Page:Elementary Text-book of Physics (Anthony, 1897).djvu/373

§ 303] of its strength can be obtained in absolute units, as with the tangent galvanometer. By a proper series of experiments, this measurement is made independent 'of the horizontal intensity of the earth's magnetism. When the current is reversed m the instrument, the couple tending to turn the suspended coil does not change. If the effects of terrestrial magnetism can be avoided, the electro-dynamometer can therefore be used to measure rapidly alternating currents.

303. Electromotive Force.—The electromotive force in a circuit is defined as before (§ 373), as the power of establishing or sustaining the conditions which make the expenditure of energy in the circuit possible,and it is measured, as before, by the energy expended in the circuit. If W represent the energy expended in unit time, we have $$W = ie,$$ where $$e$$ is the electromotive force measured in electromagnetic units. Since we may measure current in electromagnetic units by the tangent galvanometer, this relation enables us to measure electromotive force in absolute electromagnetic units.

The electromagnetic unit of electromotive force is that electromotive force which will produce the expenditure of one unit of energy in unit time, when the electromagnetic unit of current is traversing the conductor.

The dimensions of electromotive force in the electromagnetic system are obtained from the fact that the electromotive force multiplied by the current strength equals the rate of work. The dimensions of rate of work are $$\left[ \frac{W}{T} \right],$$ so that $$[e] = \left[ \frac{W}{iT} \right] = \frac{ML^2T^{-2}}{M^{\frac{1}{2}}L^{\frac{1}{2}}} = M^{\frac{1}{2}}L^{\frac{3}{2}}T^{-2}.$$

In practice another unit is used, called the volt. It contains 108 C. G. S. electromagnetic units.

It will be shown subsequently (§ 310) that the unit of electromotive force may be defined by the effects produced in a circuit by its motion m a magnetic field, the two definitions being of course consistent with each other.