RESISTANCE, Electrical, that property of electrical conductors in virtue of which the passage of a current of electricity through them is necessarily accompanied by the dissipation of a part of the energy in the form of heat. It is manifested not only in a linear conductor like a wire, but also in solids of large extent in two or three dimensions, as when a current passes from one point to another of a sheet of metal, or of a mass like an ingot or casting. It is chiefly in connection with wires, however, that electrical resistance is of practical import ally dissipated in the form of frictional heat, and the energy of the moving current of elec tricity is similarly dissipated on account of the electrical resistance of the conductor through which it is passing. The unit in terms of which electrical resistance is measured is the ohm,' which may be taken as sensibly equal to the resistance of a column of mercury 106.3 centi meters long and one millimeter in cross-section, at the temperature of freezing water. (The Britsh Board of Trade specifies that the mer cury column shall be 106.3 centimeters long and that it shall have 'a mass of 14.4521 grammes. This is supposed to be identically the same definition, but it is more convenient for practical work, because in reproducing the ohm by means of a mercury column a glass tube would be filled with mercury and the sectional area of the column would be deter mined by weighing). (See also Limn). The phenomena of electrical resistance have been studied, both mathematically and experi mentally, by many eminent physicists; but the most important contributions to our knowl edge are due to George Simon Ohm (for whom the Bohm' was named), and to James Prescott Joule. Ohm investigated the manner in which the flow of electricity through a con ductor depends upon the resistance of the con ductor, while Joule determined the law that governs the dissipation of energy from a con ductor, in the form of heat. In the present article it will be assumed that the currents in the conductors are steady, that the electro motive forces in the circuits are constant and that the conductors are stationary (so that their coefficients of induction remain constant). The laws of Ohm and Joule may still be ap plied, though in a somewhat more generalized form, to conductors in which these three con ditions are not fulfilled; but for the proper understanding of the phenomena in such cases, it is necessary to refer to the more advanced treatises on electricity.
ance, and it is only in this aspect that the subject will be here considered.
The passage of a current of electricity through a wire or rod has been likened to the flow of a current of water through a pipe, the water corresponding to the electricity, and the friction between the water and the pipe to the electrical resistance of the wire. The anal ogy is not perfect, but it is useful in forming a good conception of electrical resistance. The energy of the moving current of water is giadu One of the results of Ohm's investigation was, that in a branched circuit, in which the resistances of the two branches are precisely equal, the current divides in, such a manner that exactly one-half of it traverses each branch. By taking advantage of this fact, we can determine the resistance of a proposed conductor in the following manner : Let R, in Fig. 1, be the resistance to be measured, and let this be placed in one of the branches of the circuit. In the other branch.of the circuit is a standard Voltunnef tonrcury, whose cross section is one square millimeter, and whose temperature is that of freezing water; the' re sistance of such a column being (as noted above) one ohm • for (say). each 106 centimeters of its length-. The mercury 'column is ar+ ranged so that the curreat enters it at the left end; and the current is led away from the mercury column, again by means of the movable wire P, whose point of with mercury can be to the right or left, at will. The measurement consists moving the point P until the two galvanometers.:4 and B, one in each branch• of the circuit, show that the CUT. rents in the tvio• branches are precisely. equat We then know that the resistances In the two branches are also equal. In preparing the. en graving .it has hem awaited that.the equality has been ,observed to subsist when that part of the mercury column which is included in the circuit is 150 centimeters long, and, there fore, has a resistance of 1.5 ohms. If the.gal vanometers and,copneoting. wires are identical in both branches, it, therefore, follows, that the resistance of the coll.'? is also 1.5 ohms. The method of measuring resistances here described is Presented ,in order to illustrate funda mental 'idea. of electrical .reistance. In the practical measurement of resistances a more refined method, ,presently to be described, is employed.