# 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 ${\displaystyle {\textrm {T}}_{S}}$ 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 ${\displaystyle {\textrm {T}}_{R}}$ is the time-constant similarly defined of the power-absorbing circuit, and if ${\displaystyle {\textrm {F}}}$ is the correcting factor, and ${\displaystyle {\textrm {p}}}$ = 2π times the frequency n, then,[1]

${\displaystyle {\textrm {F}}={\frac {{1+}{p}^{2}{T}_{S}^{2}}{1+{p}^{2}T_{S}T_{R}}}}$.

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 V1 down any inductive circuit in which it is desired to measure the power absorption, and also the volt-drop V2 down an induction less resistance R in series with it, and also the volt-drop V3 down the two together. The power absorption is then given by the expression (V32 — V12— V22)/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.)

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