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THE POPULAR EDUCATOR. 



VOLTAIC ELECTRICITY. IV. 



MODE OF CONNECTING THE CELLS TOGETHER OHM'S LAWS 

 MODE OP CONVEYING THE CURRENT THE EARTH 

 ACTING AS A RETURN WIRE SHORT CIRCUITS GALVA- 

 NOMETER WHEATSTONE'S BRIDGE RESISTANCE COIL. 



HAVING prepared a number of single cells of any one of the 

 descriptions already mentioned, we have next to consider the 

 way in which they are to be connected together, and a moment's 

 thought will show us that there are several different modes in 

 which this may be accomplished. One or other of these modes 

 of arrangement is found to be the more advantageous according 

 to the use to which the battery is to be applied, and we must 

 therefore briefly examine their relative advantages. 



We will suppose that we have six cells of our battery, and, 

 for the sake of simplicity, we will suppose them to be simple 

 elements of copper and zinc, the thicker plate in the figures 

 representing the zinc. There are clearly four ways in which we 

 can connect them together. They may be arranged in a line one 

 behind the other, or, as we may call it, in Indian file, as shown 

 in Fig. 22, the zinc of one being connected with the copper of 

 the next ; or they may be arranged in two rows, each containing 

 three cells, as shown in Fig. 23 ; or three abreast, as at Fig. 24 ; 

 or, lastly, they may be ar- 

 ranged side by side, all the 

 zincs being connected to- 

 gether to form the negative 

 pole, while all the wires from 

 the copper plates unite to 

 form the positive terminus, 

 as at Fig. 25. 



Now the laws regulating 

 the different degrees of power 

 that will be obtained by these 

 different modes of arrange- 

 ment have been investigated 

 by several electricians. Pro- 

 fessor Ohm was, however, 

 the first to reduce them to 

 a few general principles, 

 which are accordingly known 

 as Ohm's laws. Further in- 

 quiries have more fully con- 

 firmed these laws, and shown 

 their great practical import- 

 ance. 



To understand them we 

 will call the power which a 

 cell possesses of evolving electricity its electro-motive force, and 

 represent it by the letter E. Now only a part of this is actually 

 transmitted along the wire connecting the poles, for there is a 

 certain amount of resistance offered to its passage by the imper- 

 fect conducting nature both of the liquid in the cells and of the 

 connecting wire. We will express the internal resistance, or 

 that in the cells themselves, by the letter K, and the external, 

 or that caused by the conducting wire, by the letter r. These 

 amounts vary with the nature of the battery employed, and 

 many other circumstances modify them more or less. The total 

 quantity of electricity which passes along the conducting wire in 

 any given time shows the strength of the current, and may be 

 signified by the letter I. The only object in using these letters 

 to denote these quantities, is to simplify the formulae which will 

 be given, and to enable them more easily to be remembered. 



Ohm's law, then, maybe enunciated as follows : The intensity 

 of the electric current is equal to the electro-motive force divided 

 by the total resistance opposed to it. This is expressed by the 

 formula 



1= 



E +r* 



When a good conductor is interposed between the poles, and 

 it is short and of sufficient size to convey the current, there is 

 but little loss from external resistance, and consequently r may 

 be omitted in the above formula. The resistance, however, in- 

 creases with the length of the conducting wire, and also with 

 its diminution of size, so that in the case of telegraph wires, 

 where the current sometimes has to travel great distances, r 

 becomes very much larger than E. 



From this we see the great practical importance, when using 



powerful batteries, of having good and large connectors. Copper 

 is usually employed for this purpose, owing to its being the best 

 conductor ; and where permanent connections are to be fitted 

 as, for instance, in conveying the current from one part of a 

 building to another flat strips of copper are frequently em- 

 ployed, as they are more easily arranged than a wire of the same 

 sectional area would be. In practice it is usually found most 

 convenient to have the battery placed at some little distance 

 from the experimenting room, so as to avoid all inconvenience 

 from the fumes, and the current is brought by these strips to 

 any place where it may be required. The ends of them are made 

 to overlap a little so as to ensure contact. If they become much 

 heated by the passage of the current, it is a sign that they are 

 too small to convey it properly. 



Now if any number, n, of elements of a battery be connected 

 together in series, there is n times the electro-motive force, and 

 also n times the internal resistance ; the external resistance, 

 however, remains the same, and thus the formula becomes 





nE 

 nE + r* 



If, however, the conducting wire is short and good as well, 

 we may neglect r, and then wo see that 



nS. ~R 



This corroborates our 

 former statement that no 

 greater quantity of electri- 

 city is produced by several 

 cells than by one. When, 

 however, there ia a great 

 resistance that is, when r 

 becomes large the advan- 

 tage will at once be seen ; 

 the current from a number 

 of cells has greater intensity, 

 and can penetrate a greater 

 resistance. In fact, when r 

 becomes very great as com- 

 pared with E, the formula 

 becomes nearly 

 nE 



1-71 



or the intensity increases 

 nearly in the same propor- 

 tion as the number of cells. 

 If the cells are joined as 

 in Fig. 25, it is as if one cell was increased in size. The electro- 

 motive force remains the same ; the internal resistance is, how- 

 ever, diminished in the same proportion as the size is increased. 

 We are now in a position to ascertain the relative advantages 

 of the four modes of connection which we have shown. 



We will first suppose r to be represented by 4 and E by 1 , 

 that is, the resistance in the lino to be four times as great as the 

 internal resistance of the cells. 



When the batteries are all connected in line, as at Fig. 22, 



1 = 



6E = 



C x 1 + 4 10 



Now let them be connected so as to be two abreast, as in Fig. 

 23, and we have then in reality three elements, each of double 

 the size ; the resistance, therefore, is now only i, and therefore 



11 



When they are connected as in Fig. 24, E = J, and the formula 

 becomes 



2E 



1 = 



_ 6E. 

 x J + 4 14 ' 



while, when all the zincs are connected together, and the copper 

 plates also, as in Fig. 25 



IL 1?. 

 ~ 25* 



I = 



We see thus that with this external resistance the greatest 

 advantage is gained by connecting them singly. If, however, we 

 suppose r to be just equal to R, these formulae will respectively 



