ERRORS ANALYSIS
Error is defined as the deviation of the true value from the desired value. It is expressed either as absolute or as a percentage of error.
Absolute error is defined as the difference between the true value of the variable and the measured value of the variable, or
Accuracy and Precision
Accuracy. It is the closeness with which an instrument reading approaches the true value of the quantity being measured. It is specified in terms of limits of errors and is expressed as either percentage of scale or range of percentage of true value.
Precision. It is a measure of the reproducibility of the measurements, i.e. for a fixed value of a quantity, precision is a measure of the degree of agreement within
a group of measurements. An indication of the precision of the measurement is obtained from the number of significant figures in which it is expressed. The more the significant figures, the greater the precision of measurement.
Types of Errors
Static Error. It is the numerical difference between the true value of a quantity and its value as obtained by measurement. These are sub-divided into
1. Gross Errors
2. Systematic Errors
3. Random Errors
1. Gross Errors. These errors are due to human mistakes in reading or in using instruments or errors in recording observations.
2. Systematic Errors. These errors occur due to shortcomings of the instrument such as defective or worn parts or ageing or effects of the environment
on the instrument.
(i) Instrumental Errors. These are inherent in measuring instruments, because of their mechanical structure. These can be avoided by selecting a suitable instrument for the particular measurement application or by applying
correction factors after determining the amount of instrumental error of calibrating the instrument against a standard.
(ii) Environment Errors. These are due to conditions external to the measuring device including conditions in the area surrounding the instrument such as effect s of changes in temperature, humidity, barometric pressure or effect of magnetic or electrostatic fields.
(iii)Observational Errors. These are errors introduced by the observer. The most common is the parallax error introduced in reading a meter scale and the error of estimation.
3. Random Errors. These are due t o unknown causes and are normally small and follow the law of probability. These are treated mathematically.
Sources of Errors
(i) Insufficient knowledge of process parameters and design conditions.
(ii) Poor maintenance.
(iii) Change in process parameters irregularities, upsets etc.
(iv) Poor design.
(v) Design limitations
(vi) Due to person operating the instrument.
When two or more quantities, each of which is subjected to error, are combined, following rules will
(1) Sum of two or more quantities
Hence the resultant systematic error is equal to the sum of the products formed by multiplying the individual systematic errors by the ratio of each
terms to the function.
(2) Difference of two quantities
ELECTRICAL MEASURING INSTRUMENTS
These are broadly divided into two classes:
(1) Absolute instruments are those which give the value of the quantity to be measured in terms of t he constant s of the instrument and t heir deflection only. No previous calibration or comparison is necessary in their case. The example of such an instrument is tangent galvanometer which gives the value of current in
terms of the tangent of defection produced by the current, the radius and number of turns of wire used and the horizontal component of earth's field.
(2) Secondary instruments are those in which the value of electrical quantity to be measured can be determined from the deflection of the instruments only when they have been pre-calibrated by comparison with an absolute instrument.
Another way to classify secondary instruments is divided them into
(i) indicating instruments
(ii) recording instruments, and
(iii) integrating instruments.
(i) Indicating Instruments These instruments indicate the instantaneous
value of the electrical quantity being measured at the time at which it is being measured. Their indications are given by pointers moving over calibrated dials. Ordinary ammeters, voltmeters and watt meters belong to this class.
(ii) Recording Instruments These instruments give a continuous record of the
variations of a quantity over a selected period of time. The moving system of the instrument carries an inked pen which rests lightly on a chart or graph that is moved at a uniform and low speed, in a direction perpendicular to that of the deflection of the pen. The path traced out by the pen presents a continuous record of the variations in the deflection of the instrument.
(iii) Integrating Instruments These instruments measure and register by a set of dials and pointers, either the total quantity of electricity (in amp-hours) or the total amount of electrical energy (in watt-hours or kWh) supplied to a circuit in a given time. This summation gives the product of time and the electrical quantity but gives no direct indication as to the rate at which the quantity or energy is being supplied because their registrations are independent of this rate provided the current flowing through the instrument is sufficient to operate it. Ampere hour and watt-hours meters fall in this class
Electrical Principles of Operation All electrical measuring instruments depend for their action on one of the many physical effects of an electric current or potential and are generally classified according to which of these effects is utilized in their
operation. The effects generally utilized are
1. Magnetic effect - for ammeters and voltmeters usually.
2. Electrodynamic effect - for ammeters, voltmeters and watt meters.
3. Electromagnetic effect - for ammeters, voltmeters, watt meters and watt hour meters.
4. Thermal effect - for ammeters and voltmeters.
5. Chemical effect - for d.c. ampere-hour meters.
6. Electrostatic effect - for voltmeters only
INDICATING INSTRUMENTS
All such instruments essentially consist of a pointer moving over a calibrated scale and attached to the moving system pivoted in jewel bearings. In order to ensure the proper operation of indicating instruments, the following three torques are needed.
