THE MAGNETIC EFFECT OF ELECTRIC CURRENTS. ELECTRICAL MEASUREMENTS
(1) THE MAGNETIC EFFECT OF ELECTRIC CURRENTS
=255. The Magnetic Effect.=--Of all the effects of electric currents, it
is generally conceded that the _magnetic effect_ is the one of _greatest
practical importance_, and it is also the one most extensively used. An
experiment illustrating this effect has been described in Art. 239. This
experiment shows that an electric current, if _parallel_ to a magnetic
needle, and _near it_ will deflect the north-seeking pole of the needle
to the right or left depending upon the _direction_ of the current flow.
This _deflection_ of the magnetic needle is due to the fact that
surrounding every electric current are magnetic lines of force. It is
this magnetic field of the current that causes the needle to turn. The
position taken by the needle is the resultant of the forces of two
magnetic fields; one, the earth's field, the other, that of the current.
=256. Right-hand Rule for a Conductor.=--To show the presence of the
magnetic field about a current, pass a thick copper wire vertically
through a sheet of paper, and connect the ends of the wire to a source
of current. While the current (this should be as much as 10 amperes if
possible) is flowing, sprinkle iron filings upon the paper and tap
gently. The filings will arrange themselves in circles about the wire
showing the magnetic field. (See Fig. 229.) The needle of a magnetoscope
tends to place itself parallel to the lines of force of this field and
from this action or tendency the _direction_ of the magnetic lines
about a current may be determined. The following rule is helpful and
should be memorized: _Grasp the conductor with the right hand with the
outstretched thumb in the direction that the current is flowing. The
fingers will then encircle the wire in the direction of the lines of
force._ This rule may be reversed, for, if the fingers of the right hand
grasp the wire so as to point with the magnetic field, then the current
flows in the direction in which the thumb points. (See Fig. 230.)
[Illustration: FIG. 229.--Magnetic field about a wire carrying an
electric current.]
[Illustration: FIG. 230.--Right-hand rule for the magnetic field of a
current.]
=257. Magnetic Field of a Helix.=--If a wire be wound about a cylinder
to form a cylindrical coil with parallel turns, it forms a _helix_ or
_solenoid_. The shape of the magnetic field about a current depends upon
the _form_ of the conductor. If the latter is in the form of a _helix_
its magnetic field resembles that of a straight bar magnet. (See Fig.
231). In fact the helix _has the properties of a magnet_ with north- and
south-seeking poles while a _current_ is _flowing_ through it. If such a
coil is suspended so as to turn freely, it tends to turn until the field
within it is parallel to the earth's magnetic field. Such a suspended
helix may therefore be used as a compass. In order to strengthen the
magnetic field of a helix or solenoid, the space within its turns is
filled with iron, often in the form of small soft-iron wires. This
bundle of iron wire is called the _core_ of the helix. The core becomes
strongly magnetized by the field of the helix while the current is
flowing and quickly loses its magnetic force when the current is
stopped. _The direction of the current in a helix_ (Fig. 232) or the
_polarity_ of its core may be determined by another _right-hand rule_.
_If the helix is grasped with the right hand so that the fingers point
in the direction in which the current is flowing, the extended thumb
will point in the direction of the north pole of the helix._ On the
other hand, if the poles of the helix are known, then, when the helix is
grasped with the right hand so that the thumb points to the
north-seeking pole, the current is flowing in the wires in the direction
that the fingers point.
[Illustration: FIG. 231.--The magnetic field of a helix.]
[Illustration: FIG. 232.--Right-hand rule for a helix.]
=258. The Electromagnet.=--These "right-hand" rules are applied in many
different devices. Among these, perhaps the most important is the
electromagnet, which is used in the electric bell, the telegraph, the
telephone, the dynamo, the motor, and many other electric contrivances.
The electromagnet is defined as a _mass of iron around which is placed a
helix for conducting an electric current_. On account of its large
permeability, the iron core of the helix adds greatly to the
effectiveness of the electromagnet, since the magnetism of the iron is
added to that of the current in the helix. The magnetism remaining in
the iron after the current stops is called the _residual_ magnetism. The
residual magnetism is small when the core is made of small wires or thin
plates, but is larger when the iron core is solid. Like artificial steel
magnets, electromagnets are usually of two forms, _bar_ and _horseshoe_.
