Chapter XVIII: Electrical Resistance

_=305. Resistance.=_ It is harder for a horse to draw a wagon through deep sand than over a smooth pavement. We may say that the sand holds the horse back--that is, it offers a resistance. The electric current does not pass through all sorts of substances with the same ease, and when it succeeds in pushing its way through a circuit of considerable resistance, we cannot expect it to arrive at the end of its journey without being weaker than when it started. Do we expect this of a man or horse? We shall soon see that there is a definite relation between resistance and the strength of the current at the end of its journey.

=EXPERIMENT 118. To study the general effect of "resistance"
upon a current.=

_Apparatus._ Galvanoscope, G V (No. 58); resistance coil, R
C (No. 79) (§ 310); two-fluid cell, 2-F C (§ 281); 4 wires
with connectors (§ 226). _Arrange_ as in Fig. 92. The current
passes as shown by the arrow, and the circuit may be opened and
closed at the metal plate, M P, or by using a key in its place.
Properly place G V.

=306. Directions.= (A) Take the reading of G V in degrees, the
current passing through the entire length of R C. (See § 310.)

(B) Change the end of wire 4 from binding-post R to M, on R C,
so that the current will pass through one-half only of R C.
Note the reading of G V.

(C) Remove R C entirely and connect wires 3 and 4 by means of a
metal plate. Compare the readings of (A), (B) and (C). What do
they show?

_=307. External Resistance; Internal Resistance.=_ When we consider a circuit like that shown in Fig. 92 we see that it is composed of two parts, and that we have two kinds of resistances. The wires, instruments, etc., make up what is called the _external resistance_ of the circuit; that is, the part that is external to the cell. The liquids in the cell offer a resistance to the current; this is called _internal resistance_. (See § 314.) The strength of the current depends upon the relation between these two resistances, as will be seen by future experiments, as well as upon the E. M. F. of the cell. As liquids are not as good conductors as metals, the internal resistance of cells may be quite high.

_=308. Unit of Resistance; The Ohm.=_ Whenever anything is to be measured, a standard, or unit, is necessary. The unit of resistance is called the ohm, in honor of Ohm, who made careful investigations upon this subject. A column of mercury having a length of a little over 3 feet has been taken as a unit. (The column taken is 106.3 cm. with a weight of 14.4521 grams; it has a cross-section of about 1 sq. mm., at a temperature of 0°C.) Mercury is a liquid, and has no "grain" to affect the resistance. For the use of students, 9 ft. 9 in. of No. 30 copper wire, or 39 ft. 1 in. of No. 24 copper wire will make a fairly good ohm. We might, of course, take any other length as _our_ standard; the above, however, will give results that are approximately correct. (See wire tables at the end of this book.)

_=309. Resistance Coils; Resistance Boxes.=_ Coils of wire, having carefully-measured resistances, are called _resistance coils_. The wire for any coil is doubled at the center before it is wound into coils or upon spools (Fig. 93) to avoid the magnetic effect. The ends of the coils are attached to binding-posts, or to brass blocks, in regular instruments, so that one or more coils can be used at a time; that is, so that they may be handled in a manner similar to that in which the different coils on the galvanoscope are used.

If we have 4 coils of 1, 2, 2, and 5 ohms resistance, we shall be able to use any number of ohms from 1 to 10 by making the proper connections. (See Apparatus Book, chapter XVII, for Home-made Resistance Coils.)

For protection and convenience, coils are usually placed in a box, the whole being called a _resistance box_. The ends of the coils are joined to brass blocks, placed near each other on the top of the box, and between which may be pressed plugs when it is desired to short circuit the coils. By removing a plug, the coil, whose ends are joined to the blocks touching it, is brought into the circuit.

=310. Simple Resistance Coil.= Fig. 94 shows a simple form of
coil, R C (No. 79). The total resistance is 2 ohms, L (left)
and R (right) being binding-posts to which the ends of the
coil, C, are joined. M (middle) connects with the middle of the
wire, at which point the wire is doubled. The coil is fastened
to a stiff pasteboard base, B.

