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an end view. C is a hollow cylindrical coil around which the cur-
rent flows. A is the end of a bar of soft iron attached rigidly to
the coil or to its frame, its length parallel to the axis of the cylinder.
B is a second bar of soft iron parallel to the first and attached to
the axis Z), which is free to rotate. P is the pointer and W is an
adjustable weight of non-magnetic metal, both attached to the

axis D. The instrument can be used
in but one position and when the weight
W is properly adjusted the pointer P
is on the zero of the scale. Suppose a
current to flow around the coil; the
bars A and B inside of the solenoid will
both be magnetized with their north
poles in the same direction. They will
therefore repel each other, B will move
off to the right, the pointer will sweep
across the scale and the weight W will
be lifted and oppose an increasing torque to the movement.

In a second class of these instruments the moving iron piece is
drawn into a solenoid around which the current flows.

Like the preceding, the scales of these instruments can not be
evenly spaced; moreover, they are liable to error due to residual
magnetism in the soft iron bars and may give different readings
for the same current depending upon whether the current has
previously been increasing or decreasing. These disadvantages
may more than compensate for the advantage of unvarying
control.

465. Need of Ammeter Shunts. We saw in Par. 457 that an
ammeter is inserted in series in the circuit and should oppose no




ELECTRO-MAGNETICS.



363



resistance to the current. Some ammeters must measure very
large currents, so large that the conductor must have a cross-
section of a number of square inches. It is impracticable to con-
struct an instrument whose coils should even approach such size,
therefore the current is divided at the instrument and some very
small but constant fraction is sent through the coil. This division
is made by means of a shunt (Par. 301). For small portable
instruments the shunt is within the case and such are said to be
self-contained. For larger switchboard instruments the shunt is
generally a separate piece of apparatus.

466. Switchboard Shunts. These are also called "station
shunts." They consist of two heavy copper terminals A and B,
Fig. 217, which are connected by one or more strips or sheets C of




Fig. 217.

a special alloy of very small temperature coefficient. The strips are
used, instead of one piece of the same cross-section, so as to offer
more surface for cooling. On each terminal there is a binding
screw D and E to which the leads to the instrument, flexible
insulated wire cords six or eight feet long, are attached. Fig. 218
shows an ammeter and its shunt in position.




Fig. 218.

Suppose the resistance of a station shunt for an ammeter reading
as high as 5000 amperes to be .00001 ohm; therefore, with full
current the drop from D to E is .05 volt, and as the resistance of
the instrument and its leads is .5 ohm, the maximum current



364



ELEMENTS OF ELECTRICITY.



through it is 0.1 ampere. The resistance of the leads is taken into
consideration in calibrating the instrument and they should on
no account be altered by lengthening or shortening. They and
the shunt are numbered to correspond to the instrument with
which they are to be used and can not be used with any other.
These leads confer a two-fold advantage; 1st, they permit of the
position of the ammeter being shifted about at pleasure and with-
out the expense caused by additional lengths of heavy copper
mains or the trouble caused by the mechanical labor in bending
and arranging these mains; 2d, the ammeter can be placed at such
a distance from the mains that it is unaffected by the field pro-
duced around them by even very powerful currents.

467. The Weston D. C. Ammeter. The Weston instruments
are both in construction and accuracy among the best. In




Fig. 219.

principle they are d'Arsonval galvanometers (Par. 378) with
certain changes by which, while overcoming the structural weak-
ness of the d'Arsonval instrument and making it fit for portable
use, the requisite sensitiveness is retained. These changes are
(a) substituting for the phosphor-bronze suspension filament
suspension of the coil by pivots in watch jewels; (b) control by
coiled hair springs instead of by torsion of the suspending fila-
ment; (c) use of a pointer of aluminum instead of reflection from
a mirror; (d) accurate balancing of the coil, enabling the instru-



ELECTRO-MAGNETICS.



365



merit to be used in any position; (e) improved damping, making
the instrument absolutely dead beat (Par. 379).

They are of many types. One of the usual forms of portable
ammeter is represented in Fig. 219. Its case is of pressed brass
or copper mounted upon a wooden base. In the larger switch-
board instruments the case is of cast iron which has the advantage
of shielding the instrumental field from perturbations due to
external fields.