(See Figs. 233 and 234.) For most purposes the horseshoe form is the
more effective since it permits a complete iron circuit for the magnetic
lines of force. (See Fig. 235.) This is the form used in the electric
bell, in the telegraph sounder, and in lifting magnets. (See Fig. 236.)
[Illustration: FIG. 233.--A bar electromagnet.]
[Illustration: FIG. 234.--A horseshoe electromagnet.]
[Illustration: FIG. 235.--A horseshoe electromagnet may have a complete
iron circuit for its lines of force.]
[Illustration: FIG. 236.--A lifting magnet.]
=259. Effective Electromagnets.=--The _magnetic_ effect of a current in
a helix is small, hence the force usually is increased by inserting a
core of iron. When at first man tried to signal with electromagnets at
a distance it was found that the current would not work the
electromagnet. An American by the name of Joseph Henry discovered the
remedy for this condition. He found that if the copper wire was
insulated by wrapping silk thread about it, and then many layers of the
silk insulated wire were wound upon a spool with an iron core, that the
magnet would work at a great distance from the source of current. If the
current is increased, the magnet is stronger than at first. Thus an
_electromagnet may be made stronger by_ (a) _increasing the number of
turns of wire in its coils_ and by (b) _sending a stronger current
through it_.
[Illustration: FIG. 237.--A simple telegraph circuit.]
=260. The Telegraph.=--The invention of an effective electromagnet by
Henry made possible the _electric telegraph_. In its simplest form it
consists of a battery, _C_, a key, _K_, and a sounder, _S_, with
connecting wires. (See Fig. 237.) The _sounder_ (Fig. 238) contains a
_horseshoe electromagnet_ and a bar of soft iron across its poles called
an armature, _A_, attached to a lever _L_. When the key is closed, the
electromagnet draws down the armature and lever until the latter hits a
stop _O_, making a click. When the key is raised, the magnet releases
the armature which is raised by the action of a spring at _S_ until the
lever hits a stop at _T_ making another click. Closing and opening the
circuit at _K_ will start and stop the current which operates _S_ which
may be 100 miles or more from _K_. One voltaic cell will work a sounder
in the same room. But if many miles of wire are in the circuit, the
E.M.F. of a single cell will not force sufficient current through the
long wire to operate the sounder.
[Illustration: FIG. 238.--A telegraph sounder.]
[Illustration: FIG. 239.--A telegraph relay.]
[Illustration: FIG. 240.--How the relay is used.]
[Illustration: Samuel F. B. Morse (1791-1872). Inventor of the
electromagnetic recording telegraph and of the dot and dash alphabet.
SAMUEL F. B. MORSE
"From Appleton's Cyclopedia of American Biography, Copyright 1888 by D.
Appleton & Co."]
[Illustration: Thomas A. Edison, Orange, New Jersey. Invented the
incandescent lamp; phonograph; moving picture; most noted inventor of
electrical appliances of the present day.
THOMAS A. EDISON
"Copyright, Photographische Gessellschaft," and "By Permission of the
Berlin Photographic Co., New York."]
A battery of several cells is then required. Even a large battery is
insufficient to operate a long line containing many sounders in circuit.
Recourse is therefore usually made to a more sensitive device called a
_relay_. (See Fig. 239.) In the relay a very small current will
magnetize its electromagnet enough to draw toward it the delicately hung
armature thereby closing a second circuit which contains a sounder and a
battery. (See Fig. 240.) when the current in the main circuit is
stopped, the armature of the relay is drawn back by a light spring. This
opens the _local_ circuit. Thus the local circuit is closed and opened
by the relay just in time with the starting and stopping of the current
in the main line. It is thus possible for a small current in the main
line by the use of a relay, to close and open a second local circuit
containing a local battery and sounder. Modern telegraph lines are
operated in this manner.
[Illustration: FIG. 241.--An electric bell and its circuit.]
=261. The electric bell= (see Fig. 241), consists of an electromagnet,
_M_, a soft iron _armature_, _A_, attached to the _tapper_, _T_, and a
post, _R_. When no current is flowing a spring at _S_ holds the armature
against the post _R_. When current flows through the helix, its core
becomes magnetized and attracts the armature, drawing it away from the
post, _R_, and causing the tapper to hit the bell. Drawing _A_ away from
the post, however, breaks the circuit at _R_ and the current stops. The
magnetism in the core disappears releasing the armature, which is then
pulled back by the spring _S_ against the post _R_. This completes the
circuit and the process repeats itself several times a second as long as
the current flows.
[Illustration: FIG. 242.--Magnetizing by the discharge of a Leyden jar.]
