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Font size is precisely the same and the bell rings at both stations.

348 ELEMENTS OF ELECTRICITY.

hook and held to the ear. The hook, freed from the weight of the
receiver, rises and breaks the circuit at G but closes it at M, N
and 0. The current coming in from D follows the route
E-F-0-R-S-B-C.

(c) To send a message. The hook being up, the transmitter-
battery-primary circuit is closed at NM. Currents through this
circuit are stepped up in the secondary S and follow the route
given above.

ELECTRO-MAGNETICS. 349

CHAPTER 34.

AMMETERS AND VOLTMETERS.

443. Electrical Quantities to be Measured. The modern
development of the science of electricity has been accompanied
and greatly aided by the production of ever improving instru-
ments of precision for the rapid and accurate measurement of
certain electrical quantities. The principal of these quantities
are:

1 Resistance,

2 Strength or intensity of current,

3 Electro-motive force,

4 Electrical power.

The measurement of resistance was explained in Chapter 26
and in the present chapter we are concerned with the measure-
ment of current and of electro-motive force.

444. Electrical Effects Used in Measurements. Electricity
not being matter, and hence being imponderable and without
physical dimensions, must be measured indirectly by its effects.
These are usually classed under four heads, viz.:

1. Thermal. A current flowing through a conductor heats it.

2. Electro-magnetic. A current flowing through a conductor
produces about it a magnetic field, (a) If flowing near a poised
magnetic needle, the needle will be deflected, or, (b) if flowing
around a soft iron core the latter will be magnetized.

3. Electro-chemical. (a) A current flowing through acidulated
water will decompose the same, releasing its component gases
hydrogen and oxygen, or (b) flowing through a solution of a
metallic salt will decompose the salt, depositing the metal upon
the cathode or plate by which the current leaves.

4. Physiological. A current flowing through a living or recently
living body will produce certain effects such as muscular twitchings
and contractions, and in a living being cause more or less painful
sensations.

350

ELEMENTS OF ELECTRICITY.

Of the above, the first three may be and are used in electrical
measurements.

445. Effect Best Adapted for Measurement. The effect best
adapted for measurement may be arrived at by a consideration
of the following experiments after Professor Ayrton. In Fig. 212

Fig. 212.

B represents a battery with which are connected in series the
various pieces of apparatus 1, 2, 3, 4, and 5, through which there-
fore the same current flows.

1 is a thermometer around whose bulb the conducting wire is
wrapped and which dips into some oil, a non-conductor of
electricity.

2 is a magnetic needle in whose vertical plane and around
whose pivot as a center the wire is bent in a circle.

3 is a soft iron core around which the wire is wrapped. On top
of this core is a piece of soft iron fastened to the hook of a spring
balance.

4 is a glass jar upon which is screwed an air-tight cover. Through
this run the two wires, each terminating in a platinum plate

ELECTRO-MAGNETICS. 351

dipping into the acidulated water with which the jar is partly
filled, and also a glass tube extending nearly to the bottom of the
jar, its upper portion expanded and graduated as shown.

5 is a glass jar partly filled with a solution of copper sul-
phate into which dip two copper plates to which the wires are
attached.

If now the key be closed and the current be allowed to flow for
a short time, t, the following effects will be noted :

1. The thermometer will indicate a rise in temperature.

2. The needle will be deflected through a certain angle and will
remain constantly at that angle as long as the current flows.

3. The soft iron core will become magnetized and will attract
the iron block so that a force of x ounces must be exerted upon
the spring balance to tear the block free.

4. Gas will be released at the surface of the two platinum plates
in 4 and its pressure will force a certain number of cubic centi-
meters of the liquid up into the graduated tube.

5. The cathode copper plate in 5 will be found to have increased
in weight due to the deposition of fresh copper upon its surface.

446. Second Experiment. If, beginning under the original
conditions of the preceding experiment, the key be closed an
interval, t', say twice as long as the original t, the following will
be observed:

1. The thermometer will indicate a temperature in general
greater than that produced by the first experiment but bearing
no definite relation to the same.

