CHAPTER 11 PRINCIPLES OF D.C. MEASUREMENT

11.1     HOT-WIRE INSTRUMENTS

Electrical quantities such as pressure (voltage) and flow (current), being invisible to the eye, can only be measured indirectly by observing their effect on other things such as a mechanical indicating system.  Even in the mechanical field steam or hydraulic pressure is indicated on a pressure gauge, and flow rate or flow volume on a flowmeter.

In the electrical world the first ‘indirect’ means of measurement used the heating effect of a current passing through a wire.  In Chapter 4 it was shown that, if a current I amperes flows through a conductor having a resistance of R ohms, then heat is generated in that conductor at the rate of I²R watts.

This heat in the wire raises its temperature until the rate of radiation away of the heat just balances the rate of heat generation.  At that point the temperature will stabilise, and it will then be a measure of the current (strictly, the square of the current) which was causing the heating.

FIGURE 11.1

HOT-WIRE AMMETER

Use of this is made in the ‘hot-wire ammeter’ shown in Figure 11.1.  A short length of platinum-iridium wire is connected electrically in series with the circuit whose current flow is to be measured.  The wire is tensioned until it is fairly taut, and from its centre is taken a silk thread tensioned by a spring and whose movement actuates a spindle to which a pointer is fixed.

When no current flows through the main wire its tautness keeps it almost straight, and the centre thread is at its left-most position.  When current flows the temperature of the wire rises, and the wire becomes longer and slacker.  The slack is taken up by the spring pulling on the centre thread and moving it to the right.  In doing so the spindle is rotated clockwise, and the pointer moves over a scale.

Since any given current causes a given I²R heating rate and therefore a given elongation of the wire and a given deflection of the pointer, for each current there is a definite position of the pointer, which depends on the square of the current.  The scale can be calibrated in current units (amperes), though it will not be an even scale, being crowded at the lower end.

The instrument described is the original ‘hot-wire ampere-meter’ (or ammeter) and was used generally until about the turn of the century.  (It is of interest that it will also indicate alternating currents, as explained in the manual ‘Fundamentals of Electricity 3’.)

FIGURE 11.2

HOT-WIRE AMMETER AND VOLTMETER

A similar instrument is used for indicating voltage, since, by Ohm’s Law 

If R is the resistance of the hot wire (considered fixed), then the current indicated by it will be proportional to V.  In Figure 11.2 a hot-wire ammeter in series with the circuit to be measured is shown on the left, and on the right is a parallel circuit operating at the same voltage.  A second hot-wire instrument is connected across this parallel circuit, but one with a high resistance in series with it.  As explained above, the current, small because of the series resistance, drawn by this second instrument will still be proportional to V, and so the instrument acts as a voltmeter and can be scaled directly in volts.  It too will have an uneven scale.

11.2     MOVING-IRON INSTRUMENTS

Whereas the hot-wire instruments described above depend on the heating effect of a current for its indirect method of indicating, another class of instruments makes use of the magnetic effect of the current discovered by Oersted.  Its development was largely due to Lord Kelvin.

FIGURE 11.3

MOVING-IRON INSTRUMENT

Figure 11.3 shows a fixed coil through which passes the current to be measured.  The coil is wound with wire of sufficient section to carry the current without overheating.

As current flows through the coil it gives rise to a magnetic field along its axis.  In one form of the instrument a small piece of soft iron is pivoted so that it lies normally well across the coil’s axis and is held there by a spiral control spring.

When current flows through the coil the soft iron is magnetised by induction and tries to align itself along the axis of the coil’s magnetic field, but it is restrained from completely doing so by the back-pull of the spring.  It takes up a balance position where the magnetic pull of the coil is just counterbalanced by the spring.

The moving-iron ‘armature’ is pivoted on a spindle carrying a pointer which moves over the instrument scale.  If the instrument has a low-resistance coil and is used in series with the circuit whose current is to be measured, it acts as an ammeter.  If however it has a high-resistance coil and is used in parallel with the circuit, it acts as a voltmeter.  There is otherwise no basic difference between the movements.

