FREDERICK A. DRAPER
Before taking up the construction of different types of batteries, it will be well to understand how best to group cells to secure the most efficient service from them, as such information will be of value in helping to determine the kind of cell to use for any particular work. The several factors to be considered in selecting cells are, the relative constancy, the electro-motive force and the ratio between the internal resistance of the cell and the external circuit. The matter of E. M. F. and constancy have already been briefly noted. The internal resistance of a cell, in its relation to the external circuit. is an important matter.
By "internal resistance" is meant the resistance to the passage of the current offered by the exciting fluid. In the so-called " dry " cells, the liquid is held by absorbent material, which in a moist state is in contact with the elements. The internal resistance is expressed in formulas as r. The external resistance, expressed as R, includes the conducting wires, instruments, lamps, etc., through which the current passes from and returning to the cell. The formula which expresses to the relations existing between the E. M. F., and internal resistance of a cell, the resistance in the external circuit, and the current developed is
E / R + r = C, in which E is the E. M. F. in volts; R the external resistance, r the internal resistance and C the current in amperes.
As the elements used in a cell determines the E. M. F. it is evident that the matter of size has no influence upon the difference of potential between the poles or voltage. On the other hand, the size has much to do with the current from a cell, or amperage. This is because the larger the plates the less the proportion ate external resistance. If plates measuring 2 x 2 in in a cell having an E. M. F. of 1 volt and so located that the internal resistance is 1/2 ohm, are replaced by plates 2 x4 in., the resistance is reduced one-half, or to i ohm, and the resulting current is doubled. The two examples would figure as follows:
1, 1 / 1/2 =2; 2, 1 / 1/4 = 4.
As a substitute for making cells of large and inconvenient size, groups of small cells may be so connected that the current obtainable will be equivalent to that from one or more large ones. This is known as multiple or parallel connection and is illustrated in Fig. 1. Here six cells are so connected that all the elements of one kind (zinc) are on one part of the circuit and the other (carton) on the other part, the resistance of the connecting wires being negligable. If each of these cells had an E. M. F. of 1.4 volts and an internal resistance of 1 ohm, the formula for the group as above connected would be: e 1.4 / 01 = 1.4 x 6 = 8.4 amperes.
If, however, we desired to increase the E. M. F., the cells would be connected as shown in Fig. 2, known as "series" connection, where the positive pole of one cell is connected to the negative pole of the next, which has the effect of adding the E. M. F. of the cells so connected. But as the resistance of each cell is interposed to the passage of the curreut, the amperes remain the same as for one cell. Assuming the E. M. F. and internal resistance to be the same as for the previous illustration, this is shown as follows: E 1.4x6= 8.4 volts and E 1.4 x 6 / rl x 6 = 1.4 amperes.
We have seen how the E. M. F. or current can be altered at will; we will now consider the important bearing this has in relation to the resistance of the external circuit. Assume that an external circuit has a resistance of 1 ohm, that the battery has an E. M. F. of 1.4 volts and an internal resistance of 1 ohm, this would give E1.4 / R1 + r1 = .7 amperes.
If the external circuit has a resistance of 1000 ohms, one cell would give E 1.4 / R1000+ r1 ---- = .001368 amperes.
With 10 cells the current would be E 1.4 x_10 / R1000+r10 = .01386 amperes and with 100 cells E1.4x100 / R1000 + r l00 = .1273 amperes. showing that the current increases at nearly the same-rate as does the number of cells. Should the cell be of a type having a high internal resistance, the result of increasing the number of cells in series is found to be quite different. The type of battery universally used on long distance telegraph work has an internal resistance of about 4 ohms, and has an E. M. F. of about .9 volts per cell. In an external circuit of 1 ohm resistance the current from 1 cell would be E.9/ Rl + r4 =1.3 amperes.
If the resistance in the external circuit be high, as in long telegraph lines, high resistance in a battery is not so objectionable, if other advantages are obtained, as will be seen by the following, assuming an external resistance of 1000 ohms. With one cell we would get and ten cells would give E.9 x 10 / Rl + r40 = 2.2 amperes.
From 100 cells we would get E.9x100 / R1 + r400 = .224 amperes. showing plainly that with a low external resistance nothing is gained by increasing the number of cells where the internal resistence is high, and also that the excess above a certain number caused a positive loss.
The several illustrations here given should enable the reader to calculate the results which any given combination of cells would give, the E. M. F. and external and internal resistance being known. It would be found that the best possible arrangement for circuits of low external resistance to give the maximum of current is where the grouping is such as to make the internal resistance equal to the external resistance. But no arrangment is economical unless the external resistance considerably exceeds the inter nal. • Hence in induction coils, the use of comparatively small wire for the primary winding, when batteries are used for current, the higher resistance of the finer wire retarding the flow of the current.
Another method of grouping cells shown in Fig. 3 partakes in part of the arrangements previously shown and is known as "series-parallel ". Combinations of this kind enable both the E. M. F. and current to be increased or varied as desired, the parts connected in series raising the volts, and the joining of these series groups increasing the current. This style of grouping is of value in exciting the coils for sparking gas engines, and other purposes where a strong, snappy current is required for steady work.