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The following considerations will show that it is impossible that



VOLTAIC ELECTRICITY. 209

the hydrogen atoms released in A should be instantly shot across
the 15 or 20 inches of electrolyte to C. By moderate exertion a
small lead ball may be thrown several hundred feet. If this ball
be cut up into fine shot the force required to throw it to this dis-
tance would be very much greater. If it be reduced to dust we
could not command sufficient force, and a particle of dust might
contain several million atoms. Finally, the hydrogen atom is over
200 times lighter than the lead atom and instead of moving
through air moves through the liquid. It is thus seen that the
force required would be beyond all reason.

As a matter of fact, the ions move from both electrodes in
opposite directions and at different rates of speed. These rates
have been accurately measured. The swiftest of the ions, the
hydrogen, moves under ordinary conditions a little faster than
one-thousandth of an inch per second.

274. Grotthus' Theory. We have already mentioned (Par. 195)
that no signs of the moving ions can be seen between the electrodes.
Grotthus in 1805 attempted to explain this by the theory that
there was an exchange of hydrogen atoms from molecule to mole-
cule of the acid between the electrodes, just as each individual in a
bucket chain at a fire passes a bucket to the person on one side
of him and receives a bucket from the person on the other side.
The correct explanation is that so long as these ions carry charges
they do not possess their ordinary properties and do not aggregate
into visible masses.

275. Electrolytes and Non-Electrolytes. In Par. 267 we saw

that solutions of all the acids, all the bases, and all the salts, and
only these, produce osmotic pressures in excess of those called for
by theory. From what has been brought out in the preceding
pages, the student will now be prepared for our final and most
startling generalization, namely, those and only those solutions
which produce abnormal osmotic pressure conduct electricity or
are electrolytes. All other solutions are non-conductors or non-
electrolytes.

276. Electrolytic Properties Depend Upon lonization. Since
the common property of these solutions, excessive osmotic pres-
sures, has been shown to result from ionization, it is but natural
to assume that their electrolytic property has the same cause. A
vast accumulation of facts points to this same conclusion.



210 ELEMENTS OF ELECTRICITY.

Sulphuric acid when free from water is a non-conductor. Per-
fectly pure water is also a non-conductor. Such water never
exists in nature and perhaps may never be prepared, but by a
special treatment to remove dissolved gases, and a final distillation
in vacuo, water has been prepared of such purity that a column
of it one millimeter (one twenty-fifth of an inch) long had the
same resistance as a copper wire of the same diameter but en-
circling the earth at the equator 300 times. A solution of sulphuric
acid in water is, however, a very good conductor.

Again, since we have seen (Par. 271) that ionization increases
with dilution, a dilute solution, the amount of dissolved substance
being kept constant, should conduct better than a strong one,
and this is found to be the case.

A solution of hydrochloric acid in water is a very good con-
ductor; a solution of the same in chloroform, no ionization taking
place, is a non-conductor. Such examples may be multiplied
indefinitely.

277. Vapor Tension. In Par. 259 illustrations were given of
the force or pressure which causes gases to diffuse through space,
and dissolved substances to spread through unoccupied solvent.
This tendency to diffuse is general. If a liquid be introduced
beneath a bell jar, a portion of the liquid passes into a state of
vapor and fills the jar and the evaporation continues until the
pressure of the vapor above the liquid balances the force which
tends to throw off the liquid into space. To this force the name
vapor tension has been applied. It is to be noted that in order to
pass from a liquid to a vapor a certain amount of heat must be
taken in by the vapor. The vapor passes off accompanied by this
latent heat which is necessarily lost by the liquid left behind.