=Connections.= When 2 ohms resistance are wanted, let the
current enter at L and leave at R (or the reverse). When 1 ohm
is wanted, let the current leave or enter at M, the other wire
being joined to L or to R. Connections should be made with
spring connectors. See § 229.

=EXPERIMENT 119. To test the power of various substances to
conduct galvanic electricity.=

_Apparatus._ Galvanoscope, G V (No. 58); dry cell, D C, or
two-fluid cell, 2-F C; pieces of different metals; wood,
dry and damp; tumbler of pure water; rubber; ebonite; silk;
glass, etc., etc. _Arrange_ as in Fig. 92, leaving out R C,
and instead of having M P between wires 1 and 2, use their
free ends to press firmly upon the ends of the substance to be
tested; that is, the body under test should take the place of M
P in the Fig. G V will show a deflection, of course, when the
particular thing under test is a conductor.

=311. Directions.= (A) Make tests with the above substances,
and with any others at hand, and note which are conductors and
which are not.

_=312. Conductors and Nonconductors.=_ It is evident, from the experiments, that bodies which conduct static electricity do not necessarily conduct galvanic electricity. The greater the E. M. F. of a current, the greater its power to overcome resistance. Some bodies, like dry wood, that readily conduct the high potential static electricity, make fairly good insulators for the low potential galvanic currents. For convenience, substances may be divided into _good conductors_, _partial conductors_, and _insulators_, or nonconductors.

_=Good Conductors.=_ Metals, charcoal, graphite, acids, etc.

_=Partial Conductors.=_ Dry wood, paper, cotton, etc.

_=Insulators.=_ Oils, porcelain, silk, resin, shellac, ebonite, paraffine, glass, dry air.

=EXPERIMENT 120. To find the effect of sulphuric acid upon the
conductivity of water.=

_Apparatus._ Galvanoscope, G V; cell; 2-F C; connecting wires;
saucer or tumbler, S; a little sulphuric acid.

_Arrange_ as in Fig. 95.

=313. Directions.= (A) Put a little pure water in S, and see
if enough current can pass through it to deflect the needle of
G V. The ends of the wires, 1 and 2, should be gradually moved
toward each other, the needle being watched.

(B) Put 4 or 5 drops of concentrated acid into the water; stir
it, then repeat the test. What effect has the acid?

_=314. Internal Resistance.=_ As found in Exp. 120, pure water is not a good conductor of galvanic electricity. The acid in the simple cell, and in other single-fluid cells, acts upon the zinc and at the same time makes it possible for the current to pass, as it reduces the internal resistance.

As seen later, this resistance in cells is greatly diminished by bringing the plates near each other, and by increasing the surface of the plates that are in contact with the acid. The larger the plates the less the internal resistance, other things remaining the same. The internal resistance of a _battery_ can be changed by connecting the cells differently. (See Chap. on Arrangement of Cells.)

=EXPERIMENT 121. To find what effect the length of a wire has
upon its electrical resistance.=

_Apparatus._ A No. 30 German-silver wire, G-S W, a little over
two meters long, un-insulated (No. 81); the two-fluid cell, 2-F
C (Exp. 113); galvanoscope, G V (No. 58); plate binding-posts,
X, Y and Z (No. 83-84-85); copper washers (No. 87).

_Arrange_ as in Fig. 96, so that the current will flow, at
first, as shown by the arrow. The metal plates, M P 1 and M
P 2, are used so that the connections may be changed without
disturbing G V. The binding-posts may be fastened directly
to the top of the table; but it will be more convenient to
permanently fix them to a board, B, as shown, so that the
same arrangement can be used for future experiments. The
binding-posts, X and Y, should be about 1/8 in. apart, just far
enough so that their edges do not touch each other.

The binding-post, Z, should be fastened to B with its inside
end 1 meter(100 centimeters, cm.) from the ends of X and Y.
Marks should be made upon B, 10 centimeters apart, as indicated
by the cross lines. This distance may be taken from the scale
on the rule (No. 88).

