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SINGLE-ENERGY TRANSIENTS. 21

This is the e.m.f, induced by the decrease of magnetic flux <I>, and

is therefore proportional to the rate of decrease of <I>, that is, to

^{ -. In the first moment of short circuit, the magnetic flux <fr still
(it

has full value <l>₀, and the currant -i thus also full value t₀. Hence,
at the first moment of short circuit, the induced e.m.f. e must be
equal to «o, that is, the magnetic flux * must begin to decrease at
such rate as to induce full voltage f«, as shown in Fig. 11(7.

The three, curves <I>, •/, and e are proportional to each other, and
as e is proportional to the rate of change of <I>, <I» must be propor-
tional to its own rate of change*, and thus also i and e* That is,
the transients of magnetic flux, current, and voltage follow the
law of proportionality, hence are simple exponential functions, as
seen in Lecture I :

(J> 5W <f>^ — fltt— J(|)_? '

(1)

<f», i_t and e decrease most rapidly at first, and then slower and
slower, but can theoretically never become zero, though prac-
tically they become negligible in a finite time,

The voltage $ in induced by the rate of change of the magnetism,
and equals the decrease of the number of linen of magnetic force,
divided by the time during which this decrease occurs, multiplied
by the number of turns M of the coil The induced voltage e
times the time during which it in induced thus equals n> times the
decrease of the magnetic flux, and the total induced voltage,
that in, the area of the induced-voltage curve, Fig. 11(7, thus
equal** n time** the total dwroiuw of magnetic flux, that i«, equals
the initial current /« time** the inductance L:

Srt ™ frtMO¹ * *•• /,i'_tt. (2)

Whatever, therefore, may be the rote of dtuwaw, or the shape
of the curvtw of «f», -/, and r, the total area of the voltage* curve must
be tin* name, and equal to w*o ^ra /**o.

If th<»n tho eum»nt i would contitiue to doereaHi^ at its initial

rate, an nhowu dotted in Fig* I IB (an could be warned, for instance,
by a gradual increase of the rtwiHt.anc(^ of the coil circuit), the

induced voltage would retain it* initial VE!UCI 00 up to the moment

of time t «* 4 + T, whore the current hm fallen to sero, as



	SINGLE-ENERGY TRANSIENTS. 21 This is the e.m.f, induced by the decrease of magnetic flux <I>, and is therefore proportional to the rate of decrease of <I>, that is, to ^{ -. In the first moment of short circuit, the magnetic flux <fr still (it has full value <l>₀, and the currant -i thus also full value t₀. Hence, at the first moment of short circuit, the induced e.m.f. e must be equal to «o, that is, the magnetic flux * must begin to decrease at such rate as to induce full voltage f«, as shown in Fig. 11(7. The three, curves <I>, •/, and e are proportional to each other, and as e is proportional to the rate of change of <I>, <I» must be propor- tional to its own rate of change, and thus also i and e That is, the transients of magnetic flux, current, and voltage follow the law of proportionality, hence are simple exponential functions, as seen in Lecture I : (J> 5W <f>^ — fltt— J(\|)_? ' (1)

	<f», i_t and e decrease most rapidly at first, and then slower and slower, but can theoretically never become zero, though prac- tically they become negligible in a finite time, The voltage $ in induced by the rate of change of the magnetism, and equals the decrease of the number of linen of magnetic force, divided by the time during which this decrease occurs, multiplied by the number of turns M of the coil The induced voltage e times the time during which it in induced thus equals n> times the decrease of the magnetic flux, and the total induced voltage, that in, the area of the induced-voltage curve, Fig. 11(7, thus equal n time the total dwroiuw of magnetic flux, that i«, equals the initial current /« time** the inductance L: Srt ™ frtMO¹ * •• /,i'_tt. (2) Whatever, therefore, may be the rote of dtuwaw, or the shape of the curvtw of «f», -/, and r, the total area of the voltage curve must be tin* name, and equal to wo ^ra /o. If th<»n tho eum»nt i would contitiue to doereaHi^ at its initial rate, an nhowu dotted in Fig I IB (an could be warned, for instance, by a gradual increase of the rtwiHt.anc(^ of the coil circuit), the induced voltage would retain it* initial VE!UCI 00 up to the moment of time t «* 4 + T, whore the current hm fallen to sero, as