278. Solution Tension. Nernst advanced the theory that a
similar state of affairs obtains for solids immersed in liquids, that
is, there is a force, designated by him solution tension, which tends
to drive particles of the solids off into solution in the liquid. We
have seen (Par. 270) that a metallic ion can go into solution only
when it carries with it a positive charge. Therefore, parallel to
the heat in the case of the vapor, the liquid about a metallic plate
becomes positively charged and the plate becomes correspond-
ingly negatively charged. Ions continue to be thrown off from the
metal until the force throwing them off, or the solution tension,



VOLTAIC ELECTRICITY. 211

is just counterbalanced by the contrary force of attraction which
tends to pull the positively charged ions back to the negatively
charged plate. To this theory the objection was advanced that
if a metal plate threw off ions it would lose weight but in many
cases no such loss can be detected by even the most delicate
measurements. The reply to this is that the quantity of elec-
tricity carried by the ions is so great that equilibrium is reached
long before there passes into solution enough ions to be detected
by our most refined methods of weighing. For example, to carry
into solution 31.8 grams of copper would require 96,540 coulombs
(Par. 231) and to carry in only one-thousandth of a gram (the
smallest amount that can be weighed in an ordinary analytical
balance) would require over three coulombs, each of which is
about three billion electrostatic units (Par. 228).

279. Theory Applied to the Simple Cell. Consider the case
of the simple cell (Par. 193). Both the zinc and the copper throw
off ions into the electrolyte but the zinc has the greater tendency
to pass into solution therefore more zinc ions go into solution and
the zinc plate becomes more negatively charged than the copper
plate. The result is that, as compared to the zinc plate, the
copper plate is positively charged. When these plates are con-
nected through the external circuit, the current flows from the
copper to the zinc, the negative charge on the zinc is partly neu-
tralized and the zinc plate can therefore throw more ions into
solution, and so on.

280. Atomic Character of Electricity. We have seen above
that the passage of a given quantity of electricity through an
electrolyte always releases equivalent weights of ions. Since
96,540 coulombs liberate one gram of hydrogen and 107.9 grams
of silver, and since this ratio is constant no matter how many
coulombs flow through the electrolyte, the quantity of electricity
that would release one microcrith of hydrogen would also release
107.9 microcriths of silver, that is, the quantity that releases one
atom of hydrogen releases one atom of silver and one atom of any
other univalent element. Since the quantity of electricity which
releases an ion is equal to the charge which the ion carries, we see
that all univalent ions carry equal charges, either positive or
negative. Bivalent ions carry twice the charge of univalent ions,
and trivalent ions carry three times this charge, and so on. Every



212 . ELEMENTS OF ELECTRICITY.

unit of valency therefore is accompanied by the same definite
quantity of electricity, either positive or negative, and since there
are no fractions of these charges and they vary by whole numbers,
or in simple ratio, Helmholtz concluded that electricity was
divided into elementary portions or atoms. These electrical atoms
which accompany ions have been named electrons. Assuming
that an ion and an atom of hydrogen are the same, the electron
has been calculated as 2.4xlO~ 10 electrostatic units.

281. Extensive Scope of Theory of Electrolytic Dissociation.

The scope of the theory of electrolytic dissociation is extensive.
Its applications to pure chemistry are even more wonderful than
those that we have just considered. It explains why water is one
of the products of most chemical reactions; why the majority do
not take place unless water be present; why, for example, dry
sulphuric acid has no effect upon blue litmus; why dry hydro-
chloric acid does not react with dry ammonia; why dry sulphuric
acid does not attack dry sodium. It also explains such facts as
why silver chloride is precipitated by the soluble chlorides yet
not by the chlorates; why KOH precipitates metallic hydroxides
yet CH 3 OH does not, etc., etc. The statement is even made,
though not yet universally accepted, that no metathetical reaction
is possible unless preceded by ionization either by solution, by
fusion, or by vaporization. It is being developed by many inves-
tigators and there is every reason to believe that remaining ob-
jections which may be advanced against it will shortly be explained
away.



VOLTAIC ELECTRICITY.



213



CHAPTER 24.

RESISTANCE.

282. Resistance. For the beginner it is helpful in forming a
physical conception of certain electrical phenomena to think of
electro-motive force as a pressure which drives or pushes, or tends
to drive or push, electric charges. If two points between which
there exists a difference of potential be connected by a conductor,
the electro-motive force will cause a flow of electricity from the
point of higher potential to that of lower, and the greater the
difference in potential between the two points the greater the
pressure and the greater the quantity of electricity that will flow
across in a given time. This movement is also affected by the
nature of the conductor between the two points. For example,
it takes a longer time for a given quantity of electricity to flow
through a long thin wire than it does through a short thick one..
We have seen (Par. 228) that the current is measured by the
quantity of electricity flowing past a given point in a unit of time,
hence the current in the long thin wire is smaller than that in the
short thick wire. The long thin wire therefore cuts down or
reduces the current by obstructing its flow. This hindrance
which the wire offers to the flow is called its resistance.