Some such instruments are provided with two fixed coils in parallel planes and arranged to assist each other magnetically.  The moving-iron armature is then placed symmetrically on their common axis. In other makes the iron may be pivoted differently, but it always moves towards the coils’ magnetic axis against some form of restraint.  Various types of damping are usually added.

Because the magnetic pull of a coil on a piece of iron magnetised by induction is proportional to the square of the current, the movement of a moving-iron instrument is proportional to I² just as was the case with the hot-wire instrument where the heating depended on I².  The scale of a moving-iron instrument, calibrated in amperes or volts, is therefore uneven and is crowded towards the lower end. Indeed it is the crowding of the scale that makes it possible to tell a moving-iron from a moving-coil instrument at a glance.

11.3        MOVING-COIL INSTRUMENTS

The moving-coil type of instrument is magnetic in principle and depends on the interaction between a coil and a magnet.  As shown in Figure 11.4, the magnet is fixed and takes the form of a permanent magnet; the ‘armature’ is a small pivoted coil to which connections are made by light flexibles.  Normally the axis of the coil lies well across the axis of the permanent magnet field and is held there by a spiral control spring.

FIGURE 11.4

MOVING-COIL INSTRUMENT

The circuit current to be measured (or a known proportion of it) flows through the coil, causing it to produce an electromagnetic field along its axis.  This field reacts with the field of the fixed permanent magnet and causes the coil to try to align its own axis with it, but it is restrained from completely doing so by the back-pull of the spring.  It takes up a balance position where the magnetic pull on the moving coil is just counterbalanced by the spring.

The coil is pivoted on a spindle carrying a pointer which moves over the instrument scale.  If the instrument has a coil of fairly low resistance and is used in series with the circuit whose current is to be measured, it acts as an ammeter.  But here it is necessary to point out that the moving coil is necessarily of light construction, and, with its flexible connections, there is a limit to the size of wire that can be used.  For heavier currents therefore such an ammeter would be used with a shunt (see para. 11.5).  If the coil has a high resistance and is used in parallel with the circuit, it acts as a voltmeter. There is otherwise no basic difference between the movements.

In a moving coil operating in a permanent magnet field, the magnetic pull on the coil depends only on the current in that coil, not on the square of the current as in the moving-iron type where the magnetisation is induced.  Therefore the movement of the coil is almost linear with the current, and the scale of a moving-coil instrument is fairly even over its whole range, not crowded at its lower end.  It is also reversible - that is, negative currents cause negative movement - and, if a ‘set-up zero’ is used, they can be scaled to show the reverse currents; a centre-zero ammeter is an example.

In order that a moving-coil instrument shall retain its accuracy, it is important that the permanent magnet retain its original strength and not weaken with the passage of time or with vibration or shock.  Therefore the magnets used in these instruments are made from specially chosen iron of high retentivity.  They then undergo a thorough artificial ‘ageing’ process and are given rigorous tests to prove that they are truly magnetically stable.  It should seldom be necessary to change a magnet.

Moving-coil instruments can only be used with d.c.; they will not function on a.c., as explained in the manual ‘Fundamentals of Electricity 3’.

11.4     DYNAMOMETER INSTRUMENTS

The dynamometer instrument is really a special case of the moving coil. There is a moving coil as already described, but the permanent magnet is replaced by a fixed coil (usually a pair, for reasons of symmetry, since they produce a nearly uniform field). (Figure 11.5.)

FIGURE 11.5

DYNAMOMETER INSTRUMENT CONNECTED AS WATTMETER

If such an instrument is used as an ammeter or voltmeter, both fixed and moving coils are in series, and the torque depends on the current in each.  So the total torque depends once again on the square of the current, giving an uneven scale.  Being more costly than moving-iron, they therefore have little advantage over the moving-iron type.  They are also inferior to the simple moving-coil instruments and are not much used in this application.

However, one application is important.  The actual torque on the moving coil depends, as stated, on both the current in the fixed coils and that in the moving coil; it is therefore proportional to their product.  If the fixed coils are connected in series with the circuit (so carrying the current) and the moving coil is connected in parallel with the circuit (so carrying a current proportional to the voltage), the instrument will indicate I x V, or d.c. watts.  This dynamometer instrument, so connected, then becomes a wattmeter.  (It is of interest that this instrument will also register a.c. watts, as explained in the manual ‘Fundamentals of Electricity 3’.)