=262. Static and Current Electricity Compared.=--The likeness between a
discharge of static electricity and an electric current may be shown by
winding a coil of insulated wire about a glass tube which contains a
steel needle. If a Leyden jar (see Fig. 242) is discharged through the
coil the steel needle is usually found to be magnetized, showing that
the discharge of the static electricity has a magnetic effect similar to
that of an electric current. Sometimes a given end of the needle has a
north pole and at other times a south pole. This is believed to
indicate that the charge of the Leyden jar is _oscillatory_, and that
in different discharges sometimes a surge in one direction and at other
times a surge in the reverse direction has been most effective in
magnetizing the needle. Compare this action with that described in Art.
233.
Important Topics
1. Right-hand rules, for conductor, for helix.
2. The electromagnet, two forms, where used?
3. Likeness between static and current electricity.
4. The electric bell, parts, action.
5. The telegraph, key, sounder, relay.
Exercises
1. What is the difference between an electric charge and a current?
2. How can a magnetic effect be produced from an electric charge?
3. What is a magnetic field? Give two evidences of a magnetic field
about a current in a wire?
4. A current is flowing north in trolley wire, what is the direction of
the magnetic field under the wire? Explain.
5. What would be the result if a hard steel core were placed in the
electromagnet? Explain.
6. If the north-seeking pole of a helix is facing you, does the current
in the coils before you move in a clockwise or in a counter-clockwise
direction? Explain.
7. A helix is placed horizontally with its north-seeking pole toward the
north. Does the current in the wire at the top of the helix move east or
west? Explain.
8. State at least six conditions any one of which will put an electric
bell circuit out of commission.
9. If one desires to insert a battery into a telegraph circuit already
in operation, how will he determine the direction of the current in the
wire?
10. If a boy who had magnetized his knife blade in a physics laboratory,
pointed end south-seeking, should lose his way in the woods on a cloudy
day, how could he determine his way out?
11. At a certain point the earth's field acts north, that of an electric
current, east. The magnetoscope needle points exactly northeast when
placed at that point. How do the two magnetic fields compare?
(2) ELECTRICAL MEASUREMENTS
=263. Galvanometers.=--In using electric currents it is often necessary
or desirable to be able to know not only that a given current is weak or
strong, but precisely what its strength is. We can determine the
relative strengths of two currents by the use of a _galvanometer_.
[Illustration: FIG. 243.--The magnet is at the center of the coil.]
[Illustration: FIG. 244.--A moving-magnet (tangent) galvanometer.]
The older or _moving-magnet_ type of galvanometer is similar to the
galvanoscope mentioned in Art. 239. It consists of a magnetic needle
mounted at the center of a coil of wire. The coil is placed facing east
and west, so that the needle will be held by the earth's magnetic field
parallel to the plane of the coil. When a current is sent through the
coil a magnetic field is produced within it. This deflects the needle,
its north end turning east or west depending upon the direction of the
current. (See Fig. 243.) The _coils_ of a moving-magnet or _tangent_
galvanometer (see Fig. 244) are _large_ and firmly fastened to the base,
while the _magnet_ is _small_.
The _moving-coil_ type of galvanometer (see Fig. 245) consists of a
_large magnet_ fastened to the frame of the device. The magnet usually
has a horseshoe form to produce as strong a field as possible. The
_coil_ is wound on a _light_ rectangular frame and is suspended between
the two poles of the magnet. To concentrate the magnetic field, a
cylinder of soft iron is usually placed within the coil. Fig. 246
represents a common form of moving-coil galvanometer.
[Illustration: FIG. 245.--To illustrate the principle of the moving-coil
galvanometer.]
[Illustration: FIG. 246.--A moving-coil (D'Arsonval) galvanometer.]
=264. Measurement of Electric Currents.=--A galvanometer enables one to
_compare_ electric currents. To _measure_ electric currents it is
necessary to employ a _unit_ of electrical quantity, just as in
measuring the quantity of water delivered by a pipe, a unit of liquid
measure is employed; thus, _e.g._, the current delivered by a given pipe
may be 2 gallons of water per second, so in measuring the flow of an
electric current one may speak of two _coulombs_ per second. The
_coulomb_ is the unit quantity of electricity just as the unit of
quantity of water is the gallon.
For most practical purposes, however, we are more interested in the
_rate_ or _intensity_ of flow of current than in the actual _quantity_
delivered. The unit of rate of flow or current is called the _ampere_.