283. Example of Effect of Resistance. The following experi-
ment will show the effect of resistance. Fig. 119 represents
diagrammatically a cell or battery A and in the external circuit

B c




Fig. 119.

two copper voltameters D and E. When the key K is closed the
current from the cell divides at B, a part going through the upper



214 ELEMENTS OF ELECTRICITY.

voltameter Z), and the remainder through the lower voltameter E.
The electro-motive force which drives the current through the
two voltameters is precisely the same, since it is due to the dif-
ference of potential between B and C, but in the upper voltameter
it has to drive it through the short stout wire and in the lower volt-
ameter it has to drive it through the longer and thinner wire. If
the key be kept closed for a convenient time and then opened and
the cathodes be weighed, it will be found that the cathode of D
has increased considerably more in weight than that of E, hence
a greater quantity of electricity has passed through D in the given
time, that is, the current through D has been greater than that
through E.

284. The Practical Unit of Resistance, the Ohm. This sub-
ject was investigated first by Ohm who showed that the resistance
of a given conductor of uniform cross-section varies directly as
its length and inversely as the area of its cross-section. At the
time when he carried on his researches there were no units of
resistance and he therefore extemporized standards by means of
definite lengths of wire of a given size which, for the sake of com-
pactness, he wrapped up into coils. He used these resistance coils
himself and distributed others among those of his scientific friends
who wished to verify his results.

The practical unit of resistance, the ohm, is named in his honor
and will be defined later (Par. 291) ; for the present we must con-
tent ourselves with the statement that it is about the resistance
of a piece of ordinary iron telegraph wire, one-sixth of an inch in
diameter and one hundred yards long; or about the resistance of
ten feet of annealed copper wire one-hundredth of an inch in
diameter.

285. Laws of Resistance. We saw above that Ohm showed
that the resistance of a conductor of uniform cross-section varies
directly as its length and inversely as the area of its cross-section.
He also showed that it depends upon the material of which the
conductor is composed. If R represent the resistance of such a
conductor, this law may be expressed



in which I is the length of the
conductor, s is the area of its cross-section, and p is a factor



VOLTAIC ELECTRICITY. 215

depending upon the material and called its specific resistance.
Resistance also varies with the temperature of the conductor.

In addition to the foregoing, there are a few substances whose
resistance varies under certain conditions in an anomalous man-
ner. For example, when bismuth is placed in a magnetic field its
resistance increases; when selenium is exposed to light its resist-
ance decreases. The resistance of some substances, notably
carbon, decreases with pressure. The prime factors of the resist-
ance of a conductor, however, are length, area of cross-section,
material and temperature and these we shall now consider in
detail.

286. Resistance Varies Directly with Length of Conductor.
This statement requires no amplification. The principle has
numberless applications. By measuring the resistance of a foot
of a given wire we can easily calculate the resistance of any speci-
fied length of it. To determine the length of a submarine cable
coiled upon a reel, it is not necessary to unwind it. We measure
its total resistance, obtain by measurement or from a table the
resistance of the wire per foot, whence we get at once the total
number of feet.

If conductors of different lengths, cross-sections or materials
be connected one after the other, or in series, the total resistance
of the resulting conductor is the sum of the separate resistances.

287. Resistance Varies Inversely as Area of Cross- Section of
Conductor. The resistance of a conductor varies inversely as the
area of its cross-section, that is, the greater this area, the less the
resistance and the less this area, the greater the resistance. For
the usual current electricity it is unaffected by the geometrical
shape of the cross-section, and whether this be circular or square
or irregular or tube like, if the area be the same the resistance is
the same. The resistance of a wire cable of many strands is the
same as that of a single conductor whose cross-section is equal to
the sum of the cross-sections of the separate strands. Since wires
are usually circular in cross-section, the resistances of equal
lengths of wire of the same material are to each other inversely as
the squares of the diameters of the wires.

