Page:Elementary Text-book of Physics (Anthony, 1897).djvu/382

368 induced current due to the loss of the tubes of induction which pass, through the circuit; this current is in the same sense as the current of the circuit. Since by Ohm's law $$i = \frac{e}{r},$$ where $$e$$ is the electromotive force impressed upon the circuit, the average electromotive force is in both these cases $$\frac{eL}{rt}\cdot$$ Now $$t,$$ the time required for the current to rise from zero to its full value, or to sink from its full value to zero, is very small, and the average electromotive force of induction may be much larger than the electromotive force of the circuit. When the current is made, this induced electromotive force diminishes the electromotive force of the circuit; so that the current is established gradually and not instantaneously. The time required to establish the current depends upon the resistance and self-induction of the circuit. When the circuit is broken, the electromotive force of induction is in the same sense as that of the circuity and produces a momentary current which is much greater than the steady current of the circuit. The induced electromotive force is frequently so high as to cause the current to leap across the gap formed where the circuit is broken, and to give rise to a spark at that gap. The induced current thus formed is often called the extra current or the current of self-induction. It should be noted that the induced electromotive force is proportional to the coefficient of self-induction of the circuit. The establishment of a current in the circuit may therefore be retarded and the extra current at the break may be increased by so arranging the circuit as to increase its coefficient of self-induction; while by so winding the circuit that its coefficient of self-induction is reduced to a minimum these effects may be almost entirely avoided. A wire doubled on itself, and coiled so that a current in it always passes in opposite directions, through immediately contiguous portions of the wire, will manifestly have a very small coefficient of self-induction; such a coil is called a non-inductive coil.

308. Alternating Currents.—If the electromotive force in a circuit be made to vary, especially if it be made to change in sense, the tubes of induction which pass through the circuit will also vary,