Within the case and nearly filling it is a permanent horseshoe
magnet M (Fig. 220). To this are attached the soft iron pole
pieces N and S which include between them a cylindrical opening.
Were these pole pieces as represented in a in the following figure
the greater part of the lines of force would cross the field at the





Fig. 220.



points where the horns of N and S approach each other most
closely. The field would therefore be crowded at these points and
thin at the intermediate points. However, as shown in b, a soft
iron cylinder C bolted to a brass cross bar B, which is in turn
bolted to the pole pieces, is fastened concentrically in the space
between the pole pieces. The air gap between the cylinder and
the pole pieces being very small and the permeability of the
cylinder being large, the lines of force are evenly distributed and
the field is very uniform (Par. 143). Pivoted in watch jewels so
as to turn in this air gap is the rectangular coil. It is of very fine
wire wrapped upon a light aluminum frame. Upon the axis of
the coil are mounted from top to bottom the upper spiral spring,
the aluminum needle, and below the coil the lower spiral spring
coiled in opposite direction to the first. The needle, to combine
lightness and stiffness, may be in cross-section either tubular or
like an inverted V. The end which travels over the scale is, in
portable instruments, compressed sidewise like a knife-blade and



366 ELEMENTS OF ELECTRICITY.

in switchboard instruments terminates in an arrow-head. The
rear end of the needle extends beyond the axis and carries an
adjustable counterweight. There are also similar weights at
right angles to the needle and by these the moving parts are so
balanced that the instrument may be used in any position.

The binding posts by which the current enters and leaves may
be placed, as shown in Fig. 219, both on one side, or may be both
at the top or may be on opposite sides. For those instruments
whose zero is at one end of the scale the post by which the current
must enter is marked conspicuously + as shown in Figs. 219 and
222.

In portable instruments with self-contained shunt, the latter
is a strip of alloy arranged similarly to the switchboard shunt
described in Par. 466 above. The fraction of the current which
flows through the coil flows first to the upper coiled spring, around
this spring to its insulated hub, thence to the coil, around the coil
and out by the lower coiled spring. Fig. 221 illustrates the actu-

^~ -^^ ating forces. The lines of force of the

field run from N to S, the current flows
up the right hand side of the coil and
down the left, the lines of force of the
coil run as shown by the short arrows.
According to Maxwell's law the coil
will therefore turn in a clockwise direc-
tion. Reflection will show that this
could not be used with an alternating
current.

The field being very uniform and the

resistance to torsion which the coiled spring offers increasing
directly with the angle through which the coil turns, the scale is
regularly spaced. Parallel to the scale and just beneath it is
fastened an arc of a mirror. By covering the reflection of the
needle in the mirror by the needle itself, the observer makes sure
that the eye is always at the same angle with reference to the
needle and to the plane of the scale and errors due to parallax are
avoided.

The aluminum coil frame rotating in the strong magnetic field
in the narrow air gap makes the instrument very dead beat. The
damping effect varies as the square of the magnetic strength.




ELECTRO-MAGNETICS.



367



468. Weston Portable D. C. Voltmeter. This instrument
closely resembles the preceding. The one represented in Fig. 222




Fig. 222.

differs externally in having above the + binding post on the right
a push-button switch by which the current through the instrument
may be closed or broken at will, and on the left two binding posts
by either of which the current may leave. The object of these is
explained below. Internally it differs in having no shunt but a
single circuit in which is a resistance coil. Suppose connection
to be made with upper left hand binding post and circuit com-




PUSH BUTTON



Fig. 223.



pleted. The current enters on the right (Fig. 223), through the
button switch, thence through the rotating coil, thence through
the resistance coil A and out. The resistance of the coil A, in
the particular instrument represented in the figure, is so adjusted
that a difference of potential between the terminals of the instru-
ment of 3 volts will drive enough current through to carry the



368 ELEMENTS OF ELECTRICITY.

needle entirely across the scale. The maximum reading is there-
fore 3 volts, the scale is graduated and numbered on the lower
side accordingly, and the corresponding binding post is plainly
marked 3.

