Chapter 49. Meter Movement – Electrical Technology, Vol2: Machines and Measurements, 1/e


Meter Movement


In this chapter you will learn about:

  • The different types of torques in metre movements
  • The associated scales in metre movements
  • Moving-coil and moving-iron instruments
  • The merits and demerits of the above instruments
  • Polarized moving-iron instruments
  • The construction and operation of dynamometer-type instruments
  • Different types of induction-type instruments
  • The details of construction and operation of hot-wire instruments
  • The operating principles of thermocouple
  • Utility of thermocouples as measuring instruments
  • Galvanometers and their use as multi-type instruments
  • Optical system associated with galvanometers
  • The principle of electrostatic voltmeters
  • The properties of electrostatic voltmeters
  • Simple problems on the above

Taut-band suspension meter movement


Metres with moving pointers are called analog metres. They measure quantities by moving through an infinite number of points on a scale. The major part of any analog multimeter is the basic metre movement. metre movements utilize the interaction of two magnetic fields. During the metre movement, at least one of the fields is created by a current passing through a coil.

All basic metre movements have a full-scale current rating. This is the coil current required to cause the metre to deflect in full scale (full-scale deflection current). metre movement with full-scale deflection currents as low as 5 μΑ are commonly available. Another important rating of a metre movement is its internal resistance. Basic metre movements have appreciable resistance because of the small-diameter wire used in the moving coil. In general, the lower the full-scale current rating is, the higher the internal resistance will be. A typical 1-μA metre has less than 100 Ω of internal resistance. A typical 50-μΑ metre has more than 900 Ω of internal resistance. As a metre movement has both a current and a resistance rating, it must also have a voltage rating. Usually, the manufacturer specifies only two of these three ratings. However, the third rating can easily be determined by using Ohm’s law. The voltage across the metre movement must be equal to the product of the full-scale deflection current and its internal resistance.


Most electrical measuring instruments depend on the magnetic effect of current for their operation, although the heating effect is of common application and particularly useful in a.c. instruments at high frequencies. Electrochemical instruments have little practical application. An important class of voltmeter, which consumes no power, is one that depends on the force between two conductors carrying a static electric charge.

Figure 49.1 Deflection Torque Uniform Radial Magnetic Field: θ Upsets the Proportional Relation Td =

Apart from the electrostatic voltmeter, most electrical measuring instruments are in effect current measuring devices, that is, the force responsible for their deflection depends on the magnitude of the current they carry through their scales, which may be calibrated in terms of pd, or resistance or of power.

The reading of most electrical instruments depends on observing the exact position attained by an indicating pointer against a calibrated scale; this scale may be considerably extended when a reflected beam of light is used as the pointer. An important class of precision instrument however, of which the Wheatstone bridge is a classic example, depends upon a non-deflectional or null method.

In a measuring instrument, the deflecting torque (Figure 49.1) produced by the current being measured is opposed by a controlling torque, which tends to maintain the pointer opposite the zero mark on the scale. The scale reading indicated by the pointer is the current value for which the two torques are equal and opposite. A suitable restoring torque may be provided preferably by the energy or a coiled spring or sometimes by gravity.

If readings are to be taken quickly, some form of damping is essential to overcome the tendency of the system to oscillate about the point where the torques are balanced; such damping is conveniently afforded by facilitating the production of eddy currents or by using pnoumatri methods if the presence of a magnetic field for the purpose is undesirable. Electromagnetic damping and mechanical damping are shown in Figure [49.2 (a), (b) and (c)].

Figure 49.2 Damping (a) Electromagnetic (Eddy Current) (b) Mechanical (Air Friction) (c) Mechanical (Fluid Friction)

To attain and maintain the greatest accuracy, a maximum torque should be produced by the moving system and its mass, however, should be kept at a minimum to reduce pivot friction: a high torque/mass ratio is a good criterion of design. Accurate balance of the movement is of primary importance practically in portable instruments, which are used in the horizontal and vertical positions indiscriminately. Rigidity and robustness are also important features.

External means are usually provided for the mechanical adjustments of the moving system so that the pointer can be reset exactly to zero, if necessary. Measuring instruments should be treated with utmost care at all times to maintain the accuracy of the delicate moving system and to retain the essential stability of the magnetic properties.

An exception to most current-measuring instruments is that the moving-coil class will operate with either direct or alternating currents. If the deflecting torque is proportional to the first power of the current (T ∝ ± 1), the direction of deflection will obviously depend on the current direction; the position of such an instrument will tend to follow the reversals of alternating currents. Such instruments naturally have a linear scale, which is evenly divided throughout its ranges (see Figure 49.3).

Figure 49.3 Derivation of a Linear Scale

Most instruments have a deflection that is proportional to the square of the current [T ∝ (±I)2 = +I2]. Since the deflection is always positive, instruments that read alternating currents have a square law scale whose divisions tend to become crowded at the lower ends. However, by controlled distortions of the magnetic fields or other such factors, the scale on these instruments can be made approximately linear. The square law scale is illustrated in Figure 49.4.

Figure 49.4 Derivation of a Square Law Scale

A linear scale is most easily read by average observers on account of its greater everyday familiarity. Moving-coil instruments and watt meters follow this law: y = x, whose graph is plotted for comparison in Figure 49.3.

A square law graph, y = x2, is plotted in Figure 49.4 to show the derived scale. This is the law fundamentally followed by most instruments. Means may be adopted to open out their scales. Apart from the crowding at the lower values, some difficulty arises in interpolating intermediate unmarked values with any degree of accuracy.

Another scale sometimes used is the logarithmic scale, y = log x, plotted in Figure 49.5 to show its derivation. It is less easy to read than a linear scale. It is found in some Ohm meters and the decibel meter and it uses the slide rule scale. The scale in Figure 49.6 depicts an Ohm meter.

Figure 49.5 Derivation of Logarithmic Scale

Figure 49.6 Derivation of Ohm Meter Scale

Instruments available for a measurement are further classified according to whether they are suitable for (1) power supply frequencies (16–100 Hz), (2) audio frequencies (100–10,000 Hz), or (3) radio frequencies (10 kHz and onwards). The effects of self-inductance and self-capacitance tend to impair accuracy at the upper frequencies.

According to particular requirements, various grades of accuracy apply to measuring instruments. These grades may be classed as (1) standard, (2) substandard, (3) first grade, (4) second grade, and (5) commercial low grade. There is an advantage in using higher grade instruments than necessitated by the requirements of the results.

In practice, all commercial instruments have their scales calibrated from a substandard instrument, which is periodically checked against an approved standard.

The design of an instrument should be such that it consumes a minimum of power from the circuit for its operation. Service metres are frequently arranged to be switched in and out of the circuits requiring measurement; hence, it is important that the circuit constants are not disturbed by the introduction of the metre.