288. Specific Resistance. If in the expression (Par. 285) for
the resistance of a conductor



216 ELEMENTS OF ELECTRICITY.

we make I =one centimeter and s = one square centimeter, we have

R = P

' But p is the specific resistance of the material of which the
conductor is composed, whence we see that this specific resistance
is measured by the resistance of a centimeter cube of the substance
or of a prism or cylinder whose cross-section is one square centi-
meter and whose length is one centimeter. The resistance of a
piece of metal of this size is so small that it is usually expressed
in millionths of an ohm, or microhms. For example, the specific
resistance of silver, which is the least, is about 1.5 microhms, that
of copper about 1.6, that of brass about 7, that of wrought iron
10 to 15, that of lead about 20, that of mercury about 95, that of
cast iron over 100. On the other hand, the specific resistance of
the ordinary electrolytes runs from 1 to 30 ohms while the specific
resistance of lead glass is given as 84 trillion ohms and that of
flint glass is two hundred thousand times greater.

289. Variation of Resistance with Temperature. The resist-
ance of all substances changes as their temperature varies. The
resistance of the metals increases as their temperature rises; on
the other hand, the resistance of electrolytes and of most non-
metals decreases with increase in temperature. This is of especial
importance in the case of carbon. The resistance of the carbon
filament in an incandescent lamp when hot and giving light is
very nearly, if not quite, fifty per cent less than when cold.

The amount of change in resistance per ohm per degree is
called the temperature coefficient. The metals therefore have a
positive temperature coefficient; the non-metals and electrolytes
have a negative coefficient. Starting at C, the resistance of
many metals decreases about ?^d for every drop of 1 C. At this
rate their resistance would entirely vanish at 273 C, which is
the absolute zero of temperature as deduced from Charles' law of
gaseous pressure. It is interesting to find this significant tempera-
ture thus indicated by an independent deduction. It must be
noted however, that recent experiments show that at the tempera-
ture of liquid air the resistances no longer decrease at the same
rate.

It is highly desirable that we should be able to prepare standards
of resistance which would be independent of temperature, and
certain alloys have been discovered whose temperature coefficient



VOLTAIC ELECTRICITY. 217

is so small that for most purposes it may be neglected. Typical
of these is manganin, composed of 84 parts copper, 4 parts nickel
and 12 parts manganese.

290. The Platinum Thermometer. This change of resistance
with temperature is utilized in the construction of certain forms
of pyrometers, thermometers for the measurement of temperatures
beyond the range of the mercurial thermometer or extending up
to 1000 C. In most of these a platinum wire is wrapped around
a slender tube of mica which is then slipped into an outer tube of
fire-resisting porcelain closed at one end. The free ends of the
wire are brought out of the other end and arranged for attachment
to a resistance-measuring instrument which may be at some dis-
tance. The porcelain tube is then inserted into an opening in the
walls of the furnace or dipped into the molten metal whose tem-
perature is to be determined. When the coil has attained the
temperature of the surrounding medium, the resistance of the wire
is measured by means to be described later (Chap. 26) and the
corresponding temperature is given by reference to a table or is
sometimes read directly from a scale which is a component part
of the apparatus.

291. The Ohm Defined in Terms of a Column of Mercury.

The comparisons in Par. 284 are only crude approximations and
can hardly be made anything more, for the resistance of iron and
of copper varies greatly with even slight traces of impurities and
with the temper and annealing. Mercury is a metal which by
simple distillation and washing is readily obtained in a high state
of purity; it is also free from the troubles of tempering and anneal-
ing and finally its resistance is nearly sixty times greater than that
of copper. The apparent disadvantage of not being able, on ac-
count of its liquid state, to obtain it in wires is easily overcome
by pouring it into glass tubes of the required size, and electric
connection with it is made by simply dipping into it the conducting
wires. The International Congress of Electricians in Chicago in
1893 (Pars. 212, 232) defined and recommended that there be
adopted "as a unit of resistance, the International Ohm . . . repre-
sented by the resistance offered to an unvarying electric current
by a column of mercury at a temperature of melting ice, 14.4521
grammes in mass, of a constant cross-sectional area and of the
length of 106.3 centimeters." This corresponds to a cross-section



218 ELEMENTS OF ELECTRICITY.

of one square millimeter but the weight of the mercury is given
instead of the diameter of the tube since, of the two, the weight
is the more easily and accurately measured.