In determining the exact _quantity_ of an electric current, physicists
make use of a device called a _coulomb meter_. (See Fig. 247.) This
contains a solution of silver nitrate in which are placed two silver
plates. The current to be measured is sent through the solution, in at
one plate and out at the other. The plate where the current goes _in_,
the _anode_, _A_ (Fig. 247), loses in weight since some of the silver is
dissolved. The plate where the current goes _out_, the _cathode_, _C_,
increases in weight since some of the silver is deposited. By an
international agreement, _the intensity of the current which deposits
silver at the rate of 0.001118 g. per second is 1 ampere_. This is equal
to 4.025 g. per hour.
[Illustration: FIG. 247.--A coulomb meter, the anode _A_ is separated
from the cathode _C_ by a porous cup.]
The _coulomb_ is defined as the quantity of electricity delivered by a
current of one ampere during one second.
A 40-watt-incandescent lamp takes about 0.4 ampere of current. An arc
lamp takes from 6 to 15 amperes. A new dry cell may send 20 amperes
through a testing meter. A street car may take from 50 to 100 amperes.
=265. The Ammeter.=--The method described above is not used ordinarily
for measuring current strengths on account of its inconvenience. The
usual device employed is an _ammeter_. This instrument is a _moving-coil
galvanometer_. It contains, wound on a light form, a coil of fine
copper wire. The form is mounted on jewel bearings between the poles of
a strong permanent horseshoe magnet. (See Fig. 248.) As in other
moving-coil galvanometers, a soft iron cylinder within the form
concentrates the field of the magnet. The form and its coil is held in
balance by two spiral springs which also conduct current into and out of
the coil.
Only a small part of the whole current measured, in some cases only
0.0001 passes through the coil, the larger part of the current passing
through a metal wire or strip called a _shunt_[L] (see Fig. 248)
connecting the binding posts of the instrument. A fixed fraction of the
whole current flows through the coil. Its field crossing the field of
the horseshoe magnet, tends to turn until its turning force is balanced
by the spiral springs. As the coil turns it moves a pointer attached to
it across a scale graduated to indicate the number of amperes in the
whole current.
[L] A shunt is a conductor or coil connected in parallel with
another conductor or circuit. It carries a part of the current.
[Illustration: FIG. 248.--Diagram of a commercial ammeter. _S_ is the
shunt.]
It should be noted that while _all_ of the current measured passed
through the ammeter, but a small _part_ goes through the coil.
=266. Resistance of Conductors.=--With an ammeter one may study the
change produced in the amount of current flowing in a wire when a change
is made in the wire conducting the current. For example, if one measures
with an ammeter the current flowing from a dry cell through a long and
then through a short piece of fine copper wire, it will be seen that
less current flows when the long piece is used. That is, the long wire
seems to hinder or to _resist_ the passing of the current more than the
short piece. In other words, the long wire is said to have more
_resistance_.
The resistance of a conducting body is affected by several conditions.
(a) It is _directly_ proportional to the _length_ of the conductor, one
hundred feet of wire having twice the resistance of fifty feet.
(b) It is _inversely_ proportional to the _square of the diameter_; a
wire 0.1 inch in diameter has four times the resistance of a wire 0.2
inch in diameter.
(c) It differs with different substances, iron having about six times as
much as copper.
(d) It varies with the temperature, metals having greater resistance at
a higher temperature.
Since silver is the best conductor known, the resistances of other
substances are compared with it as a standard.
The ratio of the resistance of a wire of any substance as compared to
the resistance of a silver wire of exactly the same diameter and length
is called its _relative_ resistance.
Purified substances arranged in order of increasing resistance for the
same length and sectional area (Ayrton-Mather) are given on p. 294.
Silver annealed 1.00
Copper annealed { from 1.04
{ to 1.09
Aluminum annealed 1.64
Nickel annealed 4.69
Platinum annealed 6.09
Iron annealed 6.56
German Silver { from 12.80
{ to 20.20
Mercury 63.30
Nichrome 67.50
Carbon { from 2700.00
{ to 6700.00
=267. The ohm, the unit of resistance=, is defined by international
agreement as follows: _An ohm is the resistance of a column of pure
mercury, 106.3 cm. long with a cross-section of a square millimeter and
at a temperature of 0°C._
It should be noted that each of the four conditions affecting resistance
is mentioned in the definition, viz., length, cross-section, material,
and temperature. Since it is inconvenient to handle mercury, _standard
resistance coils_, made of an alloy of high resistance are used in
comparing and measuring resistances.