49.3  METRES

The more common electric metres may be roughly divided into the following classes:

  1. According to the function performed as
    1. Ammeters
    2. Voltmeters
    3. Ohm meters
    4. Watt meters
  2. According to the circuit in which they are used as
    1. Direct current
    2. Alternating current
  3. According to the principle of operation as
    1. Permanent magnet moving coil (PMMC)
    2. Dynamo metre
    3. Magnetic vane
    4. Induction.

The essential parts of these instruments generally include

  1. Means for providing a deflection torque (obtained by the interaction of magnetic fields);
  2. A spring or other means to provide a counter torque; and
  3. A pointer to indicate the resultant position of the moving element of the metre.

This instrument, which is essentially for d.c. use, may be designed as an amperemeter (ammeter) or as a voltmeter. It is a fairly robust instrument; for general work, it cannot be surpassed for accuracy and reliability.

Its operation depends on the force acting on a conductor when it carries a current and is placed in a magnetic field. The assembly of its essential components is illustrated in Figures 49.7 and 49.8.

A permanent magnet NS, suitably shaped to give a compact instrument, provides a powerful magnetic field between the pole pieces, PP, shaped to produce a cylindrical air gap. A high-grade permanent magnet is used that has previously been aged to preclude risk of subsequent variation in flux density. A soft iron cylindrical core C is screned into the base of the instrument concentrically with the pole faces. This core serves to concentrate the magnetic field within the narrow gap and ensures that this field is everywhere radial and uniform within the gap. In this way, the conductor moving in a (restricted) circular path will always cut a uniform field at right angles producing a maximum torque, which will be constant for any position of the conductor. The conductor of copper wire is wound into the coil upon a rectangular frame, F, of aluminium, set normally at the angle illustrated see Figure [49.8 (a) and (b)]. The movement is restricted to the use of the uniform portion of the field. The air gap is made as small as possible to limit the reluctance of the magnetic field. The coil frame is pivoted in jewelled bearings and controlled by spiral phosphor bronze control springs (CS) fitted at the front and back. These springs provide the restoring torque and also serve to make electrical connection with the moving coil. To minimize the effect of temperature changes, these springs are arranged to work in opposition to one another. In the zero position, the springs are in equilibrium and as the pointer is deflected, the spring is either wound or unwound. The moving system carries a light pointer, which travels across the calibrated scale, the extremities of travel being limited by two stops. A small weight is fitted to counter the effect of the pointer and to preserve the balance of the moving system. The pointer is set to zero by turning an external screw, which controls the fixed point of one of the restoring springs.

Figure 49.7 Principal Parts of a Permanent Magnet, Moving-Coil Meter Movement

Figure 49.8 (a) A Typical Moving-Coil Assembly (b) Three Balance Weights are Used to Statically Balance the Unit

The current to be measured (I amperes) sets up a force (F Newton) on each conductor of the coil such that F = BIl Newton, where B is the flux density (Wb/m2) and l is the length of a conductor. If the coil has N turns (=2N conductors) of radius r m, the deflecting torque would be as follows:


T = Fr ∝ 2B1lNr        (49.1)


the product 2rl is the area Am2 of the coil, so that in general


T ∝ BINA N – m        (49.2)


Turns may be varied so that a full-scale deflection is reached with as little as 0.1 mA with a commercial instrument and with a fraction of a microampere in a suspension-type laboratory instrument. In the absence of restoring springs, the coil would set itself at right angles to the magnetic field with any value of current sufficient to overcome the inertia of the moving system. When the coil is deflected through an angle θ°, if T Nm is the torque required to twist the restoring springs through 1°, the total restoring torque is T θ. The pointer comes to rest at the position where the deflecting and restoring torques are balanced, i.e. when


T θ = BINA        (49.3)


The inertia of the system tends to cause the moving pointer to overshoot and, on account of the restoring torque, to oscillate about the correct reading. The eddy currents induced in the aluminium frame set up an opposing force, tending to resist all movement. This damping renders the instrument ‘dead beat’ and enables readings to be taken without delay.

When enclosed in an iron case or when suitably screened, the moving-coil instrument is unaffected by stray magnetic fields.

In the expression T ∝ BINA, the factors BN and A are constant for any given instrument and the deflection is directly proportional to the current I. The scale is accordingly linear. The terminals of a moving-coil instrument are clearly marked + and –, and care must be taken to connect the metre in the circuit correctly. If an alternating current is applied to such an instrument, its pointer tends to follow each half-cycle; however, on account of the inertia of the moving system, a slight vibration occurs about the zero point, and that too only at low frequencies.

With the addition of a metal rectifier, the moving-coil instrument is used to measure alternating currents or voltages. It may be used for the same purpose in association with a thermocouple.

The moving-coil instrument is adopted by a suitable resistance value to serve either as a voltmeter or as an ammeter. In a common form of high-grade instrument, a full-scale deflection is produced by a current of 10 mA. Provided this current in the moving coil is not exceeded, the metre may be shunted and used to measure higher currents, or fitted with a series resistance to measure high voltages.

The moving coil is made of copper, which has a temperature coefficient of resistance of about 0.4 percent per degree centigrade. If the instrument is unshunted, an increase in resistance consequent upon temperature rise is accompanied by an increased p.d. and there is no error in current indication. If a shunt having a negligible temperature coefficient is used, the combination will be correct at only one temperature. This source of error is avoided by joining a ‘swamping’ resistance of Eureka or constant an in series with the copper winding, so that the resistance of the copper is one quarter of the whole. In this way, a possible error of about 0.4 per cent per degree centigrade can be reduced to less than 0.1 per cent per degree centigrade, as the springs and magnet both weaken slightly with increase in temperature. In a voltmeter, the series resistance is itself α swamp and the temperature error is quite negligible.

Note: Another important type of metre movement is the taut band movement. This movement is similar to the conventional D Arsonval type, but it does not employ the bearings, spiral hair springs, or jewels. The suspension band, which supports the pointer, is α short thin strip of alloy (platinum, iridium) tightly suspended between the coiled spring terminals. The coiled-spring terminals absorb physical shock and vibration; thus the movement is quite rugged. The taut band movement has an even more important feature. As the jewel and bearing construction is replaced by a band that twists in accordance with the amount of current through it, friction is practically eliminated. Taut band movements of very high sensitivity and reasonable cost are now widely used. Metres employing taut band suspension movements and having sensitivities of 100,000 Ohms per volt, 200,000 Ohms per volt, and up to 1–2 mega Ohms per volt are currently available.

Example 49.1

The sensitivity of a moving-coil metre movement is 1000 Ω/V. What is the value of full-scale deflection current?


