=275. Internal Resistance of a Voltaic Cell.=--The current produced by a
voltaic cell is affected by the resistance that the current meets in
passing from one plate to another through the liquid of the cell. This
is called the _internal resistance_ of the cell. A Daniell cell has
several (1-5) ohms internal resistance. The resistance of dry cells
varies from less than 0.1 of an ohm when new to several ohms when old.
If cells are joined together their combined internal resistance depends
upon the method of grouping the cells.
[Illustration: FIG. 256.--The four cans exert four times the water
pressure that one can will exert.]
=276. Cells Grouped in Series and in Parallel.=--When in _series_ the
copper or carbon plate of one cell is joined to the zinc of another and
so on. (See Fig. 251.) The effect of connecting, say four cells, in
series may be illustrated by taking four cans of water, placed one above
another. (See Fig. 256.) The combined water pressure of the series is
the sum of the several pressures of the cans of water, while the
opposition offered to the movement of a quantity of water through the
group of cans is the sum of the several resistances of the cans. In
applying this illustration to the voltaic cell, we make use of Ohm's
law. Let _E_ represent the e.m.f. of a single cell, _r_ the internal
resistance of the cell, and _R_ the external resistance or the
resistance of the rest of the circuit. Consider a group of cells in
series. If _n_ represents the _number_ of cells in _series_, then Ohm's
law becomes
_I_ = _nE_/(_nr_ + _R_).
Cells are grouped in _series_ when large E.M.F. is required to force a
current through a large external resistance such as through a long
telegraph line. Cells are connected in _parallel_ when it is desired to
send a large current through a small external resistance. To connect
cells in parallel all the copper plates are joined and also all the zinc
plates. (See Fig. 257.) To illustrate the effect of this mode of
grouping cells, suppose several cans of water are placed side by side
(Fig. 258). It is easily seen that the pressure of the group is the same
as that of a single cell, while the resistance to the flow is less than
that of a single cell. Applying this reasoning to the electric circuit
we have by Ohm's law the formula for the current flow of a group of
_n_ cells arranged in parallel _I_ = _E_/((_r/n_) + _R_).
[Illustration: FIG. 257.--Four cells connected in parallel.]
[Illustration: FIG. 258.--The water pressure of the group in parallel is
the same as that of one.]
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