A piece of copper wire No. 22 (diameter 0.644 mm.) 60. 5 ft. long has a
resistance of 1 ohm. See table p. 296.
The resistance of some telephone receivers is 75 ohms, of a telegraph
sounder, 4 ohms, of a relay 200 ohms.
=268. Resistance of Circuits.=--Every part of an electrical circuit
possesses resistance. In an electric-bell circuit, for instance, the
wires, the bell, the push-button, and the cell itself, each offers a
definite resistance to the passage of the current. The resistance
_within the cell_ is termed _internal resistance_, while the resistance
of the parts outside of the electric generator is called _external
resistance_.
=269. Electromotive Force.=--In order to set in motion anything, some
_force_ must be applied. This is as true of electricity as of solids,
liquids, or gases. By analogy that which is exerted by a battery or by a
dynamo in causing current to flow is called an _electromotive force_.
The unit of electromotive force, the _volt_, may be defined as _the
electromotive force that will drive a current of 1 ampere through the
resistance of 1 ohm_. The electromotive force of a dry cell is about 1.5
volts, of a Daniell cell 1.08 volts. Most electric light circuits in
buildings carry current at 110 or 220 volts pressure. Currents for
street cars have an electromotive force of from 550 to 660 volts.
[Illustration: FIG. 249.--Diagram of a commercial voltmeter.]
=270. The Voltmeter.=--An instrument for measuring the electromotive
force of electric currents is called a _voltmeter_ (Fig. 249). It is
usually a moving-coil galvanometer, and is always of _high resistance_.
It is like an ammeter in construction and appearance. In fact, a
voltmeter is an ammeter which has had its shunt removed or disconnected.
In place of a shunt, the voltmeter uses a coil of wire of high
resistance (see _R_, Fig. 249) _in series_ with the galvanometer coil.
The high resistance of the voltmeter permits but a very small current to
flow through it. Hence a voltmeter must be placed _across_ a circuit
and not in it. In other words _a voltmeter is connected in shunt_,
while _an ammeter is in series with the circuit_ as is shown in Fig.
250.
DIMENSIONS AND FUNCTIONS OF COPPER WIRES
Column headings:
B: B. & S. gauge number
MM: Millimeters
SA: Sectional area in square millimeters
WL: Weight and length, Density = 8.9, feet per pound
R: Resistance at 24°C., feet per ohm
C: Capacity in amperes
----+--------------+----------+---------+---------+----------+------
| Diameter | | | | |
B +-------+------+ Circular | SA | WL | R | C
| Mils | MM | mils | | | |
----+-------+------+----------+---------+---------+----------+------
0000|460.000|11.684|211,600.00|107.219 | 1.56|19,929.700|312.0
000|409.640|10.405|167,805.00| 85.028 | 1.97|15,804.900|262.0
00|364.800| 9.266|133,079.40| 67.431 | 2.49|12,534.200|220.0
0|324.950| 8.254|105,592.50| 53.470 | 3.13| 9,945.300|185.0
2|257.630| 6.544| 66,373.00| 33.631 | 4.99| 6,251.400|131.0
4|204.310| 5.189| 41,742.00| 21.151 | 7.93| 3,931.600| 92.3
6|162.020| 4.115| 26,250.50| 13.301 | 12.61| 2,472.400| 65.2
8|128.490| 3.264| 16,509.00| 8.366 | 20.05| 1,555.000| 46.1
10|101.890| 2.588| 10,381.00| 5.260 | 31.38| 977.800| 32.5
12| 80.808| 2.053| 6,529.90| 3.309 | 50.69| 615.020| 23.0
14| 64.084| 1.628| 4,106.80| 2.081 | 80.59| 386.800| 16.2
16| 50.820| 1.291| 2,582.90| 1.309 | 128.14| 243.250| 11.5
18| 40.303| 1.024| 1,624.30| 0.823 | 203.76| 152.990| 8.1
20| 31.961| 0.812| 1,021.50| 0.5176 | 324.00| 96.210| 5.7
22| 25.347| 0.644| 642.70| 0.3255 | 515.15| 60.510| 4.0
24| 20.100| 0.511| 504.01| 0.2047 | 819.21| 38.050| 2.8
26| 15.940| 0.405| 254.01| 0.1288 | 1,302.61| 23.930| 2.0
28| 12.641| 0.321| 159.79| 0.08097| 2,071.22| 15.050| 1.4
30| 10.025| 0.255| 100.50| 0.05092| 3,293.97| 9.466| 1.0
32| 7.950| 0.202| 63.20| 0.03203| 5,236.66| 5.952| 0.70
34| 6.304| 0.160| 39.74| 0.02014| 8,328.30| 3.743| 0.50
36| 5.000| 0.127| 25.00| 0.01267|13,238.83| 2.355| 0.35
38| 3.965| 0.101| 15.72| 0.00797|20,854.65| 1.481| 0.25
40| 3.144| 0.080| 9.89| 0.00501|33,175.94| 0.931| 0.17
----+-------+------+----------+---------+---------+----------+------
Important Topics
(1) _Galvanometers_: (1) moving magnet, fixed coil; (2) moving coil,
fixed magnet, ammeter, voltmeter.