Full-scale deflection current = 1/sensitivity.

= 1 mA


Yet another classification of measuring instruments is absolute instruments and secondary instruments. Absolute instruments provide the quantity to be measured in terms of the instrument constant and its deflection. For example, a tangent galvanometer gives the value of the current to be measured in terms of the tangent of the angle of deflection produced, the horizontal component of the earth’s magnetic field, the radius, and the number of turns of the wire used. Such instruments are used in laboratories and in similar institutions as standardizing instruments.

Secondary instruments provide the magnitude of the electrical quantity to be measured directly and are required to be calibrated by comparison with either an absolute instrument or another secondary instrument that has already been calibrated. These instruments are widely used in practice.

49.5.1  Types of Secondary Instruments

Secondary instruments can be further subdivided into three groups as (1) indicating instruments, (2) recording instruments, and (3) integrating instruments.

  1. Indicating instruments: Indicating instruments indicate the magnitude of the electrical quantity being measured at the time when it is being measured. The indications are given by a pointer moving over a graduated dial. Ordinary ammeters, voltmeters, watt meters, frequency meters, power factor metres, etc. fall into this class.
  2. Recording instruments: These instruments keep a continuous record of variations of the magnitude of the electrical quantity to be observed over a definite period of time. In such instruments, the moving system carries an inked pen, which touches lightly a sheet of paper wrapped over a drum moving with a uniform slow motion in a direction perpendicular to that of the deflection of the pointer. Thus, a curve is traced, which shows the variations in the magnitude of the electrical quantity under observation over a definite period of time. Such instruments are generally used in power houses where the current, voltage, power, etc. are to be maintained within certain specified limits.
  3. Integrating instruments: These instruments measure the total amount of either the quantity of electricity (ampere hours) or electrical energy supplied over a period of time. The summation given by such an instrument is the product of time and the electrical quantity under measurement. Ampere-hour metres and energy metres fall into this class.

Temperature coefficient of the stiffness in a spring results in a temperature coefficient which is an indication of the instrument, and inelastic yield in the spring results in displacement in the zero position of the moving system. It is advantageous to substitute gravity control (Figure 49.9) for spring control in electrical measuring instruments. Gravity control is free from the effects mentioned above.

In gravity-controlled instruments, a small weight is attached to the moving system in such a way that it produces a controlling torque when the moving system is in a deflected position. The controlling torque can be varied quite easily by adjusting the position of the controlling weight upon the arm. The usual arrangement is illustrated in Figure 49.9.

Figure 49.9 Gravity Control

In the undeflected (zero) position of the pointer, the control weight is vertical. When the pointer is deflected, the control weight will be in a direction shown along the dotted line in Figure 49.9. In the deflected position, the controlling torque will be Wl sin θ, where W is the control weight, l the distance from the axis of rotation, and θ the deflection or Tc α sin θ. If Td ∝ I, then at the final deflected position


Td = Tc   or
I α sin θ or I = k sin θ    and    θ = sin-1(1/k)        (49.4)


Hence, in gravity-controlled instruments, the scales are not uniform but are crowded in the beginning. This, of course, is a disadvantage when the pointer lies in the lower scale values where it will not be possible to read the instrument scale accurately on account of it being cramped.

Gravity-controlled instruments must be used in a vertical position to operate the control. Gravity control is cheap, unaffected by changes in temperature, and is free from fatigue or deterioration with time, but it gives a cramped scale and the instrument has to be kept in a vertical position.

Such instruments usually have a bubble level mounted to indicate the reference plane in which they have been calibrated. By returning the instrument to the reference plan the control forces resulting from any residual unbalance in the system act in precisely the same way that they did at the time of calibration.

Example 49.2

If the deflection torque of an instrument is directly proportional to the current to be measured and the maximum current produces a deflection of 90°, compare the deflection in the spring-controlled instrument with a similar instrument having gravity control for a current equal to half the maximum value.


Deflecting torque = Td α I

In a spring-controlled instrument,

Deflection for a current equal to half the maximum value will be

In a gravity-controlled instrument,


Deflection for current equal to half the maximum value will be


There are two distinct types of moving-iron instruments. They differ according to whether deflection is produced by attraction or repulsion (see Figure 49.10). The former makes use of the attraction of iron in the electromagnetic field of a current-carrying solenoid. The latter depends on the mutual repulsion of two similarly magnetized pieces of iron within an energized solenoid, one being fixed and the other movable.

In each type, the iron forms but a small part of the magnetic circuit. Consequently, the air path reluctance is high with the result that power consumption is high, and the instrument, unless well screened, is susceptible to the influence of stray magnetic fields.

49.7.1  Attraction Type

The principle of the attraction type is illustrated in Figure 49.11(a). A light soft iron vane, V, is pivoted eccentrically close to one face of a solenoid, CC. The vane carries a light pointer capable of moving over a calibrated scale. When a current flows in the solenoid, the vane becomes magnetized by induction; consequently, it is attracted towards the centre of the solenoid. The opposing torque is provided by a spiral spring, CS. A small air piston, A, is carried upon the moving system, which is capable of moving against an air cushion within a curved cylinder; this provides the damping device. Alternatively, damping may be provided by eddy currents induced in a conducting disc, which is fixed to the same spindle as the magnet vane, and on deflection, rotates between the poles of permanent magnets as shown in Figure 49.11(b).

The magnetizing force of the solenoid is proportional approximately to the current, and so is the pole strength induced in the vane. The deflecting force, which is proportional to the product of the magnetic intensities of the solenoid and vane, becomes proportional to the square of the current. The metre scale is fundamentally a square law one, but by suitably shaping the vane, the scale may be made to approach a linear law.

Figure 49.10 Types of Moving-Iron Instruments (a) Attraction (b) Repulsion

Figure 49.11 (a) Principle of Moving Iron (b) A Magnetic (Eddy Current) Damping Mechanism

Sometimes called a moving-iron-vane instrument, it is often used for ammeters and voltmeters. This instrument depends for its operation on the reactions resulting from the current in one or more fixed coils acting on one or more pieces of soft iron or magnetically similar material in the moving system as illustrated and elaborated in Figure 49.11.

Note: If two similar and adjacent iron bars are similarly magnetized, a repelling force is developed between them, which tends to move them apart. In the moving-iron instrument, this principle is used by having one bar fixed in space and by pivoting the second so that it will tend to rotate when the magnetizing current flows. A spring attached to the moving vane opposes the motion of the vane and permits the scale to be calibrated in terms of current flowing. When current flows through the solenoid, the plunger is drawn into the coil and a measurable deflection of the instrument pointer is obtained (see Figure 49.12). However, because of high power consumption, sensitivity to zero shifts, scale difficulties, etc., this type of movement is presently used only in less-expensive instruments.