Fasten one end of the No. 30 wire, G-S W, to X. To do this
twist its end around the screw, S, between X and the copper
washer, then turn the screw in with a screw-driver until it
firmly holds X to the board. Pass the wire around the screw in
Z, and bring its free end to the other binding-post, Y, to be
fastened (Fig. 96). Two meters of wire then form a path for the
current from X to Y. Have the board wide enough so that another
set of binding-posts can be put by the side of Y. It will be
best to permanently leave the No. 30 wire upon the board, and
to fasten the No. 28 wire (next experiment) to another set of
binding-posts, placed in the same manner as those in Fig. 96.
Make holes in the wood with an awl before forcing in the screws.

=315. Note.= This experiment is usually done with a reverser in
the circuit, first taking readings with the current passing in
one direction, and then in the opposite direction. Considerable
time will be saved by taking all the readings for one direction
of the current at a time, simply using different lengths of
German-silver wire, and allowing the current to flow constantly
during each part. This obviates all danger of poor contacts
in the reverser, etc.; it saves the trouble of handling the
reverser, and much of the time needed for the needle to come to
rest.

+--------------------+----+----+----+---+---+---+---+---+----+---+
|LENGTH OF CIRC., CM.|200 |180 |160 |140|120|100| 80| 60|200 | O |
+--------------------+----+----+----+---+---+---+---+---+----+---+
|DEFLECTION; WEST |26° |28° | 30°| | | | | | 26°|67°|
+--------------------+----+----+----+---+---+---+---+---+----+---+
|DEFLECTION; EAST |25° |27° | 30°| | | | | | 25°|67°|
+--------------------+----+----+----+---+---+---+---+---+----+---+
| AVERAGE |25.5|27.5| 30 | | | | | |25.5|67 |
+--------------------+----+----+----+---+---+---+---+---+----+---+

Fig. 97.]

=316. Directions.= (A) With the circuit arranged as in Fig.
96, and with G V properly placed, take the reading of G V, the
current passing through 200 cm. of No. 30 G-S W. Record your
results in a diagram made like Fig. 97. The row of figures
across the top shows the length of the circuit. The table is
started with results from one experiment. Your results will
probably be different from these.

(B) Get the deflection with the current passing through 180
cm. of wire. To do this press a piece of copper (O, Fig. 96)
upon the wire at the mark 10 cm. from Z, another thin piece of
metal, U, having been slipped under the wire. This will allow
the current to pass across from one wire to the other. Record
the deflection in the col. marked 180.

(C) Record the deflections for the lengths, 160 cm., 140, 120,
100, 80, and 60; then repeat (A) to be sure that the cell has
been working uniformly. This deflection should agree with that
in (A).

(D) Change the direction of the current through G V; to do
this, change wire, 1, from M P 2 to M P 1, and wire 5 to M P 2.
This must be done without disturbing G V.

(E) Repeat (A), (B), and (C), and record the deflections for
the different lengths.

(F) Get the average deflections.

(G) Take, for future use, the deflection produced without G-S
W being in the circuit. Swing the end of wire, 3, that is
joined to Y, around to M P 2. The current will then pass simply
through G V. Record deflection in col. marked O.

=Note.= It is best to do the next experiment at once with the
same cell, so that the results of the two experiments can be
compared. In case this is impossible, get your cell to produce
the same deflection when you use it again, as shown in col. O,
Fig. 97. You can regulate the deflection of the needle of G V
by varying the strength and quantity of the acid in P C.

_=317. Discussion.=_ The resistance of a wire evidently depends
(Exp. 121) upon its length. The _exact_ relation between
resistance and length cannot be seen from these results,
however, which are used in the next experiment. It will be
shown later that in a wire, other things remaining the same,
the resistance varies directly as its length.

=EXPERIMENT 122. To find what effect the size (area of
cross-section) of a wire has upon its electrical resistance.=

_Apparatus._ Same as in last experiment, with one change,
however. Replace the No. 30 G-silver wire with a No. 28
G-silver wire (No. 82), or, what is better still, fasten it to
another set of binding-posts on the board and leave the No. 30
for future use. The two should be stretched side by side for
constant use.