(2) _Unit of quantity, coulomb._
(3) _Unit of current, ampere._
(4) _Unit of resistance, ohm._
(5) _Unit of electromotive force, volt._
Exercises
1. How will the resistance of 20 ft. of No. 22 German silver wire
compare with that of 10 ft. of No. 22 copper wire? Explain.
2. Where in a circuit is copper wire desirable? Where should German
silver wire be used?
3. Explain the action of the ammeter. Why does not the needle or coil
swing the full distance with a small current?
4. Why is a telegraph sounder more apt to work on a short line than upon
a long one?
[Illustration: FIG. 250.--The ammeter is connected in series and the
voltmeter in shunt.]
5. Find the resistance of 15 miles of copper telephone wire No. 12. (See
table p. 296.)
6. What will be the weight and resistance of 1,000 feet of No. 20 copper
wire?
7. A storage battery sends 4 amperes of current through a plating
solution. How much silver will it deposit in 2 hours?
8. (a) Compare the diameters of No. 22 and No. 16 copper wire.
(b) Compare the lengths of the same wires giving 1 ohm resistance.
(c) What relation exists between (a) and (b)?
9. Why is an electric bell circuit usually open while a telegraph line
circuit is usually closed?
10. A copper wire and an iron wire of the same length are found to have
the same resistance. Which is thicker? Why?
11. Why are electric bells usually arranged in parallel instead of in
series?
12. What would happen if a voltmeter were put in series in a line?
(3) OHM'S LAW AND ELECTRICAL CIRCUITS
=271. Conditions Affecting Current Flow.=--Sometimes over a long circuit
one cell will not work a telegraph sounder. In such a case, two, three,
or more cells are connected so that the zinc of one is joined to the
copper plate of the other. When connected in this way the cells are said
to be _in series_ (Fig. 251). In the figure _A_ represents a voltmeter.
It is found that _when cells are in series the E.M.F. of the battery is
the sum of the electromotive forces of the cells_. An ammeter in the
circuit shows increased current as the cells are added. Hence _if the
resistance of the circuit remains unchanged, the greater the E.M.F. the
greater is the current strength_. In this respect, the movement of
electricity in a circuit is similar to the flow of water in a small pipe
under pressure, as in the latter the flow of water increases as the
pressure becomes greater. The current in a circuit may also be increased
by lessening the resistance, since the current through a long wire is
less than that through a short one, just as the flow of water will be
greater through a short pipe than through a long one. To increase the
current flowing in an electric circuit, one may therefore either
increase the E.M.F. or decrease the resistance.
[Illustration: FIG. 251.--Diagram of cells connected in series.]
=272. Ohm's Law.=--The relation between the electromotive force applied
to a circuit, its resistance, and the current produced was discovered in
1827 by George Ohm. Ohm's law, one of the most important laws of
electricity, states that, in any circuit, _the current in amperes equals
the electromotive force in volts divided by the resistance in ohms_.
This principle is usually expressed thus:
Current intensity = electromotive force/resistance or
Amperes = volts/ohms or _I_ = _E_/_R_
[Illustration: FIG. 252.--The street cars are connected in parallel with
each other.]