292. Resistance and Conductance. The terms resistance and
conductance are reciprocals. The less the resistance of a conductor,
the greater its conductance; the greater its resistance, the less its
conductance. The unit of resistance is the ohm. There is no
need for a unit of conductance yet it has been given a name, the
mho (the word ohm backwards). A body whose resistance is
three ohms has a conductance of one-third mho.

There is no conductor devoid of resistance; so also there is no
absolute non-conductor. Substances may be arranged in order of
their relative conductance or, as it is frequently called, their
conductivity, this being the reciprocal of specific resistance, also
called resistivity. Silver is the best conductor and copper comes
next. Conductivity is expressed in percentage, that of annealed
copper being taken as 100 since copper and not silver is the stand-
ard material for electric wiring. The following table gives the
conductivity of the commoner metals as determined by Fleming
and others.

Metal Conductivity

Silver, pure 108.60

Copper, annealed a. . .100.00

Gold : 97.80

Aluminum 63.00

Zinc 27.72

Brass 22.15

Iron, wrought, average 15 . 00

Steel 11.60

Lead 7.82

German Silver 5.32

Mercury 1 . 69

293. Resistance of Conductors in Parallel. If an electric
circuit splits into two or more portions which again unite, it Is
called a divided circuit. Such a circuit of three branches is repre-
sented in Fig. 120. The three branches are said to be in parallel.
A turnout which enables cars travelling at different speeds, or in
opposite directions on a single track, to pass each other is some-
times called a shunt. From analogy, any branch of a divided



VOLTAIC ELECTRICITY. 219

circuit may be called a shunt for the remaining branch or
branches.

It frequently becomes necessary to determine the resistance of
a divided circuit, that is, the joint resistance of two or more con-
ductors in parallel. Suppose we have in parallel two wires, one of

A



Fig. 120.

ten ohms and the other of one ohm resistance; what is their joint
resistance? The tendency for a beginner is to say the average of
the two, but reflection will show that the two wires side by side
are equivalent to a single wire of greater cross-section and hence of
less resistance than either. In other words, the joint resistance
of any number of resistances in parallel is always less than that
of the least.

Joint resistance may be determined as follows: If A, B and C
be the resistances of the branches in Fig. 120, their conductance

is -j> ^ and ~. Their joint conductance is the sum of the
separate conductances or

i ' I 4_ I = AB + AC + BC

A + B "*" C ABC

Their joint resistance is the reciprocal of this or

p _ ABC

~ AB + AC + BC

and in general the

joint resistance of any number of resistances in parallel is the
reciprocal of the sum of the reciprocals of the separate resistances.
If there be but two resistances, the formula becomes



or the joint resistance is
the product of the two divided by their sum.
Should A, B and C be equal, the expression becomes

R = -

and in general the joint



220 ELEMENTS OF ELECTRICITY.

resistance of any number of equal resistances in parallel is equal to
that of a single resistance divided by the number in parallel.

294. Internal Resistance of Cells. In the employment of
voltaic cells as a source of electrical energy, the question of their
resistance is of great importance. In Par. 288 we saw that while
the specific resistance of copper is about 1.6 microhms (million ths
of an ohm), that of the usual electrolytes runs from 1 to 30 ohms,
that is, the resistance of the electrolyte is on an average 10,000,000
times greater than that of the copper. This resistance, spoken of
as the internal resistance of the cell, follows the same laws as other
resistances (Par. 285). With a given electrolyte, we may reduce
the internal resistance of a cell in two ways. First, by bringing the
plates of the cell closer together we may shorten the path which
the current has to follow. Second, by increasing the area of the
plates we increase the number of available paths for the current,
or increase the cross-section of the total path. A thin sheet of
copper parallel and close to the zinc plate offers far less resistance



Online LibraryWirt RobinsonThe elements of electricity → online text (page 18 of 46)