2. The needle will be deflected through the same angle as before.

3. The same pull will be required to release the soft iron block
from the electro-magnet.

4. Twice the volume of gas will be released in 4.

5. Twice the weight of copper will be deposited on the cathode
in 5.

Assuming that the current has been the same in these two
experiments, we may conclude

(a) That the temperature indicated by the thermometer in 1
varies in some indeterminate manner with the time and that
consequently the heating effect is not suitable for measurement.

352

ELEMENTS OF ELECTRICITY.

(b) That the electro-chemical effects vary directly with the
time and hence if reduced to a common unit of time will give a
definite measure.

(c) That the electro-magnetic effects are independent of time
and give a direct measure without reduction.

447. Third Experiment. A third experiment will throw further
light upon this subject.

In Fig. 213 B represents, as before, a battery.

Fig. 213.

1 and 1A thermometers, as before, but 1A has more turns of
the wire around its bulb than has 1 and they may be in different
sized jars which contain different amounts of oil and perhaps
different kinds of oil.

2 and 2 A magnetic needles with circular coils in their vertical
plane, the coil around 2 being of less diameter and of a greater
number of turns than that around 2A.

3 and 3 A electro-magnets differing in size and in the number
of turns of the wire.

4, 4A and 4B gas voltameters, 4 being two in parallel, 4A a
large one with plates far apart, 4B a small one with plates closer
together.

ELECTRO-MAGNETICS.

353

5, 5A and 55 copper voltameters arranged similarly to the gas
voltameters.

The key now being closed for an interval t, during which the
same current flows through the entire system, the following will
be observed:

1. The two thermometers will indicate a rise of temperature
but the indications will not be the same and will bear no apparent
relation to each other.

2. The magnetic needles will be deflected and will remain
constantly deflected as long as the current flows but the angles

4A

4B

Fig. 213.

will differ in the two cases and will bear no apparent relation to
each other, except that the deflection is greater in the instrument
with the greater number of turns.

3. The electro-magnets will require pulls of x and y ounces
respectively to separate the iron blocks but these pulls will bear no
apparent relation to each other.

4. The amount of gas released in each of the two gas voltameters
in series and the sum of the amounts released in the two in parallel
will be exactly equal.

5. The amount of copper deposited in each of the two copper
voltameters in series and the sum of the amounts deposited in
the two in parallel will be exactly equal.

354 ELEMENTS OF ELECTRICITY.

We conclude from the above:

(a) That the heating effect is unsuitable for measurement.

(b) That the electro-magnetic effect, while constant for the
same current for any one instrument, is yet a function of the
mechanical arrangement of the instrument and would be different
for every different instrument.

(c) That the electro-chemical effect is, within wide limits, inde-
pendent of the size, shape, and arrangement of the instruments.

448. Electro-Chemical Effect Selected as Standard. As a

logical consequence of the above, the electro-chemical effect has
been selected as a standard for the measurement of electrical
currents and the Act of Congress of July 12, 1894, legalized the
resolution of the International Congress of Electricians of the
preceding year and defined the practical unit of current, the
ampere, as that unvarying current which flowing through an
aqueous solution of nitrate of silver deposits silver at the rate
of .001118 gram per second.

449. Why Silver Selected. The current is defined in terms of
silver deposited, partly because silver is one of the precious metals
and when deposited from solution can be dried and weighed with-
out appreciable error due to increase of weight by oxidation or
other chemical change, but mainly because it combines high
atomic weight (107.9) with monovalency while the next most
suitable metal, copper, whose atomic weight is 63.6, is bivalent,
so that a given current flowing for a given time will deposit nearly
three and a half times as great a weight of silver as of copper.
Silver is therefore used in delicate measurements of small currents
but it is expensive and for large currents copper is employed.

450. Reason for Weight Selected. It may naturally be asked
why this particular weight of silver was selected instead of some
even number, such as .001 gram for instance. The reply to this
is that the absolute C. G. S. unit of current had already been
defined, the definition being bsed upon electro-magnetic effects
(Par.i355), and from many elaborate and accurate experiments
the amount of silver deposited by the unit current, and hence the
amount deposited by an ampere, had been determined.

