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
1 For the proof of this formula see J. A. Fleming, The Alternate Current Transformer in Theory and Practice, i. 168.
power factor in those cases in which the circuit is inductive and the current alternating.
Take first the simplest case of a .noninductive powerabsorbing circuit. If an electrodynamometer, made as above described, has its fixed circuit connected in series with the powerabsorbing circuit and its movable coil (wound with fine wire) connected across the terminals of the powerabsorbing circuit, then a current will flow through the fixed coil which is the same or nearly the same as that through the powerabsorbing circuit, and a current will flow through the high resistance coil of the wattmeter proportional to the potential difference at the terminals of the powerabsorbing circuit. The movable coil of the wattmeter 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 powerabsorbing 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 toil 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, wattmeter. In those cases in which the powerabsorbing circuit is inductive, the coil of the wattmeter connected across the terminals of the powerabsorbing circuit must have an exceedingly small inductance, else a considerable correction may become necessary. This correcting factor has the following value: If Ts stands for. the timeconstant of the movable circuit of the wattmeter, commonly called the potential coil, the time constant being defined as the ratio of the inductance to the resistance of that circuit, and if T. is the timeconstant similarly defined of the powerabsorbing circuit, and if F is the correcting
factor, and p =2r times the frequency n, then,' +. p2Ts2
F = +p2TsTx•
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 wattmeter and the powerabsorbing circuit have negligible inductances, and (ii.) when the same two circuits have equal timeconstants. If these conditions are not fulfilled, the wattmeter readings, assuming the wattmeter 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 instrument must be completely nonmetallic, 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. DuddelI and Mather. W. E. Sumpner, however, has devised forms of wattmeter 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 wattmeters. If the quadrants of an electrometer '(q.v.) are connected to the ends of a noninductive circuit in series with the powerabsorbing circuit, and if the needle is connected to the end of this last circuit opposite to that at which the inductionless resistance is connected, then the deflexion of the electrometer will be proportional to the power taken up in the circuit, since it is proportional to the mean value of (A—B) {C—2 (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 powerabsorbing 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 Vi down any inductive circuit in which it is desired to
measure the power absorption, and also the voltdrop V2 down an inductionless resistance R in series with it, and also the voltdrop V3 down the two together. The power absorption is then given by the expression (V32V12V22)/2R. For methods of employing the heating power of a current to construct a wattmeter see a paper by J. T. Irwin on " Hotwire 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 polyphase 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 (19o0); 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 Ironcored Instruments for Alternate Current Working," Jour. Inst. Elec. Eng., 36, 421 (1906). (J. A. F.)
End of Article: WATTMETER 

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