Specific Resistance

Consider a cube of conducting material having each edge one centimetre in length. Let two opposite faces of this be maintained at different potentials, a current will'be produced through the cube, and the number of units in the resistance of the cube is called the specific resistance of the material of which the cube is composed.

Let ρ be the specific resistance of the material of a piece of wire of length l and cross-section a, and let R be the resistance of the wire. Then

For, suppose the cross-section to be one square centimetre, then the resistance of each unit of length is ρ and there are l units in series; thus the whole resistance is ρL But the resistance is inversely proportional to the cross-section, so that if this be a square centimetres, the resistance R is given by the equation

Again, it is found that the resistance of a wire depends on its temperature, increasing in most cases uniformly with the temperature for small variations, so that if R₀ be the resistance at a temperature zero and R that at temperature t, we have

where α is a constant depending on the nature of the material of the wire; this constant is called the temperature coefficient of the coil. For most materials the value of a is small. German-silver and platinum-silver alloy are two substances for which it is specially small, being about 0.00032 and 0.00028 respectively.

Its value for copper is considerably greater, being about 0.003, and this is one reason why resistance coils are made of one of the above alloys in preference to copper. Another reason for this preference is the fact that the specific resistance of the alloys is much greater than that of copper, so that much less wire is necessary to make a coil than is required if the material be copper.