If connection be made at the lower left hand binding post the
current after leaving the moving coil passes through the resistance
coil B and out. The resistance of B is so adjusted that the instru-
mental resistance is now 50 times greater than before, therefore
a voltage 50 times greater, or 150 volts, would be required to
carry the needle entirely across the scale. This binding post is
therefore marked 150 and the upper side of the scale is numbered
to correspond.

The two scales are usually selected so that the larger is ten or
some multiple of ten times the smaller, therefore the graduation
of the two scales is the same and it is only necessary to use two
sets of numbers.

The resistance through the smaller coil of a 15-150 voltmeter
of this class was found to be 1772 ohms, that through the larger
coil 17,720 ohms.

These instruments are calibrated by comparison, usually
through a potentiometer, with standard cells. The importance
of accuracy in calibration will be realized when the statement is
made that in electric lighting an increase of 3 per cent above
the normal voltage shortens the useful life of a lamp one-half
while a decrease of 4 per cent below normal reduces the candle
power of the lamp one-fifth.




Fig. 224.



469. Multipliers. The foregoing will enable us to understand
an auxiliary piece of apparatus used with voltmeters and called
a multiplier. If there be connected in series with a voltmeter,
as shown in Fig. 224, a resistance MP which is so adjusted that
the resistance between C and M is ten times what it is between



ELECTRO-MAGNETICS.



369



C and D, to produce a given deflection of the needle will require
a difference of potential between C and M ten times greater than
that between C and D. Hence to get the correct difference of
potential between C and M the readings of the scale must be
multiplied by ten. Therefore, a multiplier is a resistance which,
when connected in series with a voltmeter, has the effect of multi-
plying the value of the scale divisions by a certain factor. This
factor is usually marked upon the case of the multiplier.

Multipliers are not interchangeable but must be used with the
particular voltmeter for which they are constructed. The second
coil B in Fig. 223 is in effect a self-contained multiplier.

470. The Weston D. C. A. C. Voltmeter. Consider Fig. 221
and suppose the current to be alternating. The direction of the




Fig. 225.

field due to the permanent magnet remains constant while that
through the coil changes with change of direction of the current.
Hence at one instant the needle would tend to turn in a clockwise
direction and at the next instant in a counter-clockwise direction
and if it moved at all would only quiver. Therefore, such instru-
ments cannot be used with alternating currents.

The Weston D. C. A. C. voltmeter, to overcome this objection,
employs the principle of the dynamometer (Par. 382). There is
no permanent magnet but within the case and perpendicular to
the middle of the scale arc there is a thin tubular brass frame



370



ELEMENTS OF ELECTRICITY.



around which are wrapped many turns of fine wire. This cylinder
is separated into two parts by a narrow gap in its middle (shown
diagrammatically and much exaggerated in Fig. 225) and in this
gap there turns a vertical axis which carries the needle, controlling
spiral springs, movable coil, etc., as in the instruments already
described. The movable coil C is circular instead of rectangular
and normally its plane makes an angle of 45 with the axis of the
cylinder. The current enters at E, flows around the coil A, thence
to the upper spiral spring, then around the movable coil but
opposite to its direction around A, thence to lower spiral spring,
thence around coil B in same direction as around A, thence
through a resistance coil and out.




A


\
\ >

> \/







s

Fig. 226.

The current flowing as shown by the arrows in Fig. 226, the
field of the fixed coils will be in the direction SN, that of the
movable coil will be in the direction C and, in accordance with
Maxwell's law, the needle will move in a clockwise direction.
When the current reverses its direction both fields are also reversed
and the tendency is still' for the needle to turn in a clockwise
direction, hence this instrument can be used for both alternating
and direct currents.

When the movable, coil has turned until it is at right angles to
the outer coils the deflecting force is of maximum effect. The
graduations of the center of the scale are therefore more widely
spaced than those towards the extremities.



ELECTRO-MAGNETICS.



371



The movable eoil turning in a weaker field than in the D. C.
instruments, the damping effect is much less. To check the
oscillations of the needle and bring it more quickly to rest, there
is near the bottom of the coil shaft a circular plate D (Fig. 225)
against which a light spring brake can be made to press.

471. The Thomson Inclined Coil Instruments. These are
primarily intended for alternating currents and in principle do not
differ greatly from the one just described, that is there is a movable
inner coil which rotates in the field of the fixed outer coil.




Fig. 227.