Figure 49.12 Working Principles of the Moving-Iron-Vane Instrument

49.7.2  Repulsion Type

In the repulsion type of instrument (Figure 49.13), two thick soft iron wires are placed close together within an air-cored solenoid (CC), with their lengths parallel to the axis of this coil. One iron wire (F) is fixed to the instrument case and the other (M) is pivoted and carries the pointer. When a current flows in the solenoid, the iron pieces are magnetized similarly by induction and their mutual repulsion provides the deflecting force. The controlling force is provided by the spiral spring, S. Damping is normally by air piston (A). The pole strength of each iron is approximately proportional to the current in the coil. As the force of repulsion is proportional to the product of these pole strengths, the deflection is fundamentally dependent on the square of the current. The flux density does not follow the current changes exactly over the working range. Also, the induction and the repulsive force decrease as the distance between the fixed and moving iron increases (f ∝ 1/d2). This produces a slightly more uniform scale.

Some improvement in the form of scale is obtained by the use of specially shaped pieces of iron instead of simple bars. The design of such an instrument is shown in Figure 49.14(a), the moving and fixed iron pieces M and F being shown in the plan in Figure 49.14(b), and in the developed form in Figure 49.14(c). The fixed iron covers a larger area than the moving iron and it is narrow shaped at one end than at the other. When the solenoid is energized, the moving iron is repelled towards the narrow end of the fixed iron. The controlling spring is shown at CS. B is an adjustable balance weight and Z is the zero adjustment lever. Damping is affected by the air piston and chamber at A (Figure 49.13).

Figure 49.13 Principle of Moving-Iron Metre Repulsion Type

Moving-iron instruments may be designed either as voltmeters or as ammeters. They may be employed for measuring either direct or alternating circuits as their deflection is independent of current direction. In the former case (d.c.), the direction of current flow through the instrument is, of course, immaterial. When used for a.c., the instrumental measures r.m.s. values.

Figure 49.14 Moving Iron Metre: Construction of Repulsion Type

Used as a voltmeter, as with the moving-coil instrument, α swamping noninductive resistance of low temperature coefficient is used in series with the solenoid to reduce the temperature error. This instrument produces a further gain as the inductance is also swamped, which reduces the frequency error and the difference between d.c. and a.c. readings. Shunts may be used to increase the instrument range in both d.c. and a.c. instruments of this class.

The main advantages of the moving-iron instrument are its relative simplicity, low cost of production, and its robust character (as the coil is fixed, it can be readily wound to suit its purpose). In contrast, the power consumption of moving-iron instruments is somewhat high and their accuracy does not equal that of the moving-coil instrument. Moving-iron instruments are subject to slight error if used in the vicinity of stray magnetic fields. They are also liable to hysteresis errors a given current value giving a smaller reading when the current is rising than when it is falling; however, these disadvantages are largely overcome by using nickel iron alloys of low hysteresis.

The inductance of moving-iron instruments is relatively high and they are not independent of frequency on account of their hysteresis and eddy current effects. They are also affected by changes in coil resistance with variations in temperature. Hence, as an a.c. instrument, the moving-iron metre is the most suitable for power supply frequencies of approximately sine-waveform.

The moving-iron instrument operation well or d.c. on a.c. and first-grade accuracy is possible. On a.c. measurements, the scale reads r.m.s. values, but errors may occur with a waveform containing harmonics that reach saturation in the permeability curve. Moving-iron instruments are suitable for reading up to a few kilovolts and down to a few volts. As ammeters, the range is from a few mA up to about 500A, above which current transformers can be used for a.c. readings. The d.c. ranges are rather narrower than the a.c. ranges.


  1. The instrument differs in construction principles from the previously described moving-iron-vane instrument in that the magnetic vane embedded in the side of the coil has definite N and S poles at the points shown (Figure 49.15). The moving vane will be magnetized by induction with the polarities as shown. Notice that the north pole of the moving vane is closest to the North Pole on the piece of magnetic material embedded in the coil; the South Poles are also similarly placed. Hence, the vane tends to move away or be repelled from the stationary magnetic pole.
  2. If alternating current is applied to the instrument, the two vanes will simultaneously change polarities as the current varies throughout the cycle; thus, the instrument also operates on alternating current. In fact, the instrument finds its greatest application in a.c. measurements.

A polarized type of moving-iron instrument is also used. The moving system is simply a soft iron armature carrying a pointer; being polarized by a small permanent magnet, the instrument is essentially for d.c. use with a linear scale. A coil carrying the current to be measured is mounted near or around the armature but has its axis at right angles to that of the normal position of the armature. When current flows, the coil produces a field at right angles to the permanent field; the resultant field is distorted and the armature is deflected. No restoring spring is fitted as the armature is normally controlled by the permanent magnet field. Although such instruments do not have a high grade of accuracy, they are very cheap to produce. Figure 49.16 shows a simple central zero pattern. NS is the permanent magnet, A the armature, and C is a two-turn coil, which, in the metre illustrated, produces a magnetomotive force of ±40 ampere turns.

Figure 49.15 Principle of a Simple Magnetic-vane Repulsion-type Metre

Figure 49.16 Polarized Moving-Iron Instrument

Example 49.3

The torque of an ammeter varies as the square of the current passed through it. If a current of 10A produces a deflection of 90°, what deflection will be required for a current of 5A when the instrument is (1) spring controlled and (2) gravity controlled.


Deflection torque Td I2

  1. In spring-controlled instruments, since-controlling torque Tc α θ and deflection

    For a deflection of 5-A current, or

  2. In gravity-controlled instruments

    Controlling torque Tc α sin θ, and sin θ α I2

Example 49.4

The torque of an ammeter is directly proportional to the current flowing through it. If a current of 10A causes a deflection of 60°, determine the value of current for a deflection of 40° when the instrument is (1) spring controlled and (2) gravity controlled.



I1 = 10 A, θ1 = 60º, θ2 = 40º
  1. In a spring-controlled instrument
  2. In a gravity-controlled instrument

Example 49.5

A moving-coil millivoltmeter has a resistance of 200 Ω and the full-scale deflection is reached when a p.d. of 100 mV is applied across its terminals. The moving coil has effective dimensions of 30 mm × 25 mm and is wound with 100 turns. The flux density in the gap is 0.2 Wb/m2. Determine the control constant of the spring if the final deflection is 100°.


Deflecting torque Td = B I l.N = 0.2 × 0.5 × 10-3 × 30 × 10-3 × 25 × 10-3 ×100

= 75 × 10-3 N.m

Full-scale deflection torque, θFSD = 100°

Control constant

Example 49.6

The resistance of a moving-coil voltmeter is 12,000 Ω. The moving coil has 100 turns and is 4-cm long and 3-cm wide. The flux density in the air gap is 6 × 102 Wb/m2. Find the deflection produced by 300 V, if the spring control gives a deflection of one degree for a torque of 25 × 103 N.m.


