In the whole of a circuit=_current_ in webers x _electro-motive force_
in volts / 746. In any part of circuit=_current_ in webers x _difference
of potential_ at the two ends of the part of the circuit in question /
746. Or, =square of current in webers x resistance of the part in ohms /
746.
If there are a number of generators of electricity in a circuit, whose
electromotive forces in volts are E_1, E_2, etc., and if there are also
opposing electro-motive forces. F_1, F_2, etc., volts, and if C is the
current in webers, R the whole resistance of the current in ohms, P
the total horse-power taken at the generators, Q the total horse-power
converted into some other form of energy, and given out at the places
where there are opposing electro-motive forces, H the total horse-power
wasted in heat, because of resistance, then:
(E_1+E_2+etc.)-(F_1+F_2+etc.)
C = -----------------------------
R
[TEX: C = \frac{(E_1+E_2+\text{etc.})-(F_1+F_2+\text{etc.})}{R}]
C C
P = ---((E_1+E_2+etc.); Q = ---(F_1+F_2+etc.)
746 746
[TEX: \frac{C}{746}(E_1+E_2+\text{etc.});\ Q =
\frac{C}{746}(F_1+F_2+\text{etc.})]
C² R
H = ----- .
746
[TEX: H = \frac{C^2 R}{746}.]
The lifting power of an electro-magnet of given volume is proportional
to the heat generated against resistance in the wire of the magnet.
The future of many electrical appliances depends on how general is the
public comprehension of the lessons taught by these wall sheets. If
a few capitalists in London would only spend a few days in learning
thoroughly what these mean, electrical appliances of a very distant
future would date from a few months hence.
A number of experiments were shown, in some of which electrical energy
was converted into heat, in others into sound, in others into work. At
this part of the lecture reference was made to the work of Prof. Ayrton
and his pupils at Cowper street (City and Guilds of London Institute
Classes). They measure (1) the gas consumed by the engine, (2) the
horse-power given to the dynamo machine, (3) the current in the
circuit in webers, and (4) the resistance of the circuit. Thus exact
calculations can now be made as to the horse power expended in any
part of the circuit, and the light given out in any given period by
an electric lamp. The dynamometers used in these measurements were
described, but at present, in some cases, the description given is for
various reasons incomplete, so that we shall take a future opportunity
of writing of these instruments. To measure the light a photometer,
constructed by Profs. Ayrton and Perry, is used, which obviates the
necessity of large rooms, and enables the operator to give the intensity
in a very short period of time. A number of measurements of the
illuminating power of an electric lamp were rapidly made during the
lecture with this photometer. By means of a small dynamo machine, driven
by an electric current generated in the Adelphi arches, a ventilator,
a sewing machine, a lathe, etc., were driven; in the latter a piece of
wood was turned. "What," said the lecturer, "do these examples show
you?" "They show that if I have a steam-engine in my back yard I can
transmit power to various machines in my house, but if you measured the
power given to these machines you would find it to be less than half
of what the engine driving the outside electrical machine gives out.
Further, when we wanted to think of heating of buildings and the boiling
of water, it was all very well to speak of the conversion of electrical
energy into heat, but now we find that not only do the two electrical
machines get heated and give out heat, but heat is given out by our
connecting wires. We have then to consider our most important question.
Electrical energy can be transmitted to a distance, and even to many
thousands of miles, but can it be transformed at the distant place into
mechanical or any other required form of energy, nearly equal in amount
to what was supplied? Unfortunately, I must say that hitherto the
practical answer made to us by existing machines is, 'No;' there is
always a great waste due to the heat spoken of above. But, fortunately,
we have faith in the measurements, of which I have already spoken, in
the facts given us by Joule's experiments and formulated in ways we can
understand. And these facts tell us that in electric machines of the
future, and in their connecting wires, there will be little heating, and
therefore little loss. We shall, I believe, at no distant date, have
great central stations, possibly situated at the bottom of coal-pits
where enormous steam engines will drive enormous electric machines. We
shall have wires laid along every street, tapped into every house, as
gas-pipes are at present; we shall have the quantity of electricity used
in each house registered, as gas is at present, and it will be passed
through little electric machines to drive machinery, to produce
ventilation, to replace stoves and fires, to work apple-parers and
mangles and barbers' brushes, among other things, as well as to give
everybody an electric light."
It is possible, as Prof. Ayrton first showed in his Sheffield lecture,
that electrical energy can be transmitted through long distances by
means of small wires, and that the opinion that wires of enormous
thickness would be required is erroneous. The desideratum required was
good insulation. He also showed that, instead of a limiting efficiency
of 50 per cent., the only thing preventing our receiving the whole of
our power was the mechanical friction which occurs in the machines. He
showed, in fact, how to get rid of electrical friction. A machine at
Niagara receives mechanical power, and generates electricity. Call this
the generator. Let there be Wires to another electric machine in New
York, which will receive electricity, and give out mechanical work.
Now this machine, which may be called the motor, produces a back
electromotive force, and the mechanical power given out is proportional
to the back electromotive force multiplied into the current. The
current, which is, of course, the same at Niagara as at New York, is
proportional to the difference of the two electromotive forces, and the
heat wasted is proportional to the square of the current. You see, from
the last table, that we have the simple proportion: power utilized is
to power wasted, as the back electromotive force of the motor is to the
difference between electromotive forces of generator and motor. This
reason is very shortly and yet very exactly given as follows:
Let electromotive force of generator be E; of motor F. Let total
resistance of circuit be R. Then if we call P the horse-power received
by the generator at Niagara, Q, the horse-power given out by motor
at New York, that is, utilized; H, the horse-power wasted as heat in
machines and circuit; C, the current flowing through the circuit: