Page:Elementary lectures on electric discharges, waves and impulses, and other transients (Steinmetz 1911).djvu/20

change of the stored energy, of whatever form this energy may be, leads to a transient.

Electrical transients have been studied more than transients of other forms of energy because:

(a) Electrical transients generally are simpler in nature, and therefore yield more easily to a theoretical and experimental investigation.

(b) The theoretical side of electrical engineering is further advanced than the theoretical side of most other sciences, and especially:

(c) The destructive or harmful effects of transients in electrical systems are far more common and more serious than with other forms of energy, and the engineers have therefore been driven by necessity to their careful and extensive study.

4. The simplest form of transient occurs where the effect is directly proportional to the cause. This is generally the case in electric circuits, since voltage, current, magnetic flux, etc., are proportional to each other, and the electrical transients therefore are usually of the simplest nature. In those cases, however, where this direct proportionality does not exist, as for instance in inductive circuits containing iron, or in electrostatic fields exceeding the corona voltage, the transients also are far more complex, and very little work has been done, and very little is known, on these more complex electrical transients.

Assume that in an electric circuit we have a transient current, as represented by curve $i$ in Fig. 4 ; that is, some change of circuit condition requires a readjustment of the stored energy, which occurs by the flow of transient current $i$. This current starts at the value $i_{1}$, and gradually dies down to zero. Assume now that the law of proportionality between cause and effect applies; that is, if the transient current started with a different value, $i_{2}$ it would traverse a curve $i'$, which is the same as curve $i$, except that all values are changed proportionally, by the ratio

${\frac {i_{2}}{i_{1}}}$; that is, $i'=i\times {\frac {i_{2}}{i_{1}}}$.

Starting with current $i_{1}$, the transient follows the curve $i$; starting with $i_{2}$, the transient follows the proportional curve $i'$. At some time, $t$, however, the current $i$ has dropped to the value $i_{2}$, with which the curve $i'$ started. At this moment $t$, the conditions in the first case, of current i, are the same as the conditions in