=318. Directions.= (A) See that your cell is in the same
condition as for Exp. 121; that is, it should produce the same
deflection of the needle of G V as before, when the two, only,
are in the circuit. (See Exp. 121, G.) The deflection may be
changed by changing the strength and quantity of the dilute
acid and copper solution.

(B) Find the average deflection of the needle with the 2 meters
of No. 28 G-s wire in the circuit, arranged as in Fig. 96.

(C) Compare this average deflection with the results obtained
in Exp. 121, in order to find what length of the No. 30
wire has the same resistance as 2 meters of No. 28 wire. To
find how many times greater one length is than another, we
divide the larger length by the smaller; hence, to find the
relation between the two lengths of wire that gave the same
deflection,--lengths of equal resistance,--we divide the 200
centimeters (the length of the No. 28) by the length of No. 30
found as directed.

(D) From the wire tables it will be found that the area of
cross-section of No. 28 wire is about 1.59 times that of No.
30 wire. How does this quotient, or ratio, compare with that
found in part (C)? What is the relation between the area of
cross-section of a wire and its resistance? (See § 319, also
Exp. 136.)

_=319. Discussion.=_ If we find that a certain wire, X, which is 576 feet long, has the same resistance as a shorter one, Y, 360 feet long, we see (576 divided by 360) that the ratio of their lengths is 1.6. This means that the longer one, X, is 1.6 times as good a _conductor_ as Y; or, in other words, that the _resistance_ of Y is 1.6 times that of X.

It is easier for water to flow through a large pipe than it is through a small one. The same general principle is true of electricity. A large wire offers less resistance to the current than a small one of the same material. If one wire is twice the size of another of equal length, it will be twice as good a conductor as the other; that is, it will have one-half the resistance of the smaller, provided they are of the same material. (See Laws.)

=EXPERIMENT 123. To compare the resistance of a divided circuit
with the resistance of one of its branches.=

_Apparatus._ Same as in last experiment. Arrange as in Fig. 98.

=320. Directions.= (A) Note the deflection of the needle when
the current passes through 1 meter of G-s wire, as shown. This
will be considered as one branch of the divided circuit.

(B) Still allowing the current to pass as in part (A), press
a piece of copper firmly across the binding-posts X and Y, to
electrically connect them, and note the reading of the needle.
In this case the current divides at Z through the two branches.
What is learned from the results of (A) and (B)?

(C) See if you can show the same results with apparatus
arranged as in Fig. 99.

_=321. Discussion.=_ Two wires placed side by side as in (B), Exp. 123, really form a conductor having twice the size (area of cross section) of one of the branches. The more paths a current has in going from one place to another, the less the resistance. (See Exp. 135.) The wires are said to be in "parallel" or in "multiple arc."

=EXPERIMENT 124. To study the effect of decreasing the
resistance in one branch of a divided circuit.=

_Apparatus._ Galvanoscope, G V (No. 58); resistance coil, R
C (No. 79); two-fluid cell, 2-F C (§ 281), or a dry cell; 6
connecting wires; metal plates, M P.

_Arrange_ as in Fig. 100, so that the current divides into two
branches at M P 1. The branches unite at M P 2.

=322. Directions.= (A) Take the reading of G V with 2 ohms
resistance in the lower branch; that is, with the whole of R C
in circuit.

(B) Take the reading of G V with one ohm in circuit; that is,
with the end of wire, 5, connected to M instead of to R.

(C) Cut out R C from the lower branch by replacing it with a
metal plate, thus joining wires 3 and 5. Compare the results
from (A), (B), and (C), and explain.

_=323. Current in Divided Circuits.=_ Let us consider a circuit like that shown in Fig. 101. If the points, C and Z, were at the same potential, no current would pass from C to Z. As the current does pass, Z must be at a lower potential than C; there is a _fall of potential_ from C to Z. If the branch, A B, has the same resistance as R X, the same amount of current will pass through each. Exp. 124 has shown that when the branches have unequal resistances, most of the current passes through the one of small resistance. If R X has a greater resistance than A B, most of the current will pass through A B.