Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/371

CHAPTER VI.

LINEAR ELECTRIC CURRENTS.

On Systems of Linear Conductors.

273.] Any conductor may be treated as a linear conductor if it is arranged so that the current must always pass in the same manner between two portions of its surface which are called its electrodes. For instance, a mass of metal of any form the surface of which is entirely covered with insulating material except at two places, at which the exposed surface of the conductor is in metallic contact with electrodes formed of a perfectly conducting material, may be treated as a linear conductor. For if the current be made to enter at one of these electrodes and escape at the other the lines of flow will be determinate, and the relation between electromotive force, current and resistance will be expressed by Ohm's Law, for the current in every part of the mass will be a linear function of $E$. But if there be more possible electrodes than two, the conductor may have more than one independent current through it, and these may not be conjugate to each other. See Art. 282.

Ohm's Law.

274.] Let $E$ be the electromotive force in a linear conductor from the electrode $A_{1}$ to the electrode $A_{2}$. (See Art. 69.) Let $C$ be the strength of the electric current along the conductor, that is to say, let $C$ units of electricity pass across every section in the direction $A_{1}A_{2}$ in unit of time, and let $R$ be the resistance of the conductor, then the expression of Ohm's Law is

$E=CR.$

(1)

Linear Conductors arranged in Series.

275.] Let $A_{1}$, $A_{2}$ be the electrodes of the first conductor and let the second conductor be placed with one of its electrodes in contact