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NATURE AND ORIGIN OF TRANSIENTS. 7

that is, c is the reciprocal of the projection T = tj^ on the zero line
of the tangent at the starting moment of the transient.

Since c = -^j

di ,

that is, the percentual change of current is constant, or in other

words, in the same time, the current always decreases by the same
fraction of its value, no matter what this value is,
Integrated, this equation gives:

log % = — ct + C,

or, i«,4<r^

that is, the curve is the exponential.
The exponential curve thus is the expression of the simplest

form of transient* This explains its common occurrence in elec-
trical and other transients. Consider, for instance, the decay of
radioactive substances: the radiation, which represents the decay,

is proportional to the amount of radiating material; it is ^ » cm,

which leads to the name exponential function.

Not all transients, however, are of this simplest form. For
instance, the deceleration of a ship does not follow the exponential,
but at high velocities the doorcase of speed in a greater fraction of
the speed than, during tho name time⁴ interval at lower velocities,
mid the speed-time cxirves for different initial speeds are not pro-
portional to each other, but are an shown in Fig. 5. The reason
in, that the frictional resistance is not proportional to the speed,
but to the sqxiare of the speed.

5, Two classes of transients may occur:

1. Energy may be stored in one form only, and the only energy
change which can occur than is an increase or a decrease of the
stored energy.

2. Energy may be stored in two or more different forms, and the
possible energy changes thus are an increase or decrease of the
total stored energy, or a change of the stored energy from one form
to another. Usually both occur simultaneously.

An instance of the first case is the acceleration or deceleration



	NATURE AND ORIGIN OF TRANSIENTS. 7 that is, c is the reciprocal of the projection T = tj^ on the zero line of the tangent at the starting moment of the transient. Since c = -^j di ,

	that is, the percentual change of current is constant, or in other words, in the same time, the current always decreases by the same fraction of its value, no matter what this value is, Integrated, this equation gives: log % = — ct + C,

	or, i«,4<r^ that is, the curve is the exponential. The exponential curve thus is the expression of the simplest form of transient* This explains its common occurrence in elec- trical and other transients. Consider, for instance, the decay of radioactive substances: the radiation, which represents the decay, is proportional to the amount of radiating material; it is ^ » cm, which leads to the name exponential function. Not all transients, however, are of this simplest form. For instance, the deceleration of a ship does not follow the exponential, but at high velocities the doorcase of speed in a greater fraction of the speed than, during tho name time⁴ interval at lower velocities, mid the speed-time cxirves for different initial speeds are not pro- portional to each other, but are an shown in Fig. 5. The reason in, that the frictional resistance is not proportional to the speed, but to the sqxiare of the speed. 5, Two classes of transients may occur: 1. Energy may be stored in one form only, and the only energy change which can occur than is an increase or a decrease of the stored energy. 2. Energy may be stored in two or more different forms, and the possible energy changes thus are an increase or decrease of the total stored energy, or a change of the stored energy from one form to another. Usually both occur simultaneously. An instance of the first case is the acceleration or deceleration