Since the dynamometer instrument indicates the product of V and I, then if I reverses, the torque also reverses and the instrument indicates backwards.  If its zero is ‘set up’, it can be scaled to indicate both normal (forward) and reverse power that is to say, it is directional.  Whenever it is desired to take direction into account (such as for some relays in protective schemes), a dynamometer or ‘wattmetric’ type of movement is always used.

If the currents to be measured are too high for the coils of the instrument, the series (fixed coil) current can be taken through a shunt (see para. 11.5 below), thereby using only a known proportion of the circuit current.  Similarly the voltage coil (moving coil) can be fed through a ‘dropping’ resistance of known value, so that only a known fraction of the circuit voltage is applied.

11.5     SHUNT-CONNECTED INSTRUMENTS

Most instruments receive an input from the circuit whose current is to be measured, but, due to their construction, they can in most cases accept only a small, but accurately known, proportion of that current.  It is therefore necessary to divide the circuit current into two parts: the main part carrying the majority of the current, and the other part a known fraction of it - in many cases only an infinitesimal fraction, perhaps one-thousandth part.

FIGURE 11.6

INSTRUMENT WITH SHUNT

In Figure 11.6 the line current is I and is shown in heavy line.  It passes through a ‘shunt’ which usually for the heaviest currents takes the form of two brass blocks connected together by strips of conducting metal of very small, but not negligible, resistance.  In parallel with this shunt is the instrument’s current coil with a relatively high resistance, perhaps many thousand times that of the shunt.  The line current will divide in inverse proportion to the resistances.  For example, if the shunt resistance were 0.001 ohm and that of the instrument coil 1.0 ohm, a current of, say, 100A would divide approximately 99.9A through the shunt and 0.1A through the coil.  The instrument would then actually measure only 0.1A, but it would be scaled one thousand times up to read ‘100A’.

When instruments receive their current input through a shunt, it is important that they be calibrated by the maker with their own shunt and with the actual connecting leads with which they will eventually be installed.  Because of the great disparity between the resistance of the shunt itself and of the parallel instrument circuit, small errors in the latter could cause considerable errors in the instrument reading; hence the need to calibrate all together.

When an instrument is being installed with its shunt, the leads must never be altered or shortened; any extra length must be left in and flaked out.  Shunt-operated instruments should all be marked with their associated shunt serial number and used with no other.  For example, in the case quoted, one-tenth of an ohm cut out of the shunt leads would lead to a 10% error in the instrument’s reading.

11.6     TERMINOLOGY

The words used with indicating instruments and similar devices are often misused, and below is a summary of the terms and their correct usage:

‘Indicating Instrument’ or simply ‘Instrument’.  An indicating device to show the instantaneous value of the quantity being measured.  Note that, although the terms ‘voltmeter’, ‘ammeter’, ‘wattmeter’ etc. are generally used, the generic term ‘meters’ should never be used for indicating instruments.

‘Integrating Meter’.  A device for integrating a quantity over a period of time. Usually associated with watts and vars, the total quantity shown by dial or digitally as watt-hours (Wh) or var-hours (varh).  Such integrating devices are known collectively as ‘meters’ (as distinct from ‘instruments’ above).

‘Recording Instrument’ or ‘Recorder’.  A device for continuously recording the instantaneous value of a quantity, the record being made by pen-on-paper or similar device, or digitally on paper or tape.

‘Set-up Zero’.  When an instrument is carrying no current, the position taken up by its pointer under the influence of the control spring is its ‘zero’, and it is usually at the extreme left-end of the scale.  However, instruments can be arranged so that the zero is not at the extreme end but at some distance to the right; it is then said to have a ‘set-up zero’.  This allows the instrument to register, in part at least, in the negative or reverse direction.  It can only be applied to moving-coil or dynamometer instruments.  A centre-zero ammeter showing battery charge and discharge is an example of a set-up zero.

Each group of devices has a separate British Standards symbol.

The letter within shows the quantity being measured, for example A (amperes), Wh (watthours), V (volts), etc.