February 26, 2017

Global Differentiable Dynamics by Hajek O., Lohwater A.J., McCann R. (eds.)

By Hajek O., Lohwater A.J., McCann R. (eds.)

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F. f. f. is consumed by the current in the resistance and by the potential difference at increases, the condenser. f. is available for the resistance, that is, the current decreases again, zero, when the condenser is fully its and ultimately becomes charged. , and so retards somewhat the decrease of current. the impressed Fig. f. , and e = 1000 volts. f. e Q current still exists. f. 7 1000 1000 volts 2GO ohms 100 mh. 10 mf. S2->--400

Phenomena of the same character, but with space instead TRANSIENT PHENOMENA 24 time as independent variable, are the distribution of voltage and current in a long-distance transmission line; the phenomena of occurring in multigap lightning arresters; the transmission of current impulses in telephony; the distribution of alternating current in a conductor, as the rail return of a single-phase rail- way; the distribution of alternating magnetic flux in solid mag- netic material, etc. Some of the simpler and discussed forms of transient terms are investigated in the following pages.

By e , G it =- = current in permanent or stationary condition after the change of circuit condition. f. f. consumed by inductance di where i = current in the circuit. 25 L is is TRANSIENT PHENOMENA 26 or, = e Hence, = substituting e ^r, +L ir > (1) and transposing, i This equation is integrated --t = where by log(-i - i t) - However, for Substituting t = 0, i = ii i = i c$ ^ . this, gives I i hence, = il Q = ^ + c, - (i \) the equation of current in the circuit. f. of self-inductance hence a maximum for t e?

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