# 1911 Encyclopædia Britannica/Wattmeter

**WATTMETER**, an instrument for the measurement of electric
power, or the rate of supply of electric energy to any circuit.
The term is generally applied to describe a particular form of
electrodynamometer, consisting of a fixed coil of wire and an
embracing or neighbouring coil of wire suspended so as to be
movable. In general construction the instrument resembles
a Siemens electrodynamometer (see Amperemeter). The fixed
coil is called the current coil, and the movable coil is called the
potential coil, and each of these coils has its ends brought to
separate terminals on the base of the instrument. The principle
on which the instrument works is as follows: Suppose any
circuit, such as an electric motor, lamp or transformer, is receiving
electric current; then the power given to that circuit reckoned
in watts is measured by the product of the current flowing through
the circuit in amperes and the potential difference of the ends of
that circuit in volts, multiplied by a certain factor called the
power factor in those cases in which the circuit is inductive and
the current alternating.

Take first the simplest case of a non-inductive power-absorbing
circuit. If an electro-dynamo meter, made as above described, has
its fixed circuit connected in series with the power-absorbing circuit
and its movable coil (wound with fine wire) connected across the
terminals of the power-absorbing circuit, then a current will flow
through the fixed coil which is the same or nearly the same as that
through the power-absorbing circuit, and a current will flow through
the high resistance coil of the watt meter proportional to the potential
difference at the terminals of the power-absorbing circuit. The
movable coil of the watt meter is normally suspended so that its
axis is at right angles to that of the fixed coil and is constrained by
the torsion of a spiral spring. When the currents flow through the
two coils, forces are brought into action compelling the coils to set
their axes in the same direction, and these forces can be opposed by
another torque due to the control of a spiral spring regulated by
moving a torsion head on the instrument. The torque required to
hold the coils in their normal position is proportional to the mean
value of the product of the currents flowing through two coils
respectively, or to the mean value of the product of the current in
the power-absorbing circuit and the potential difference at its ends,
that is, to the power taken up by the circuit. Hence this power
can be measured by the torsion which must be applied to the
movable coil of the wattmeter to hold it in the normal position
against the action of the forces tending to displace it.
The wattmeter can therefore be calibrated so as to give direct
readings of the power reckoned in watts, taken up in the circuit;
hence its name, watt meter. In those cases in which the power absorbing
circuit is inductive, the coil of the watt meter connected
across the terminals of the power-absorbing circuit must have
an exceedingly small inductance, else a considerable correction
may become necessary. This correcting factor has the following
value. If stands for the time-constant of the movable
circuit of the watt meter, commonly called the potential coil, the
time constant being defined as the ratio of the inductance to the
resistance of that circuit, and if is the time-constant similarly
defined of the power-absorbing circuit, and if is the correcting
factor, and = 2π times the frequency *n*, then,^{[1]}

- .

Hence an electrodynamic wattmeter, applied to measure the electrical power taken up in a circuit when employing alternating currents, gives absolutely correct readings only in two cases—(i.) when the potential circuit of the watt meter and the power-absorbing circuit have negligible inductance's, and (ii.) when the same two circuits have equal time-constants. If these conditions are not fulfilled, the wattmeter readings, assuming the watt meter to have been calibrated with continuous currents, may be either too high or too low when alternating currents are being used.

In order that a wattmeter shall be suitable for the measurement
of power taken up in an inductive circuit certain conditions of
construction must be fulfilled. The framework and case of the
mstrument must be completely non-metallic, else eddy currents
induced in the supports will cause disturbing forces to act upon
the movable coil. Again the shunt circuit must have practically
zero inductance and the series or current coil must be wound or
constructed with stranded copper wire, each strand being silk
covered, to prevent the production of eddy currents in the mass
of the conductor. Wattmeters of this kind have been devised by
J. A. Fleming, Lord Kelvin and W. Duddell and Mather. W. E.
Sumpner, however, has devised forms of watt meter of the dynamometer
type in which iron cores are employed, and has defined
the conditions under which these instruments are available for
accurate measurements. See" New Alternate Current Instruments,"
*Jour. Inst. Elec. Eng.*, 41, 227 (1908).

There are methods of measuring electrical power by means of
electrostatic voltmeters, or of quadrant electrometers adapted for
the purpose, which when so employed may be called electrostatic
watt meters. If the quadrants of an electrometer (*q.v.*) are connected
to the ends of a non-inductive circuit in series with the
power-absorbing circuit, and if the needle is connected to the end
of this last circuit opposite to that at which the induction less resistance
is connected, then the reflexion of the electrometer >vill be
proportional to the power taken up in the circuit, since it is proportional
to the mean value of (A–B) {C-½ (A+B)}, where A and
B are the potentials of the quadrants and C is that of the needle.
This expression, however, measures the power taken up in the
power-absorbing circuit. In the case of the voltmeter method of
measuring power devised by W. E. Ayrton and W. E. Sumpner in
1891, an electrostatic voltmeter is employed to measure the fall of
potential V_{1} down any inductive circuit in which it is desired to
measure the power absorption, and also the volt-drop V_{2} down an
induction less resistance R in series with it, and also the volt-drop V_{3}
down the two together. The power absorption is then given by the
expression (V_{3}^{2} — V_{1}^{2}— V_{2}^{2})/2R. For methods of employing the
heating power of a current to construct a wattmeter see a paper
by J. T. Irwin on " Hot-wire Wattmeters," *Jour. Inst. Elec. Eng.*
(1907), 39, 617.

For the details of these and many other methods of employing
wattmeters to measure the power absorption in single and poly phase
circuits the reader is referred to the following works: J. A. Fleming,
*Handbook for the Electrical Laboratory and Testing Room* (1903);
Id., *The Alternate Current Transformer in Theory and Practice*
(1905); G. Aspinall Parr, *Electrical Engineering Measuring Instruments*
(1903); A. Gray, *Absolute Measurements in Electricity and*
*Magnetism* (1900); E. Wilson, " The Kelvin Quadrant Electrometer
as a Wattmeter," *Proc. Roy. Soc.* (1898), 62, 356, J. Swinburne,
" The Electrometer as a Wattmeter," *Phil. Mag.* (June 1891);
W. E. Ayrton and W. E. Sumpner, " The Measurement of the Power
given by an Electric Current to any Circuit," *Proc. Roy. Soc.* (1891),
49, 424; Id., " Alternate Current and Potential Difference Analogies
in the Method of Measuring Power," *Phil. Mag.* (August 1891);
W, E. Ayrton, " Electrometer Methods of Measuring Alternating
Current Power," *Journ. Inst. Elec. Eng.* (1888), 17, 164; T. H.
Blakesley, " Further Contributions to Dynamometry or the Measurement
of Power," *Phil. Mag.* (April 1891); G. L. Addenbrooke,
" The Electrostatic Wattmeter and its Calibration and Adaptation
for Polyphase Measurements," *Electrician* (1903), 51, 811; W. E.
Sumpner, " New Iron-cored Instruments for Alternate Current
Working," *Jour. Inst. Elec. Eng.*, 36, 421 (1906).(J. A. F.)

- ↑ For the proof of this formula see J. A. Fleming,
*The Alternate**Current Transformer in Theory and Practice*, i. 168.