451. Unsuitableness of Electro-Chemical Effect for Industrial

Needs. While, as shown above, the electro-chemical effect is
selected as a standard, in its practical application to most in-

ELECTRO-MAGNETICS. 355

dustrial needs it has certain insuperable objections. The principal
of these are (a) time consumed in a determination and hence
inability to take instantaneous observations and (b) lack of sensi-
tiveness and hence inability to measure small effects.

(a) For example, just as the steam engineer must without inter-
mediate calculations be able to read his steam gauge at any
moment, so the electrician should be able to read at any instant
his voltage and current. The determination of a current by a
voltameter observation is a laborious matter of hours, while what
is needed is an instrument which can be read just like a steam
gauge instantly and with a minimum expenditure of labor. To
make another comparison, to use a voltameter is as if a person
desiring to find out the time was compelled to take a set of astro-
nomical observations and by tedious calculations arrive at his
result. Naturally it is simpler, and in most cases preferable, to
read from a clock even though it should be several minutes fast
or slow.

(b) Again, the sensitiveness of a voltameter is not great and
can hardly be increased. Many currents with which electricians
have to deal are so small that they would have to flow for days
before they would produce enough chemical effect to be suscep-
tible of accurate measurement and even this supposes what is
very doubtful, that is, that a current could be kept constant for
that length of time.

452. Electro- Magnetic Effect Best for Practical Measurements.

As we saw in the account of the preliminary experiments in
Pars. 445, 446, and 447, the magnetic needle in each case
instantly took up a certain position and retained it as long as the
current remained constant. This then is the basis of the majority
of instruments in practical use.

453. Why not Selected as Standard. The question now arises
why then was not the electro-magnetic effect selected at the
outset as the standard. The reply is that it is well-nigh impossible
to construct two galvanometers which shall be duplicates, and it
would be even more difficult to construct a duplicate following
the specifications which such a definition would have involved.
On the other hand, as we have seen above, the electro-chemical
effect is, within wide limits, independent of instrumental size and
shape and accurate measurements can be made with such appara-

356 ELEMENTS OF ELECTRICITY.

tus as is found in any laboratory. An instrument maker could
therefore accurately calibrate a galvanometer by the somewhat
tedious voltameter method, as explained in the next paragraph,
and thereafter use this calibrated galvanometer as a standard for
the rapid calibration of others.

454. Calibration of Galvanometer. The galvanometer to
measure current is calibrated by connecting it in series with a
voltameter, noting the point at which the needle stands, deter-
mining the current by means of the voltameter and marking the
galvanometer scale to correspond, then repeating this, varying
the current, and so on.

For small currents it is not possible to calibrate the galvanom-
eter directly by this method, but since galvanometers follow the
fixed law that the deflecting force is directly proportional to the
number of turns in the coil, it may be calibrated as follows. It
is first calibrated for large currents as explained above, with say
only one turn in the coil. The soil is then re- wrapped with finer
wire and say 100 turns are put on. A small current is now sent
through the coil and produces a deflection which corresponds to i
amperes in the original calibration. We know that the effect of
the actual current has been multiplied 100 times by the number
of turns, consequently the current is actually only 2/100 amperes
and the scale can be so marked, and so on.

The sensitiveness of a galvanometer can be increased to a very
high degree. Ayrton states that it is possible to measure accurate-
ly with one a current so small that it would have to flow for a
million years through a voltameter before it produced as much
chemical action as a current of one ampere could produce in one
hour.

455. Difference between Ammeters and Voltmeters. The

galvanometers used to measure current are called Ammeters;
those to measure voltage are called Voltmeters. The moving parts
of an ammeter and of a voltmeter, of the kind shortly to be
described, are indistinguishable. They both move under the effect
of the current which flows through them. Ohm's law can be
written E = RI. As applied to a voltmeter or to an ammeter, R
is the instrumental resistance and is constant, whence it is seen
that the voltage is always some constant times the current through
the instrument and it might be thought that one and the same

ELECTRO-MAGNETICS. 357

instrument could be- used either as a voltmeter or as an ammeter.
If its scale were graduated in amperes, the readings need only be
multiplied by the constant R to convert them to volts, or there
might perhaps be two parallel scales under the same needle, one
reading amperes and the other volts. If, as will be shown later
(see Par. 474), an additional piece of apparatus be employed, the
foregoing conclusion is correct, but alone, ammeters and volt-
meters are not interchangeable. The following explanation of
their use will make it clear why they are not.

456. Essential of Measuring Instruments. The first require-
ment of every measuring instrument is that when used it should
not alter the quantity which it is to measure. Consequently,
neither the ammeter nor the voltmeter when properly connected
should change the resistance in the original circuit. Should this
resistance be changed, the current will change in accordance with
Ohm's law and this will also involve change in voltage. It is
interesting to see how these two instruments fulfill this require-
ment by apparently diametrically opposite methods.

457. Ammeters. An ammeter measures the current flowing
in the circuit at the point at which it is connected. It is inserted
in series in this circuit and should it have any appreciable resist-
ance it would reduce the current, that is, change the quantity
it is to measure. The resistance of an ammeter must therefore
be so small that its effect on the current is negligible.

B

VOLTMETER )

<"""> / AMMETER

k oLJo *'

DIMETER

<^J

Fig. 214.

458. Voltmeters. A voltmeter measures the difference of po-
tential between the two points to which it is connected. These
two points are never adjacent but in general are far apart elec-
trically. For example, they may be the terminals of a battery
(Fig. 214) or the brushes of a dynamo or the leads of an electric
light circuit. Two cases may arise: (a) there may be a broken
circuit between the two points, or (b) there may be between them

358 ELEMENTS OF ELECTRICITY.

a closed circuit over which a current is flowing. In either case, in
order that the original status of the circuit as regards current
should be changed as little as possible* the resistance of the volt-
meter must be great.

(a) If the circuit between the two points be broken, the resist-
ance between them may be considered as infinite, and no current
flows. When the voltmeter is inserted, therefore, its resistance
must be so great that the current which flows through it is so
small as to be negligible.

(b) If a current is flowing between the two points, in order that
it may be inserted between them and yet not disturb the original
circuit, the voltmeter must be connected in shunt. The voltmeter
and the original circuit are therefore in parallel and constitute a
divided circuit whose resistance is less than that of the original
circuit (Par. 293). In order to alter the original resistance as
little as possible the resistance of the voltmeter must be as great
as possible. This statement hardly requires proof but may be
shown mathematically as follows: let R be the resistance of the
original circuit between the two points and x be the resistance of
the voltmeter. The joint resistance is (Par. 293)

Rx

This may be written

7?2

R-

R+x

whence it is seen that the joint resistance is less than the original
resistance by the fraction and approaches the original

resistance as this fraction approaches zero, which it does as x
increases.

Practically, the resistance should not be made excessive for
enough current must be let through the voltmeter to actuate the
moving parts. The average resistance of a voltmeter reading up
to 100 volts is about 15,000 ohms.

459. Summary. To sum up

(a) The moving parts of an ammeter and of a voltmeter are
the same.

ELECTRO-MAGNETICS. 359

(b) An ammeter is always connected in series and its resistance
should be as near zero as possible.

(c) A voltmeter between two points in a circuit carrying a
current must always be connected in shunt and its resistance
should be great, so great that the current through it is neg-
ligible.

460. Numerical Example, Voltmeter Between Two Points of
a Circuit. The following numerical example will bring out the
effect of altering the resistance of a voltmeter.

Suppose we wish to measure with a voltmeter the difference of
potential between AB, the terminals of the battery represented
in Fig. 214. Suppose the E. M. F. of the battery to be 10 volts,
the internal resistance to be 1 ohm, the external resistance 9 ohms.

T^r -j rv

The current is ^ - = Q 1 = 1 ampere. The internal drop is
KI ~\~ T y ~i -L

Ir = 1x1 = 1 volt, hence the difference of potential between
A and B is 9 volts. To measure this we connect up as shown.
Suppose the resistance of the voltmeter to be 9 ohms. The joint
resistance between A and B is now 9/2 =4.5 ohms, the current

amperes and the difference of potential between

4 5 4- 1

A and B is 4.5x1.8 = 8.1 volts or 0.9 less than it was before the
voltmeter was connected up.