Current flowing through the coil

Deflecting torque Td = NBI lr = 100 × 6 × 10-2 × 0.025 × 0.04 × 0.03

= 18 × 10-5 N.m


Controlling torque Tc = 25 × 103 θ N.m where θ is the deflection in degrees produced by 300 V.


For steady-state deflection, Tc = Td and


25 × 10-7 θ = 18 × 10-5

In general construction, this class of instrument is similar to the moving-coil metre but instead of a permanent magnet the field is provided by an electromagnet. The characteristics of the dynamometer instrument depend on the excitation of the electromagnet in addition to that of the moving coil. If a direct current of constant magnitude is applied to the field coils, the instrument will have the same performance as in a moving-coil metre. In contrast, if the field coils and moving coil are energised (either in series or in parallel) both from the same source, the deflecting torque depends on the product of the currents in the moving coil and in the field coils. Accordingly, in this case, the instrument will have a square law scale and being no longer polarized it will be equally suitable for a.c or d.c.

If the permanent magnet is replaced with stationary coils arranged as shown in Figure 49.17 and the moving and stationary coils are connected in series, the moving coil will be deflected by an alternating current. This deflection is obtained because, when the alternating current reverses, the current in the fixed and moving coils reverses at the same instant, resulting in a pulsating torque, which is always in the same direction. The amount of deflection depends directly on the amount of alternating current flowing through the coil system.

Figure 49.17 Arrangement of Coils in a Dynamometer-Type Metre

The principle of operation of this type of metre has resulted in the design of the modern dynamometer as shown in Figure 49.18. Regardless of the degree of refinement used in the construction of this instrument, it takes a considerably larger amount of current than the permanent magnet type employed in direct-current measurement. Here, the current being measured must supply energy not only for the moving coil, but also for the field winding, which was supplied by the magnet in the case of the permanent-magnet instrument.

Figure 49.18 Principal Parts of a Dynamometer Mechanism

The instrument may be designed as a voltmeter (Figure 49.19(a)) or as an ammeter (Figure 49.19(b)), and can be used to measure either a.c or d.c supplies. The air gap field is parallel and not radial owing to the absence of any iron core; hence, the torque decreases as the deflection increases. This factor results in some opening out of the scale. The restoring torque is usually provided by a coiled spring. Damping is by an air piston and cylinder owing to the undesirability of the presence of a permanent magnet for eddy current damping.

There is no advantage in using this instrument for d.c. voltage and current measurement, as its power consumption is greater than that of the moving-coil instrument in which most of the power is provided by the permanent magnet. The main field of application for the dynamometer instrument is as a Wattmeter. In this case, the moving coil is a pressure coil and it is connected across the supply leads. It carries a current proportional to the applied p.d. The coil is wound upon a non-magnetic frame and to prevent error due to temperature changes, a noninductive winding of magnanin is connected in series with the coil having a four times greater resistance than the latter. Two field coils are provided and connected in series. They are of heavy gauge wire or strip to carry the load current or a part of it.

An air core is normally employed throughout, but recent developments in low-hysteresis nickel-iron alloys have made possible a ferromagnetic path and have brought about a reduction in power consumption. A diagram showing the connections of the instrument as a watt meter is given in Figure 49.19(c).

Without iron losses, the dynamometer measures true power (V I cos ϕ watts); the scale is linear, the deflection being proportional to both V and I. This instrument is liable to be affected by stray magnetic fields, but with an air core, it is practically independent of frequency and waveform, errors and power losses due to hysteresis and eddy currents are minimized by reducing all metal parts to a minimum and laminating where necessary.

Figure 49.19 Arrangement of a Dynamometer When Used to Measure (a) Voltage (b) Current and (c) Power Consumption


These instruments can only be used on a.c. circuits. Their main advantages are (1) a full-scale deflection of about 300° can be achieved, giving a long and open scale, (2) the effect of stray magnetic fields is small, and (3) damping is easier and more effective.

These instruments depend for their action on the torque produced by the reaction between a flux, whose magnitude depends on the values of the current and voltage to be measured, and eddy currents, which are induced in a metal disc or drum by another flux, whose value again depends on the current or voltage to be measured.

We know that (1) the magnitude of eddy current is proportional to that of the flux inducing it; (2) the torque at any instant is proportional to the square of the current or voltage producing it; and (3) the mean torque is proportional to the mean value of this current or voltage.

Consider a flux ϕ, producing a torque by the force it exerts on an eddy current I lagging this flux in phase by an angle ∝. Then


ϕ = ϕmax sin θ   and  I = Imax sin (θα)        (49.5)


The instantaneous torque is proportional to the product of instantaneous current and instantaneous flux, and we have Tr α ϕ I

The mean torque is given by


Tm α I ϕ cos α        (49.6)


where, φ and I are the r.m.s values of the current and flux., if α = 90º, Tm = 0.

Therefore, some means have to be provided for producing an eddy, which is either appreciably less than or greater than 90° out of phase with the flux. This is achieved by two general methods, leading to two general types of induction instruments: the Ferraris type and the pole-shading type.

49.10.1  Ferraris-type Induction Instruments

This method employs splitting of the winding of the electromagnet in which the flux exists into two portions, one that is highly inductive and the other that is noninductive. This type of instrument works on the same principle as the induction motor. A rotating field is produced by two pairs of coils wound on a laminated magnet system, as shown in Figure 49.20, wherein P is the pointer, LM the laminated magnet core, and A the aluminium drum. The two pairs of coils are supplied from the same source, but the currents flowing through them are about 90° out of phase. This phase shift is obtained by connecting an inductor L in series with one pair of coils and a high resistance R in series with the other. The rotating field induces currents in an aluminium drum, causing it to follow its rotation. However, if the drum were free to the rotate, it would rotate at a speed slightly less than that of the rotating field and in the same direction as the latter. If a control spring prevents such continuous rotation, the drum will rotate through some angle less than 360° i.e., until the operating torque is balanced by the controlling torque of the spring.

The drum and the moving system are carried by a spindle whose ends fit in jewelled cups or bearings. The drum has a cylindrical laminated iron core on the inside to strengthen the magnetic field cutting the drum. The spindle also carries an aluminium damping disc, the edge of which moves in the air gaps of the two permanent magnets.

Figure 49.20 Ferraris-type Instrument

49.10.2  Shaded-Pole Type

This type, as shown in Figure 49.21, splits the phase of the working flux by a copper band placed round a portion of the poles of the electromagnet. A thin aluminium disc is mounted on pivots and jewel bearing springs are employed to provide the controlling torque. Half of each of the pole faces is surrounded by a copper band to split the working flux. The copper band acts as a single-turn short-circuited secondary winding.