Figure 227 represents diagrammatically one of these instru-
ments, a voltmeter with edgewise scale. The fixed coil A makes
an angle of 45 with the horizontal base of the instrument. Rotat-
ing vertically through the center of this coil is the shaft which
carries the two non-magnetic (phosphor bronze) spiral control
springs, the needle, the movable coil B and a crescent-shaped
aluminum disc D. The plane of the rotating coil makes an angle



372



ELEMENTS OF ELECTRICITY.



of 45 with the base of the instrument and is also placed askew
to the plane of the fixed coil. The current enters at C, flows
around A in the direction shown by the arrow, thence to the upper
spiral spring, thence around the coil B in the direction shown,
thence to the second spiral spring and out through a resistance
coil. According to Maxwell's law, the rotating coil tends to turn
until its axis is parallel to that of the fixed coil and the needle
travels across the scale to the right.




Fig. 228.

The inclined coil ammeters differ from the voltmeters just
described in having no rotating coil but in its place a vane or flat
sheet of soft iron V (Fig. 228) mounted upon the axis at the same
angle as that made by the axis of the rotating coil in the voltmeter.
When a current flows through the fixed coil, the vane tends to
turn to the position V parallel to the lines of force through the
fixed coil (Par. 143).




Fig. 229.



In the switchboard instruments of this type, damping is effected
by the aluminum crescent D in Fig. 227 turning between the jaws



ELECTRO-MAGNETICS.



373



of two jew's-harp shaped permanent horseshoe magnets as shown
in Fig. 229. In the portable instruments a friction brake or air
vane is used.

472. Use of Transformers with A. C. Instruments. Alternating
current ammeters, due to the effects of self-induction in the coils,




AMMETER

SLJO-N
xxr




Fig. 230.

do not work satisfactorily with shunts and if the current to be
measured is of such size that in a D. C. instrument a shunt would
be used, the current through the ammeter is stepped down by
means of a series transformer as shown in Fig. 230.

On the other hand, if the pressure in an alternating current circuit
exceeds about 1000 volts, it is not considered safe to bring this



VOLTMETER




Fig. 231.

voltage direct to a voltmeter and it is stepped down by a potential
transformer as shown in Fig. 231. These instruments are, of
course, graduated to read the current or the voltage in the primary-
circuit.



374 ELEMENTS OF ELECTRICITY.

473. Millivoltmeters. If there be constructed an instrument
like the voltmeter described in Par. 468 but of very much less
internal resistance (10 instead of 1700 ohms) a slight difference
of potential between its terminals will drive enough current
through the coil to move the needle over an extended portion of
the scale. The scale can therefore be graduated to show much
smaller fractions of a volt than is possible in an ordinary volt-
meter. Such an instrument reading to thousandths of a volt is
called a millivoltmeter.

474. Millivoltmeters as Ammeters. Suppose a millivoltmeter
to be connected to the extremities of a shunt AB as shown in
Fig. 232. Suppose it has a scale reading to 300 millivolts and that
its resistance, including that of the leads which accompany it, is




Fig. 232.

10 ohms. A difference of potential between AB of three- tenths
of a volt will throw the needle entirely across the scale. In this
case the current through the instrument is from Ohm's law

E 3

-5 = fpr = .03 ampere. Suppose a current of 300 amperes to be

1 1U

flowing in the main circuit. At A it divides inversely proportional
to the resistances of the shunt AB and of the instrument and its
leads. If the resistance of AB be made ?k%v ohm, then 299.97
amperes will flow through AB and .03 ampere through the
instrument and the needle will move entirely across the scale.
The divisions on the scale will therefore correspond to the amperes
in the main circuit.

If the resistance of A B be made ^VV ohm, then 30 amperes in
the main circuit will cause the needle to move entirely across the
scale and the scale divisions will each correspond to one-tenth
of an ampere.



ELECTRO-MAGNETICS.



375



Finally, if the resistance of AB be made if ohm, the scale
divisions will correspond to one-hundredth of an ampere in the
main circuit.

It is therefore possible, by employing a shunt, to use a milli-
voltmeter as an ammeter.

