Lightning and lightning protections . tning on the protector,rather than on the linewe must arrange it in such way that the impedance of the protectorshoul be very small in comparison with the impedance of the these two reasons we will not change very much the characterof current discharge by supposing i„ = 0. The form of the equation will be modified for accordingfound in general case. We may show according to the exponentialcurve whethBr the root3 of the characteristic equation are real orimaginary. Now one or several these component parts will besuppressed by their amplitudes is su
Lightning and lightning protections . tning on the protector,rather than on the linewe must arrange it in such way that the impedance of the protectorshoul be very small in comparison with the impedance of the these two reasons we will not change very much the characterof current discharge by supposing i„ = 0. The form of the equation will be modified for accordingfound in general case. We may show according to the exponentialcurve whethBr the root3 of the characteristic equation are real orimaginary. Now one or several these component parts will besuppressed by their amplitudes is sufficiently weak to enable us 37 to think that this expression does not alter much the form of dis-charge current. We can in this way study the principle of discharge consid-ered by itself and deduce it3 potential parallel to the point will then come back to the current in the line which in realityinterested from the point of view of the protection of the line. The circuit of discharge thus simplified as shown in Fig. Keeping the same notation as proceeding wemay write the three equations for the threeunknowns as i^ ig and i^. ^2 (V) di 1 r r +L — +ri = V - - )- 1 1 dt C° 1 dt ... (2*) (3f) In deriving the equation (2*) respect to t,we get di dilr1 fL d2i 1 + r— = - -i dt d t dt C (4») Now from (3) we may get the value of igwhich is replaced in (l*) gives,di i = i1+riC2—dt Differentiating this equation twice we have, di dii d2i dt dt + rlC2~odt^ d2i d2i ! d3i dt2 dt2 1 *<Lt* 38 In troducing these values intu the equation (4*) and arrang-ing terms, we nave d3ii d2ii dii fa ~ +o i1 = 0 (5*) dt3 dt2 dt when 1 r a = 1 - r!C2 L rx(C + C2 ) r C b = — — L G2C c = L C2C rj We must notice that we would have this equation directly if we introduce the hypothesis that Cg= 0 or r-j = correspondingly i3 = 0 intu the equation of the general case . Its auxiliary eqyation will be, m3ta m2+bmtc = 0 (6*). Entire discussion will be rest upon the equation (6f). Let u
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectlightning, bookyear19