Figure 49.21 (a) Shaded-Pole Induction Type Instrument (b, c) Phasor Diagram

Let ϕ, be the flux of the unshaded portion of the pole. The flux ϕ1 will induce an e.m.f. E in the ring, as shown in Figure 49.21, which lags the flux ϕ1 by 90°. The induced EMF will cause a current, say I, to flow in the copper ring, which will be lagging behind the flux ϕ1 by 90°. The current flowing in the copper ring will produce its own magnetic field, say ϕ2, in phase with currents.

Let the fluxes ϕ1 and ϕ2 in unshaded and shaded portions of the pole, respectively, induce e.m.f.s E1 and E2 in the disc, each of which is 90° in phase behind the flux inducing it. These induced e.m.f.s E1 and E2 will induce eddy currents (say I1 and I2) in the disc lagging by a small angle (say α) behind its voltage due to the inductance of the path in the disc. The phasor diagrams in Figure [49.21 (b) and (c)] show that each of the currents I1 and I2 has a component in phase with the other flux, such as I1 and I2. Hence, two torques acting on opposite directions are developed in the instrument. These two torques result in an operating torque.

Deflecting torque T = K (ϕ2I1ϕI2)where, K is α constant

= K [ϕ2I1 cos{90° – (βα)} – ϕ1I2 cos(90° + α + β)]

= K [ϕ2I1 sin (βα) – ϕ1I2 sin(β + α)]


If ϕ1, ϕ2, I1, and I2 are all r.m.s values

Eddy e.m.f.s, E1 α f ϕ1 and E2 α f ϕ2

and eddy current, where Z is the impedance of the eddy current path

and eddy current

Mean deflecting torque, where, K is another constant

The above equation for mean deflecting torque shows the following:

  1. The deflecting torque is directly proportional to cos α. Therefore, to obtain the largest possible deflecting torque, angle α should be as close to zero as possible. For this, it is necessary that the path of the eddy currents should be highly resistive.
  2. The deflecting torque is directly proportional to sin β; therefore, to have α large deflecting torque, angle β should be as close to 90° as possible.
  3. Maximum torque will be developed when α = 0° and β = 90°, i.e. when the path of the eddy currents is purely resistive and the two fluxes ϕ1 and ϕ2 are displaced by 90°.

49.10.3  Induction-type Watt Meters

Induction-type watt meters, the principle of which is the same as that of induction ammeters and voltmeters, are only used on a.c. circuits: dynamometer watt meters can be used in either a.c. or d.c. circuits.

Induction instruments are useful only when the frequency and supply voltage are approximately constant.

The instrument has two laminated electromagnets, as can be seen in Figure 49.22, where one is excited by the load current (or a definite fraction of it) and the other by a current proportional to the voltage of the circuit in which the power is to be measured. A thin aluminium disc is mounted so that it is cut by the flux of both these magnets; the deflecting torque is produced by the interactions between these fluxes and the eddy currents that may induce in the disc. One or more copper rings are fitted on one core limb of the shunt magnet, i.e., the magnet excited by the voltage coil, and its current winding to cause the resultant flux in the magnet to lag in phase by exactly 90° behind the applied voltage.

Figure 49.22 shows two common forms of magnets with their windings in the magnets being placed, in each case, one above and one below the moving disc of the instrument. The positions and shapes of the magnets are such that the flux from both the shunt and series magnets cuts the moving disc.

In the form of instrument as shown in Figure 49.22(a), the two voltage coils, connected in series, are wound so that they both send flux through the centre limb. The series magnet in the instrument carries two small current coils in series; they are wound so that they both magnetize the coil, upon which they are wound, in the same direction. The positions of the copper shading bands can be adjusted to obtain the correct phase displacement between the shunt and series magnet fluxes.

In the instrument shown in Figure 49.22(b), there is only one voltage coil and one current coil. A copper shading band, whose position is adjustable, surrounds the two projecting pole pieces of the shunt magnet.

Both types are spring controlled and have the advantage of a long and uniform scale (up to 300°).

Currents up to about 100 A can be managed directly in such instruments. For higher currents, a current transformer is used in conjunction with the watt meter. Unlike the dynamometer wattmeter, the voltage-coil circuit of the induction instrument is made as inductive as possible so that the flux of the shunt magnet may lag by nearly 90° behind the applied voltage.

Figure 49.23 gives a simplified vector diagram for the wattmeter. The flux ϕsh of the shunt magnet is assumed to lag exactly 90° behind the applied voltage. This is actually brought about by adjusting the shading bands, as the angle of lag would be somewhat less than 90° unless such bands were used.

Figure 49.22 Induction Watt Meters

Figure 49.23 Vector Diagram for Induction Watt Meter

It is also assumed that the flux ϕsc of the series magnet is proportional to and in phase with the line current, and that hysteresis and saturation effects in the iron are negligible. Owing to the large air gap in the core, these assumptions are justifiable.


Operation of the hot-wire instrument depends on the expansion of a wire when its temperature is increased by the passage of the current being measured. The essential components of the system are shown in Figure 49.24. The hot wire A is made of a material with a high melting point and high resistivity, which is usually platinum silver. It is held taut between the terminals TT, one of them being adjustable to provide for zero correction. A second wire B made of phosphor bronze is attached on one end to the hot wire near its centre and the other end to an insulating block. Both wires are maintained in tension by means of a silk fibre F stretched between the phosphor-bronze and a flat steel spring S; this fibre passes around a small pulley, which carries the pointer. When a current in the heater increases its temperature and causes it to expand, the sag is taken up and magnified by the second wire and the fibre, the latter producing a rotation of the pulley and a deflection of the pointer. Damping is normally provided by eddy currents induced in a small vane (K) fitted to the moving system to rotate between the poles of a permanent magnet M (see Figure 49.25).

Figure 49.24 Hot-Wire Ammeter (a) Contribution (b) Principle

To allow for variations of atmospheric temperature, the metre base upon which the heater wire is supported is usually made of an alloy that has the same temperature coefficient as the heater wire. In some instruments, the centre point of the heater wire is connected to one terminal of the instruments and current flows through the two halves of the heater wire in parallel.

The heat developed is proportional to I2Rt, i.e., to the square of the instantaneous current, and the hot wire metre has a square law scale.

This metre may be used to measure either direct or alternating currents; in the latter case the pointer-reads r.m.s. values, the scale being calibrated from a sub-standard metre. Owing to the time factor, hot-wire instruments tend to be sluggish in action.

