Page:Elementary Text-book of Physics (Anthony, 1897).djvu/333

§ 276] '''275. Specific Conductivity and Specific Resistance.'''— If two points be kept at a constant difference of potential, and be joined by a homogeneous conductor of uniform cross-section, it is found that the current in the conductor is directly proportional to its cross-section and inversely to its length. The current also depends upon the nature of the conductor. If conductors of similar dimensions, but of different materials, are used, the current in each is proportional to a quantity called the specific conductivity of the material. The numerical value of the current set up in a conducting cube, with edges of unit length, by unit difference of potential between two opposite faces, is the measure of the conductivity of the material of the cube. The reciprocal of this number is the specific resistance of the material. If $$\rho$$ represent the specific resistance of the conducting material, $$S$$ the cross-section, and $$l$$ the length of a portion of the conductor of uniform cross-section between two points at potentials $$V_{1}$$ and $$V_{2},$$ Ohm's law for this special case is presented in the formula The specific resistance is not perfectly constant for any one material, but varies with the temperature. In metals the specific resistance increases with rise in temperature; in liquids and in carbon it diminishes with rise in temperature. Upon this fact of change of resistance with temperature is based a very delicate instrument, called by Langley, its inventor, the bolometer, for the measurement of the intensity of radiant energy.

276. Joule's Law.—If we modify the equation $$H = I (V_{1} - V_{2})$$ by the help of Ohm's law, we obtain The heat developed in a homogeneous portion of any circuit is equal to the square of the current in the circuit multiplied by the resistance of that portion. This relation was first experimentally proved by Joule in 1841, and is known as Joule's law. It holds true for any homogeneous circuit or for all parts of a circuit which are