475. Millivoltmeter Shunt. Instead of separate shunts as
described above, several are usually assembled in one case as
represented in Fig. 233. The current
to be measured is always brought in
at the upper right hand post and
leaves by one of the others in the
upper row. The millivoltmeter is
connected with the corresponding
posts in the lower row. The circuits
are as shown in the figure which repre-
sents connections made to read a cur-
rent of a maximum of 1.5 amperes.
The current in the case represented
enters at A and leaves at B. AC is a
heavy copper bar. D, D r , D" repre-
sent diagrammatically strips of resist-
ance alloy. The numbers on the
binding posts indicate the number of




Fig. 233.



amperes to produce a total scale deflection of the needle when
connection is made at the corresponding post. These shunts and
their leads must be used with the particular instrument for which
they are constructed.



376 ELEMENTS OF ELECTRICITY.



CHAPTER 35.

HEATING EFFECT OF ELECTRIC CURRENT.

476. Work Done by Electric Current. To produce an electric
current, an expenditure of energy or a performance of work is
required. According to the fundamental principle of mechanics,
this energy is not lost but only transmuted and must be given back
in one form or another by the current. In a cell, for instance, there
is an expenditure of chemical energy which results in moving Q
units of electricity through a difference of potential V. The work
done is therefore W=QV (Par. 72). Since there is no current
unless there be a complete circuit, each of these Q units of elec-
tricity must return to its starting point and in doing so passes
back through the same difference of potential through which it
was moved, or gives back the energy expended upon it in the first
place. A current flowing in a circuit must, therefore, perform
work of some kind, (a) In Par. 215 we saw that a current always
heats the conductor through which it flows, (b) It may, in
addition, perform electrolytic (chemical) work, or (c) it may,
through the medium of machinery, do mechanical work, or finally,
(d) it may do magnetic work. Energy is also expended by the
current in establishing a magnetic field about the conductor, but
this energy need not be considered for it is restored when the
circuit is broken. If the current performs neither chemical, nor
mechanical, nor magnetic work, then its entire energy is spent in
heating the circuit.

We shall now examine into this heating effect of the current.

477. Determination of Laws of Heating Effect. An experi-
mental determination of the laws governing the heating effect of
a current was made by Joule with an apparatus similar to that
shown in Fig. 234. Through the cork of a wide-mouthed glass
jar containing turpentine, or some similar non-conducting liquid,
were run two heavy wires and a thermometer, T, all of which
dipped below the surface of the liquid. Between the ends A and B
of the large wires, there was connected a slender bare wire of



ELECTRO-MAGNETICS.



377



known resistance, preferably of manganin (Par. 289). The jar
was then connected in series with a battery, a key and an ammeter.
Upon closing the key, the current flowed through the circuit and
heated the small wire, which, in turn, heated the turpentine. The
strength of the current was read from the ammeter. The increase
in temperature of the turpentine was determined by the thermom-
eter, whence, knowing its weight and its specific heat, the number
of heat units gained could be determined. The length of time
that the current flowed was also measured. As a result of this




Fig. 234.

experiment, Joule found that the amount of heat produced varied
(a) as the square of the current, (b) as the resistance of the con-
ductor and (c) as the length of time during which the current
flowed.

478. The Joule. Representing by H the quantity of heat
produced, Joule's results may be given mathematical expression
as follows:



If in this expression / be one ampere, R be one ohm, and t be
one second, we have H = 1. This electric unit of heat, the quantity
of heat produced by a current of one ampere flowing for one
second through a resistance of one ohm, has been named the joule.
It is, however, a redundant unit since we already have in the
C. G. S. system the small calorie, the amount of heat required to



378 ELEMENTS OF ELECTRICITY.

raise one gram of water through one degree Centigrade (Par. 11),
The joule is a shade less than one-quarter of a calorie. One joule
is .24 of a calorie and hence one calorie is 4.2 joules. If, therefore,
H represents the number of calories produced, Joule's law becomes



479. Theoretical Deduction of Joule's Law. Joule's law, as
given in the preceding paragraph, may also be deduced from
theoretical considerations. Thus, suppose a current of strength /
is flowing through a simple conductor whose resistance is R. The
difference of potential between the ends of this conductor is IR
(Par. 298), and is measured by the work done in moving a unit
quantity of electricity from one point to the other (Par. 72). If



Online LibraryWirt RobinsonThe elements of electricity → online text (page 29 of 46)