One advantage of this class of instruments is that it is free from the drawbacks of the magnetic instruments for a.c. It is also relatively cheap to construct. In account of its low self-inductance and capacitance, which make it practically independent of frequency and waveform, it can be used for work related to audio and radio frequencies. In contrast, its mechanism is somewhat delicate and the instrument can stand very little current overload without damage. It has a fairly high power consumption, and its zero tends to vary with changes in atmospheric temperature, necessitating frequent readjustment of the zero point.

The metre may be shunted to read currents up to a few amperes, but owing to the variation of heater resistance with temperature, it cannot be used with different values of shunt resistance. For high current measurements (a.c.), it is customary to utilize a current transformer rather than a shunt. As a voltmeter, its range may be extended using a series resistance in the usual manner. Its main use is as an ammeter for audio and radio frequency currents, its range being roughly between 100 mA and 10 A.

Figure 49.25 Hot-Wire Metre Showing Damping

Figure 49.26 Constructional Details of the Hot-Wire Metre

Example 49.7

How will you adopt a hot-wire ammeter, having a resistance of 0.1 Ω and giving a full-scale deflection with a current of 10 A, to measure a maximum current of 100 A?


The p.d. across the 0.1 Ω metre to give a full-scale deflection, which is 10 A is (0.1 × 10) = 1V. To measure 100 A, the metre should be shunted to direct 90 A, the p.d. across the shunt should be 1V, and the resistance should be 1/90 = 0.011 Ω.


The operation of this instrument (see Figure 49.27) depends on the e.m.f. generated at a bimetallic junction on increase of its temperature. The thermocouple element comprises a heater wire of a high-resistance alloy, such as constantan were, which carries the current being measured through the terminals HH. At the centre of this heater wire, the junction of an iron eureka or a similar couple is welded. According to the heat developed by the current in the heater wire, an e.m.f. is generated at the hot junction. The p.d. so produced at the cold terminals CC is applied to an ordinary moving-coil milli voltmeter. The readings on the milli voltmeter are proportional to the square of the heater currents; however, if the thermo couple is applied to a moving-coil instrument whose air gap is suitably modified to give an inverse square law scale, it results in an almost linear scale.

Figure 49.27 Principle of Thermocouple (a) Thermo Junction (b) Thermocouple

A thermocouple element is illustrated in Figure 49.28. Alternative constructional forms of the thermocouple are (a) the heater and the metallic strip are enclosed in exhausted glass envelopes and (b) the elements are mounted in a standard four-pin base of the electronic valve pattern. The vacuum type is sensitive due to the absence of air cooling by convection.

The thermocouple is sensitive to very small currents; having exceedingly low values of inductance and capacitance, it is independent of frequency and waveform and is particularly suited for measurements at radio frequencies. The instrument is also suitable for measuring alternating currents at radio-frequencies, and also direct currents. It is available as a voltmeter or as an ammeter. A fairly wide range may be covered, up to several hundreds of volts and from a few milli amperes to several hundreds of amperes.

Similar to hot-wire metres, thermocouple instruments are inclined to be sluggish in action and liable to be easily damaged by overload currents.

An insulated type has one or more couples held close to, but not in contact with, the heater. Vitreous glass is used for good heat conduction to assist in rapid response and good electrical insulation.

Figure 49.28 Thermocouple Element


A galvanometer is an instrument that can indicate a small electric current. It is not usually scaled quantitatively. The pivot galvanometer is essentially a moving-coil instrument with a very high degree of sensitivity, which can obtained by a reduction bearing friction consequent upon the use of a single pivot for the moving coil.

Galvanometers are usually used to determine a balance condition, by determining the absence of current flow between parts of a circuit. As the moving-coil movement is a current-sensing device, producing a deflection depending on the direction of the applied current and proportional to its magnitude, it is ideally suited for this purpose. Hence, a satisfactory detector for use in d.c. bridge circuits can be devised by arranging for the zero current condition to occur when the pointer is positioned at the centre of the scale and the pointer being free to move in a positive or negative direction depending on the direction of the current in the coil. The pointer versions have limited sensitivity (typically –50 to +50 μA). To measure very small currents, or for use as a sensitive null detector, galvanometers of high sensitivity (typically 430 mm/μA) are required, which means the coil should have a large number of turns (bounded together for maximum strength and stability) and suspended by a high tensile alloy strip. This type of suspension strip, as shown in Figure 49.29, provides the small control torque and also acts as connections to and from the coil. A small amount of fluid damping may be included, but the major part of damping is electromagnetic. To obtain a large deflection for a small movement of the coil, the reflection of a light spot is used by means of an optical system within the galvanometer, which results in a larger magnification.

49.13.1  The Principle of Optical System

The principle of the optical system is shown in Figure 49.30. On account of the use of a reflected beam of light, the incident and reflected rays making equal angle with the normal, the deflection shown by the light spot is twice as great as the deflection, which would be given by a pointer. Furthermore, the light beam acts as a point of indefinite length, and by increasing the distance between the seat and the mirror, the sensitiveness of the system may be enhanced.


This instrument depends for its action on the force of attraction between two conductors carrying unlike charges, one conductor being fixed and the other forming the moving system. The principle of construction is shown in Figure 49.31. The instrument is essentially a variable capacitor.

An aluminium vane or set of vanes (M) is mounted on a spindle, which is fitted between jewelled pivots and carries a light pointer. Each vane is capable of rotating between a pair of electrically connected fixed brass plates F. Except for a glass window, the instrument is totally enclosed within a metal case that acts as an electrostatic screen and is mounted on an insulating base. To minimize errors from possible electrification of the glass, the glass may be coated with a transparent conducting varnish, which is electrically connected to the case by a metal foil.

Figure 49.29 Light Spot Moving-coil Galvanometer (a) Galvanometer Movement (b) Optical System

Figure 49.30 The Principle of Optical System

Figure 49.31 Principle of Electrostatic Voltmeter: Vane Arrangement

The moving vane is generally in electrical contact with the case, from which the fixed plates are insulated.

When a p.d. is established from the instrument terminals across the fixed and moving vanes, they carry equal and opposite charges. The resulting force of attraction draws the moving vanes into the space between the fixed plates and deflects the pointer. An opposing torque is provided by a spiral spring, whose normal position is the pointer on the zero mark.

The deflecting force is proportional to the product of the charges on the fixed and moving vanes [F = Q1Q2 / 4πε0εrr2]. For a constant capacitance, these charges are proportional to the p.d. (Q = CV) and the deflection is normally proportional to the square of the applied p.d. There is some variation in capacitance as the overlapping area of the vanes changes with deflection, and the scale is somewhat modified from the square law. The square law scale may be modified by shaping the vanes so that the change in capacitance is not directly proportional to the change in angle. The electrostatic voltmeter is calibrated against a substandard.

