8°70. Induction Type Instruments Ammeters and voltmeters which depend upon magnetic induction fot the operation are suitable for a.c. measurements only. In fact they have very serious disadvantages which overweigh their advantages and hence induction instruments are not $ used as ammeters or voltmeters. The induction principle finds its widest x application in energy meters as discussed in Chapter 11, ‘g:, 8°69. Principle of Operation. Let us first consider. the torque produced by interaction of a flux and a current, Let their instantaneous values be : . ! $= On sin «of, Jo sin (wt--e) (See Fig, 8°72). Fig, 672 ANALOG, AMMITERS, VOLTMBTHRS AND. OHMMETERS 2m ‘The ‘instantaneous torque is proportional to the product of the instantaneous current and the instantaneous flux. 1. Instantaneous torque #4i a Palm sin wt sin (wt—«), The mean torque over a cycle having a time period 7, T i an Onn ae [ota sa (ot—#) ds Oe Ie gg} sn in ay at, « SSP cos 0 08°40, Klectrodynamometer (Electrodynamic) xype Instruments "ThE necessity for thé a,c. calibration. of moving iron instruments as well as. other types ol instruments which cannot be correctly ‘calibrated’ requires the use of a transfer type of instrument which is equally accurate on both ac, and d.c. ‘This is necessary since all measurements, and herice, the alibration of all indicating instruments, myst eventually be éferred to standards of voltage and resistance. These standards are precision resistors and the Weston standard cell (which is a dic. cell). . It is obvious, therefore, that it would ‘be impossible to calibrate an a.c. instrument directly against the fundamental standards. The calibration of an‘d:e. instrument may be performed as follows ; The transfer instrument is first calibrated of d.c.. This calibration is then transferred. to the a.c. instrument on alternating current, using operating eonditions tinder which’ the Jatter/operates properly. Blebicgdjnamic igithumients atticapable of sérvtoy.as tcansfér instruments, Indeed, tieir piin- cipal use as bniméters and voltmeters in laboratory ard‘méasurenient wotk is for the transfer calibra- . tion of working instruments, . Electrodynamometer type of instruments are used as-a.c. voltmeters and ammeters both in the range of power frequencies and lower part of the audio frequency range, Théy are used as watt- metérs, varmeters and with some modification as"power factor meters and frequency meters, 16 ELECTRICAL MEASUREMENTS AND MEASURING INSTRUMENTS 841, Operating Principle. We cari have an idea of the working principle of this instrument by taking up a permanent maguet moving coil instrument and considering how it would behave on.a.c, Jt would have a torque in one direction during one half of the cycle and an equal effect in844. Electrodynamometer Awmeters, Fiz. 8:43 shows that the arrangement of coils of an electrodynamometer ammeter. In this case tho fixed and moving coils are connected in series and, therefore, carry the same current fe. h=/=/ and $=0. J Detecting torque Trait (Sen Bao, 863) *.(865) . : and deflection = 4p Got (8466) Due to some considerations explained later, the current through the moving coil should not exceed 200-mA and, therefore, the arrangement of Fig. 8°40 is suitable for ammeters having a. range upto 200 mA. . For ammeters of higher capacity, the arrangement shown in Fig. 8°42 is used, In this case the moving coil is connected in series with its swamping resistance across a shunt together with fixed “Coils. Thus there are two separate parallel branches for fixed and moving coils. In order that the ammeter may indicate correctly at all frequencies, the currents in the fixed and moving coils must be in phase. ‘This requires the time constant L/R of two branches to be equal as otherwise the currents in the two branches. will not be. independent of frequency, Using this arrangement we can easily make L/R ratio equal for-both branches, “h Swamping Moving , resistance al laden te! 4) dr £ Shunt , \ Fived wal tao , Fined caits ‘ _ fesistance lO ———— V, Supply ———- Supply Te | boas‘PNG. O96, EucctrouyOamometer A MMeree, Bie U2. AHCC OC yRaMOMeicr FONMCEE, (Above 200 mA) 848, Eléctrodyaamometer Voltmmeters. ‘The clectrodynamometer smovement is used as a voltmeter by connecting the fixed and moving coils in series with a high noa-inductive resistance, The arrangement is shown in Fig. 8°43. « Dellecting torque Ta=N1la cos ¢ it k In this case a=had andg=0 0°, Ta= g . t aie ve aM, + Z db (8°67) 240 ‘ELECTRICAL MEASUREMENTS AND MBASURING INSTRUMENTS where V=voltage across the instrument, Z=impedance of the instrument circuit. j : ve dat. | j Deffection 6 kB a +»:(8°68) + { Blectrodynamometer type voltmeter is the most accurate type of ac. voltmeter. But the | sensitivities are low in comparison with-the dc.