Suppose the resistance of the voltmeter to be 91 ohms. The

9X 91
external resistance becomes = 8.19 ohms and the current

1.08 -f amperes. The difference of potential between A and B
is now 1.08x8.19=8.85 volts, or only .15 volt less than the
original voltage.

Again, increase the resistance of the voltmeter to 991 ohms.
The external resistance becomes 8.919, the current, 1.008 and
the difference of potential between A and B, 1.008 X 8.919 = 8.99
volts, or only .01 less than the original voltage.

The scales of voltmeters, even of small range, are hardly ever
graduated closer than to the nearest tenth and by estimate the
position of the needle can be read to the nearest hundredth, there-
fore the above reading is within the limits of accuracy of the
instrument. A further increase in the resistance would still
further increase the theoretical accuracy. The resistance of the

360

ELEMENTS OF ELECTRICITY.

usual voltmeter is considerably greater than the 991 ohms assumed
above.

461. E. M. F. of a Cell or Battery. Let Fig. 215 represent a
cell or battery whose E. M. F. is E and whose internal resistance

Fig. 215.

is r, and suppose it to be connected up with a voltmeter whose
resistance is R. The current through the circuit is by Ohm's law

-
~ R + r

which obviously decreases
as R increases. The above may be written

IR + Ir = E
whence IR = E Ir

But IR, the external drop, is what the voltmeter reads and this
is always less by the quantity Ir, the internal drop, than E, the
total E. M. F. However, this internal drop decreases as / gets
smaller, and we have shown above that / gets smaller as R, the
resistance of the voltmeter increases, therefore, the greater the
resistance of the voltmeter, the more nearly the latter will read
the E. M. F. of the cell or battery.

462. Classification of Ammeters and Voltmeters. Ammeters
and voltmeters may be classified in a number of ways.

1st, according to the kind of current for which they are intended
as those for

(a) Direct Current,

(b) Alternating Current.

Some alternating current instruments may, by taking certain
precautions, be used with direct currents but direct current
instruments can not be used with alternating currents.

ELECTRO-MAGNETICS. 361

2d, according to the principle upon which they work, as

(a) Hot Wire Instruments,

(b) Moving Iron Instruments,

(c) Moving Coil Instruments,

(d) Induction Instruments.

3d, according to the controlling force, as those with

(a) Gravity Control,

(b) Spring Control,

(c) Magnetic Control.

Bifilar control, control by torsion and control by the earth's
magnetism can not be used in these instruments and gravity
control is unsuitable for the portable class.
4th, according to the manner of their use, as

(a) Portable,

(b) Switchboard.

5th, according to the arrangement of their scales, as

(a) Dial Instruments, those whose pointer moves over an arc

of a circle like the face of a clock.

(b) Edgewise Instruments, the scale being on the surface of a

cylinder which may be either horizontal or vertical, the

pointer moving parallel to the elements of the cylinder.

They occupy less space on the switchboard than the dial

instruments.

Dial scales and horizontal edgewise scales usually have the zero
on the left, but for some purposes it is of advantage to have the
zero at the center although this shortens the available scale length
by one-half. For instance, a zero center ammeter may be used to
measure the current used in charging a storage battery and also
the current given out in the opposite direction by the battery
on discharge.

The number of kinds is so great that the mere enumeration of
them would be voluminous, therefore description will be limited
to certain typical forms in general use in this country.

463. Hot Wire Instruments. In these the current flows
through a long and thin platinum wire one end of which is fastened
rigidly, the other directly or through a system of multiplying levers
to a movable needle. The wire is drawn taut by a spring fastened
to the needle. When a current flows through the wire it is heated

362 ELEMENTS OF ELECTRICITY.

and expands. The slack is taken up by the spring and this causes
the needle to move over the scale. Since the heating effect varies
as the square of the current, the divisions on the scales of these
instruments can not be evenly spaced. They may be used with
both direct and alternating currents. They are not largely used.

464. Moving Iron Instruments. These are also called "soft
iron" and "gravity control" instruments, and are largely used
abroad and to a less extent in this country. They may be used for
both direct and alternating currents. There are many kinds, but
the following will illustrate their , principle. Fig. 216 represents

Online LibraryWirt RobinsonThe elements of electricity → online text (page 28 of 46)