. Electrical world. ssed by the above equations in terms of n, and, ofcourse, indirectly in terms of x is given in Fig. 2. For convenience / b y / b ^ ^ ^^ in the application of these equations to transformer design a curveshowing the ratio of the total exposed area multiplied by the lineardimensions, a, to the volume of the iron link is included in thisfigure. The use of this curve is illustrated below. So far as efficiency is concerned, without reference to relative costof material, conditions of operation, etc., it is easy to see that thebest results will be obtained when the heat dissipate
. Electrical world. ssed by the above equations in terms of n, and, ofcourse, indirectly in terms of x is given in Fig. 2. For convenience / b y / b ^ ^ ^^ in the application of these equations to transformer design a curveshowing the ratio of the total exposed area multiplied by the lineardimensions, a, to the volume of the iron link is included in thisfigure. The use of this curve is illustrated below. So far as efficiency is concerned, without reference to relative costof material, conditions of operation, etc., it is easy to see that thebest results will be obtained when the heat dissipated in the coilsis equal to that dissipated in the iron. Let the heat dissipated inthe iron be H^ and that in the coil M C^R, where C is the currentin the primary coil. Then the efficiency is MEC — MCR — H, Hence, M^nc d e M C-R — H. dC C2 which, when equated to zero, gives M C-R = H^. Again the heats dissipated in the coils and in the iron are eachproportional to the volume of these parts. Hence, if there be no. FIG 3.—THREE LINKS. preference as to which volume should be greatest the total volumemay be taken as constant while v and v^ are varied so as to givethe least total heat dissipation. This gives the following equations: av = a V = heats dissipated in coils and iron respectively,a t + a^i;^ = // = total heat dissipated, V -{- v^ ^ V, a , it follows that a ^= a^ and i = v^ for greatest this is the case the links become both equal and similar. Itfollows from equations (9) and (10) that a. b — a a b + 3a hence. b — 2a b — 3a = o,or 6 = 30 = 33^ = fcj. It appears, therefore, that for a given volume of iron and copper,supposed equal to each other so as to obtain the highest electricalefficiency, the ratio of length to breadth of cross-section shouldbe 3 in the two-link type when rectangular links are used. The total exposed areas of two links of the kind here assumedand fitting closely to each other is (2aj + fcj) (40^ + 20 + 6) + (20
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectelectri, bookyear1883