-insteaments, and range from 10 to 30 Q/¥,8°47, Use on D.C. and A.C. The electrodynamometer type of instrument can be used on both dic. and a.c, When being used on a.c the instantaneous torque is proportional to i? (for an ammeter), As the current varies the torque also varies but always remains in the same direction. The pointer is not able to follow the individual torque pulsations but takes up a position where the average torque is equal to the controlling torque. Thus the instrument can be usd on both ac.andd.c. The instrument if initially calibrated on d.c., the calibration holds true for ac, as well in which case the instrument reads the rms value of the current.8°27. Moving Iron Instruments The mest common ammeters and voltmeters for laboratory of switch-board use at power frequencies are the moving iron instruments. ‘These instruments can be constructed to measure current and voltage to the accuracy needed in most engineering works and still be cheap as compared with any other type of a.c..instrument of same accuracy and ruggedness. A plate or vane of soft iron or of high permeability steel forms the movidg clement of the system, This iron vane is so situated that it cam move in a magnetic field produced by a stationary coil, The coil is excited by the current or voltage under measurement. When the coil is excited, it becomes an electromagnet and the iron vane moves in such a way so as to increase the flux of the electromag- net, This is because the vane tries to occupy a position of minimum reluctance, Thus the force (or torque)’ produced is always in such a direction as to increase the inductance of the coil (As induct- ance increases as reluctance decreases), . 8°28, General Torque Equation An expression for the torque of a moving iron instrument may be derived by considering the energy ielations when there is a small increment in current supplied to the instrument. When this happens there will be a small deflection d and some mechanical work will be done, Let Ta=deflecting torque . Mechanical work done=73. a Alongside there will be a change in the energy stored owing to inductance. Suppose the initial current is J, the instrument inductance Z and the deflection @ If the current increases by d/ then the deflection changes by @9 and the inductance by dL. In order to effect an inerement di in the current there must be an increase in the applied voltage given by ata. ar) tuyatG tL at ‘The electrical energy supplied eldt=/2dE-+-ILar ‘The stored energy changes from=4/°L to 4(-+df)® (Lt dL).10°3. Electrodynamometer Wattmeters ‘These instruments are similar in design and construction to electrodynamometer type ammeters and voltmeters described in Chapter 8. The two coils are connected in different circuits for measurement of power. The fixed coils or “field coils” are connected in series with the load and so carry the current in the circuit, The fixed coils, therefore, form the “ourrent coil” of the watt= meter. The moving coil is connected across the voltage and therefore, carries a current proportional to the voltage. .A bigh non-inductive resistance is connected in series with the moving coil to limit ‘the curtent to small value. Since the moving coil carries a cutrent proportional to the'voltage, it is called the “pressure coll” or “voltage coil” of the wattmeter. 10°4. Construction 1. Fixed Coils, The fixed coils-carry the current of the circuit. ‘They are divided into two: halves. The reason for using fixed coils as current coils is that they can be made more massive and can be easily constructed to carry considerable current since ‘they present no problem of getting the current in or out. The fixed coils are wound with heavy wire. This wire is stranded or laminated especially when carrying heavy currents inorder to avoid eddy current losses in conductors. . They ate first varnished and baked to exclude moisture and clamped into place, thus forming a rigid solid ‘ assembly. In early wattmeters, the current coils were sometimes built to carry load currents of 100 of more.’ But in such constructions, it{s very difficult to avold eddy currents. Also the use-of | beavy current leads introduces atray field ¢rrore. Becauso’of these and other errors modern practice