=273. Resistance of Conductors in Series.=--A study of the _resistance_
of conductors when alone and when grouped in various ways is of
importance _since, the current flow through any circuit is dependent
upon its resistance_. The two most common methods of combining several
conductors in a circuit are in _series_ and in _parallel_. Conductors
are in _series_ when all of the current passes through each of the
conductors in turn (Fig. 218), thus the cell, push-button, wires, and
electric bell in an electric-bell circuit are in series. Conductors are
in _parallel_ when they are so connected that they are side by side and
a part of the whole current goes through each. None of the current that
passes through one conductor can go through the conductors in parallel
with it. Thus the electric street cars are in _parallel_ with each
other. (See Fig. 252.) It is easily seen that none of the current
passing through one car can go through any of the others. When the
conductors are in _series_ the combined resistance is the _sum_ of the
several resistances. Thus in an electric-bell circuit if the battery has
a resistance of 1 ohm, the bell of 2 ohms, and the wire 1 ohm, the total
resistance in the circuit is 4 ohms. When conductors are in _parallel_
the combined resistance is always _less_ than the separate resistances.
Just as a crowd of people meets less resistance in leaving a building
through several exits, so electricity finds less resistance in moving
from one point to another along several parallel lines, than along one
of the lines.
=274. Resistance of Conductors in Parallel.=--If three conductors of
equal resistance are in parallel, the combined resistance is just
one-third the resistance of each separately (Fig. 253). The rule that
states the relation between the combined resistance of conductors in
parallel and the separate resistances is as follows:_The combined
resistance of conductors in parallel is the reciprocal of the sum of the
reciprocals of the several resistances_. For example, find the combined
resistance of three unequal resistances in parallel; the first being 4
ohms, the second, 6 ohms, and third 3 ohms. The reciprocals of the three
resistances are 1/4, 1/6, and 1/3. Their sum equals 6/24 + 4/24 + 8/24 =
18/24. The reciprocal of this is 24/18 which equals 1-1/3 ohms, the
combined resistance.
FIG. 253.--The three conductors are connected in parallel.
This rule may be understood better if we consider the _conductance_
of the conductors in parallel. Since the conductance of a two ohm
wire is just one-half that of a one-ohm wire, we say that the
conductance of a body is inversely as the resistance, or that it is
the _reciprocal of the resistance_. The conductance of the 4-, 6-,
and 3-ohm coils will therefore be respectively 1/4, 1/6, and 1/3,
and since the combined conductance is the sum of the several
conductances, the total conductance is 18/24. Also since this is
the reciprocal of the total resistance, the latter is 24/18 or
1-1/3 ohms.
When two or more conductors are connected in parallel each one is said
to be a _shunt_ of the others. Many circuits are connected in _shunt_ or
in parallel. Fig. 254 represents four lamps in parallel. Incandescent
lamps in buildings are usually connected in parallel, while arc lamps
are usually connected in series. Fig. 255 represents four lamps in
series.
Important Topics
1. Conditions affecting current flow, (a) E.M.F., (b) resistance.
2. Ohm's law, three forms for formula.
3. Resistance of conductors: (a) in series, (b) in parallel; how
computed, illustrations.
[Illustration: FIG. 254.--The four lamps are connected in parallel.]
[Illustration: FIG. 255.--The four lamps are connected in series.]
Exercises
1. What current flows through a circuit if its E.M.F. is 110 volts and
the resistance is 220 ohms?
2. A circuit contains four conductors in series with resistances of 10,
15, 6, and 9 ohms respectively. What current will flow through this
circuit at 110 volts pressure? What will be the resistance of these four
conductors in parallel?
3. What is the combined resistance of 8 conductors in parallel if each
is 220 ohms? What current will flow through these 8 conductors at 110
volts pressure?
4. What is the resistance of a circuit carrying 22 amperes, if the
E.M.F. is 20 volts?
5. What E.M.F. will send 8 amperes of current through a circuit of 75
ohms resistance?
6. How does the voltmeter differ from the ammeter?
7. How can one determine the resistance of a conductor?
8. The resistance of a hot incandescent lamp is 100 ohms. The current
used is 1.1 amperes. Find the E.M.F. applied.
9. What is the resistance of the wires in an electric heater if the
current used is 10 amperes, the voltage being 110?
10. The resistance of 1000 ft. of No. 36 copper wire is 424 ohms. How
many feet should be used in winding a 200 ohms relay?
11. The resistance of No. 00 trolley wire is 0.80 ohm per 1000 ft. What
is the resistance of a line 1 mile long?
12. A wire has a resistance of 20 ohms. It is joined in parallel with
another wire of 6 ohms, find their combined resistance.
13. The separate resistances of two incandescent lamps are 200 ohms and
70 ohms. What is their combined resistance when joined in parallel? When
joined in series?
(4) METHODS OF GROUPING CELLS AND MEASURING RESISTANCE
=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.]
