Page:Elementary Text-book of Physics (Anthony, 1897).djvu/334

330 homogeneous. The heat which is sometimes evolved by chemical action, or by the Peltier effect, occurs at non-homogeneous portions, of the circuit.

277. Counter Electromotive Force in the Circuit.—In many cases the work done by the current does not appear wholly as heat developed in accordance with Joule's law.

Besides the production of heat throughout the circuit, work may be done during the passage of the current, in the decomposition of chemical compounds, in producing movements of magnetic bodies or in heating junctions of dissimilar substances. Before discussing these cases separately we will connect them all by a general law, which will at the same time present the various methods by which currents can be maintained. They differ from the simple case in which the work done appears wholly as heat throughout the circuit, in that the work done appears partly as energy available to generate currents in the circuit. To show this we will use the method given by Helmholtz and by Thomson. The total energy expended in the circuit in the time $$t,$$ which is such that, during it, the current is constant, is $$IEt.$$ It appears partly as heat, which equals $$I^2 Rt$$ by Joule's law, and partly as other work, which experiment proves is in every case proportional to $$I,$$ and can be set equal to $$IA,$$ where $$A$$ is a factor which varies with the particular work done. Then we have $$IEt = I^2 Rt + IA,$$ whence It is evident from the equation that $$E - \frac{A}{t}$$ is an electromotive force, and that the original electromotive force of the circuit has been modified by work having been done by the current. In other words, the performance of the work $$IA$$ in the time $$t$$ by the circuit has set up a counter electromotive force $$\frac{A}{t}\cdot$$ The separated constituents of the chemical compound, the moved magnet, the heated junction, are all sources of electromotive force which oppose that