Since the electrostatic voltmeter has a deflection that is independent of the direction of the applied p.d., it can be used for d.c. or a.c. (r.m.s) voltage measurements. It requires, a fairly high p.d. to produce deflection.

49.14.1  Properties of Electrostatic Voltmeter

  1. It measures true r.m.s values because the deflecting torque is proportional to V2 and the core; therefore, it can be used as a transfer instrument.
  2. It is used for d.c. and a.c., where it constitutes a capacitive load, thus limiting its general application to frequencies below 100 Hz. However; it may be used in radiofrequencies, where it can be employed for aerial tuning, although its use in applications other than measuring low frequency high voltages is comparatively rare.
  3. It is a comparatively fragile and expensive instrument.
  4. It is a high-input impedance instrument, for direct voltages its input resistance is that of the leakage path through the insulation.
  5. It has a nonlinear scale, approximately square law, but this may be modified by the shape of the vanes.
  1. All basic metre movements have a full-scale current rating and an internal resistance.
  2. Most electrical measuring instruments depend on the magnetic effect of current for their operation.
  3. Except for the electrostatic voltmeter, most electrical measuring instruments are in effect current-measuring devices.
  4. External means are usually provided for mechanical adjustment of the moving system.
  5. The essential parts of measuring instruments include the means to provide a deflecting torque, means to provide a controlling torque, and a pointer to indicate the position of the moving element of the metre.
  6. Moving-coil instruments are essentially meant for d.c. use.
  7. Moving-coil instruments can be designed as ammeters or as voltmeters.
  8. Moving-coil instruments may be used to measure a.c. current or voltages in association with a metal rectifier.
  9. Moving-iron instruments are also known as moving-iron-vane instruments.
  10. Moving-iron instruments measure r.m.s values.
  11. The dynamometer-type instrument may be designed as a voltmeter or as an ammeter and used to measure either a.c or d.c supplies.
  12. Induction-type instruments are useful only when the frequency and supply voltage are approximately constant.
  13. Hot-wire instruments have a square law scale.
  14. Owing to the time factor, hot-wire instruments tend to be sluggish in action.
  15. The hot-wire instrument has a fairly high power consumption and its zero tends to vary, necessitating frequent readjustments.
  16. The thermocouple is sensitive to very small currents.
  17. The thermocouple is independent of frequency and waveform and particularly suited for measurements at radio frequencies.
  18. A galvanometer is an instrument for indicating small electric currents.
  19. The sensitivity of the galvanometer may be enhanced by the use of an optical system.
  20. The scale of an electrostatic voltmeter may be suitably modified by shaping the vanes.
  21. Electrostatic voltmeters are high-input impedance instruments.
  1. Which instruments need a pre-calibrated scale?
    1. Absolute
    2. Secondary
    3. Indicating
    4. Recording
    5. Integrating
  2. The deflecting torque is
    1. > Controlling torque
    2. = Controlling torque
    3. < Controlling torque
  3. The two control springs are
    1. Wound in opposite directions
    2. Wound in the same direction
    3. Not wound
  4. The control spring should have a
    1. Large number of turns
    2. Small number of turns
  5. In zero position of the pointer, the control weight in gravity-controlled instruments is
    1. Horizontal
    2. Inclined at an angle
    3. Vertical
  6. Which instrument is used for measuring d.c. only
    1. Moving coil
    2. Moving iron
    3. Hot wire
    4. Thermocouple
    5. Electrostatic
  7. Friction is practically eliminated in
    1. Moving-coil instruments
    2. Taut band suspension instruments
    3. Moving-iron instruments
  8. Eddy current damping cannot be employed in
    1. Moving-coil instruments
    2. Moving-iron instruments
    3. Hot-wire instruments
  9. No-return springs are used in
    1. Moving-coil instruments
    2. Moving-iron instruments
    3. Electrodynamometer instruments
  10. A crossed-coil movement is used in
    1. Electrodynamometer instruments
    2. Moving-coil instruments
    3. Moving-iron instruments
  11. Which instrument is slow to respond to changes?
    1. Moving coil
    2. Thermocouple
    3. Hot wire
    4. Electrostatic
  12. Which instrument cannot be adapted to measure current or resistance?
    1. Moving coil
    2. Electrostatic
    3. Moving iron
  13. Damping used in moving-iron instruments is
    1. Air friction
    2. Eddy current
    3. Fluid friction
    4. Any one of these
  14. In a permanent moving-coil instrument, the deflecting torque is proportional to
    1. I2
    2. 1/I
    3. I
    4. 1/I2
  15. The resistance of a voltmeter compared with that of an ammeter is
    1. Very low
    2. Equal
    3. Very high
    4. Equal to twice
  16. Ammeters and voltmeters come under the category of
    1. Indicating instruments
    2. Recording instruments
    3. Integrating instruments
    4. Standard instruments
  17. Dynamometer-type moving-coil instruments can be used to measure power in
    1. a.c circuits only
    2. d.c circuits only
    3. Both a.c and d.c circuits
    4. None of these
  18. In instruments provided with spring control
    1. Td α I
    2. Tc α I
    3. Tc α θ
    4. Td α θ
  1. (b)
  2. (b)
  3. (a)
  4. (a)
  5. (c)
  6. (a)
  7. (b)
  8. (b)
  9. (c)
  10. (a)
  11. (b)
  12. (b)
  13. (a)
  14. (c)
  15. (c)
  16. (d)
  17. (c)
  18. (c)
  1. What are the different torques in indicating instruments? How are they produced?
  2. Derive an expression for the deflecting torque of a moving-coil instrument.
  3. What is the difference between an ammeter and a voltmeter?
  4. Differentiate between moving-coil and moving-iron instruments.
  5. With the help of a suitable sketch, explain in detail the working of a moving-iron repulsion type metre.
  6. Explain why some instruments have uniform (linear) scales while others have cramped (nonlinear scales).
  7. Compare the moving-coil movement with the moving-iron movement.
  8. How does a hot-wire instrument work? What are its limitations?
  9. How is a taut band suspension movement superior to a moving-coil movement?
  10. Compare the merits and demerits of moving-iron instruments and dynamometer-type instruments. Which one is superior and why?
  11. A permanent magnet moving-coil instrument has a full-scale deflection of 90° for a current of 2A. Find the current required for a deflection of 30° if the instrument is (1) spring controlled and (2) gravity controlled.
  12. A weight of 5 g is used as the controlling weight in a gravity-controlled instrument; find its distance from the spindle if the deflecting torque corresponding to a deflection of 60° is 1.13 × 10–3 N.m.

11.  (1) 1.18 A (2) 1.414 A

12.  26.6 mm