=277. Illustrative Problems.=--Suppose that four cells are grouped in
parallel, each with an E.M.F. of 1.5 volts and an internal resistance of
2 ohms. What current will flow in the circuit if the external resistance
is 2.5 ohms? Substitute in the formula for cells in parallel the values
given above, and we have _I_ = 1.5/(0.5 + 2.5) = 1.5/3 = 0.5 ampere.
Suppose again that these four cells were grouped in series with the same
external resistance, substituting the values in the formula for cells in
series we have _I_ = 4(1.5)/(4 × 2 + 2.5) = 6/10.5 = 0.57 ampere.
=278. Volt-ammeter Method for Finding Resistance.=--Measurements of the
resistance of conductors are often made. One of these methods depends
upon an application of Ohm's law. It is called the volt-ammeter method
since it employs both a voltmeter and an ammeter. If the conductor whose
resistance is to be measured is made a part of an electric circuit,
being connected _in series with the ammeter_ and _in shunt with the
voltmeter_, the resistance may easily be determined, since _R_ = _E/I_.
(See Fig. 250.) If, for example, the difference in E.M.F., or as it is
often called, the _fall of potential_ between the ends of the wire as
read on the voltmeter is 2 volts, and the current is 0.5 ampere, then
the resistance of the wire is 4 ohms. This method may be readily applied
to find the resistance of any wire that is a part of an electric
circuit.
=279. The Wheatstone Bridge.=--To find the resistance of a separate wire
or of an electrical device another method devised by an Englishman named
Wheatstone is commonly employed. This method requires that three known
resistances, _a_, _b_, _c_, in addition to the unknown resistance _x_
be taken. These four resistances are arranged in the form of a
parallelogram. (See Fig. 259.) A voltaic cell is joined to the
parallelogram at the extremities of one diagonal while a moving-coil
galvanometer is connected across the extremities of the other diagonal.
The known resistances are changed until when on pressing the keys at _E_
and _K_ no current flows through the galvanometer. when this condition
is reached, the four resistances form a true proportion, thus _a_: _b_ =
_c_: _x_.
Since the values of _a_, _b_, and _c_ are known, _x_ is readily
computed. Thus if _a_ = 10, _b_ = 100, and _c_ = 1.8 ohms, then _x_, the
unknown resistance, equals 18 ohms, since 10: 100 = 1.8: 18. This method
devised by Wheatstone may be employed to find the resistance of a great
variety of objects. It is the one most commonly employed by scientists
and practical electricians.
[Illustration: FIG. 259.--Diagram of a Wheatstone bridge.]
Important Topics
1. The internal resistance of voltaic cells.
2. Ohm's law applied to groups of cells. (a) Cells in series, (b) cells
in parallel.
3. Measurement of resistance: (a) volt-ammeter method, (b) Wheatstone
bridge method.
Exercises
1. What is the resistance of an electric bell circuit where the E.M.F.
is 3 volts and the current is 0.6 ampere?
2. A telegraph wire is broken somewhere, the ends lying upon damp
ground. If an E.M.F. of 30 volts is applied from the ground to the wire
and a current of 0.1 of an ampere flows, what is the resistance of the
part connected to the ammeter. (The earth which completes the circuit
from the end of the wire has very small resistance.) Why?
3. How far away is the break in the wire if the latter has a resistance
of 80 ohms to the mile? Diagram.
4. What current will flow through a bell circuit of 8 ohms resistance if
it contains three cells _in series_ each with an E.M.F. of 1.5 volts and
an internal resistance of 1/3 ohm?
5. If the same three cells are connected in parallel on the same circuit
what current flows? Is the current in problem 4 or 5 the larger? Why?
6. If four cells each with 1.5 volts E.M.F. and an internal resistance
of 0.4 ohm are connected with a circuit having an external resistance of
0.8 ohm, what current will the parallel connection give? The series
connection? Which gives the larger current? Why?
7. Four Daniell cells each having 1 volt E.M.F. and 3 ohms internal
resistance are connected in series with 2 telegraph sounders of 4 ohms
each. The connecting wires have 6 ohms resistance. Find the current
intensity.
8. A battery of 2 cells arranged in series is used to ring a door bell.
The E.M.F. of each cell is 1.5 volts, internal resistance 0.3 ohm, and
the resistance of the bell is 4 ohms. What is the current in amperes?
9. In the above problem find the current if the cells are connected in
parallel.