bad conductors if they offer a high resistance. Copper, for example, is used for almost all electrical wiring because it is a good conductor. However, a copper wire can have a very high resistance, perhaps a million ohms, if it is made long enough and thin enough. This does not mean that copper is a bad conductor; it simply means that when considering resistance, the dimensions of the conductor must be taken into account as well as the material from which it is made.
If the flow of electrons through a conductor is compared with the flow of water through a pipe, it is fairly easy to see that just as a long pipe offers a greater opposition to the water than does a short pipe, so a long wire offers a greater resistance to the electrons than does a short wire. Similarly, just as a wide pipe offers less opposition to the water than does a narrow pipe, so a thick wire offers less resistance to the electrons than does a thin wire. The longer the wire, the greater is its resistance; the thicker the wire the smaller is its resistance.
For any wire the resistance R (measured in ohms), is related to the length l (measured in meters), and the area of cross-section A (measured in square meters), by the equation R = ρl/A, where ρ, the resistivity or specific resistance, is a number that depends on the material of which the wire is made. In the case of copper, for example, ρ = 0.0000000178 ohm-meters (1.78 × 10-8 ohm-meters) at room temperature. For silver, ρ = 1.63 × 10-8 ohm-meters, so the resistivity of silver is less than that of copper, and silver is therefore a better conductor than copper. The resistivity of a material is quite independent of the dimensions of whatever specimen of the material is being considered.
To find the resistivity of a specimen, say a wire, it is necessary to measure its resistance, its length, and its cross-sectional area, so that ρ can be found from the equation just given. The resistance can be measured by means of a Wheatstone bridge. Since wires are nearly always circular in cross-section, the cross-sectional area can be found by measuring the diameter of the wire with a micrometer screw gauge. Half the diameter is the radius r, and the area of cross-section is given by the formula πr2.