(i) Deflecting torque
(ii) Controlling torque
(iii) Damping torque
(i ) Deflecting Torque (Td)
One important requirement in a indicating instruments is the arrangement for producing deflecting or operating torque when the instrument is connected in the electrical circuit to measure the given electrical quantity. The deflecting torque causes the moving system (and hence, the pointer attached to it) to move from zero position when the instrument is connect ed in t he circuit to measure the given electrical quantity.
(ii) Controlling Torque (Tc)
Under the action of deflecting torque, the pointer will continue to move indefinitely and shall be independent of the value of electrical quantity to
be measured. This necessitates that the controlling torque must be provided. This controlling torque should oppose the deflecting torque and should
increase with the deflection of the moving system so that the pointer is brought to rest at a position when the two opposing torques are equal.The controlling torque performs the following two functions.
(a) It oppose the deflecting torque and increases with the deflection of the moving system. It thus, limits the movement of the pointer so that the
magnitude of deflection is always the same for the given value of electrical quantity to be measured.
(b) If brings the pointer back to zero position when the deflecting torque is removed. If it were not provided, the pointer once deflected would not
return t o zero position on removing the deflecting torque. The controlling or restoring or balancing torque is provided either by a spring or by gravity. A
hair spring usually of phosphor -bronze is attached to the moving system of the
instrument. With the movement of pointer, the spring is twisted in opposite direction. This twist in spring produces restoring torque. Gravity control is obtained by attaching a small adjustable weight to the moving system. Such
that the two exert torques in opposite directions.
(iii )Damping Torque
If the moving system is acted upon by deflecting and controlling torque alone, then the pointer due to its inertia will oscillate about final position before
coming to rest. These oscillations are undesirable and must be prevented. In order to avoid these oscillations of the pointer and to bring it quickly to its deflected position, damping torque is provided which opposes the movement (backward or forward) of the pointer and operates only when the system is moving.
It is worthwhile to mention here that damping torque acts only when the pointer is in motion. The degree of damping decides the behavior of the moving system. If the instrument is under damped,the pointer will oscillate about the final position and take some time to come to rest. On the other hand, if the instrument is over damped, the pointer will become slow and lithargic. However, if the degree of damping is adjusted to such a value that the pointer moves and quickly comes to its final position, the instrument is said to be dead beat. Fig. 1 shows the graph for under damping, over damping and critical damping (dead beat). Damping force can be produced by air friction, eddy currents and fluid friction. In air friction damping an aluminium piston attached to the moving system is arranged to travel in a fixed air chamber closed at one end. The necessary damping effect is produced by movement of piston in the chamber. Fluid friction is similar in action to the air friction. Damping is produced by movement of piston in oil. The most efficient type of damping is obtained by eddy-current damping. A non-magnetic metallic disc, attached t o the moving system, cuts the magnetic flux. Hence, eddy currents are produced in the disc which produce a damping force in such
a direction to oppose the cause producing them, i.e. the motion of moving system
Indicating instruments are of the following types:
(i) Moving iron instruments
(ii) Moving coil instruments
(iii) Dynamometer type instruments
(iv) Hot wire instruments
(v) Electrostatic instruments
(vi) Induction type instrument
Moving Iron Instruments
Moving iron instruments are of two types :
1. Attraction type
2. Repulsion type
1. Attraction Type Moving Iron Instruments Principle. These instruments are based on the principle that when an unmagnetised soft iron piece is placed in the magnetic field of a coil, then the piece is attracted towards the coil. The moving
system of the instrument is attached to the soft iron piece and the operating current is passed through a coil placed near it. The operating current sets up
magnetic field which attracts the iron piece and thus moves the pointer over the scale.Construction. It consists of a hollow cylindrical coil or solenoid which is kept fixed as shown in the Fig.2. An oval shaped soft iron pieces is attached to the
spindle in such a way that it can move in or out of the coil. The pointer is attached to the spindle so that it is deflected with the motion of the soft iron piece. The controlling torque on the moving system is provided by spring control method while damping is provided by air friction
When the instrument is connected in the circuit, the operating current flows through the coil. The current sets up magnetic field in the coil. In other words, the coil behaves like a magnet and, therefore, it attracts the soft iron piece towards it. The result is that the pointer attached to the moving system moves from zero position.
If current in the coil is reversed, the direction of magnetic field also reverses and so does the magnetism produced in soft iron piece. Therefore, the direction of deflecting torque remains unchanged. It follows, therefore, that such instruments can be used for both D.C. as well as A.C. work.
Deflecting torque. The force F pulling the soft iron piece towards the coil depends upon:
(i) Field strength H produced by the coil.
(ii) Pole strength m developed by the piece.
instruments is non-uniform, being crowded in the beginning. In order to make the scale of such instruments uniform, suitably shaped (tongue shaped) iron piece is used.
2. Repulsion type Moving Iron Instruments
Principle- These instruments are based on the principle of repulsion between the two iron pieces similarly magnetized.
Construction. It consists of a fixed cylindrical hollow coil which carries operating current (Fig. 3.) Inside the coil, there are two soft iron pieces or vanes, one of
which is fixed and other is movable. The fixed iron piece is attached to the coil whereas the movable iron piece is attached to the pointer shaft. Under the action
of deflecting torque, the pointer attached to the moving system moves over the scale. The controlling torque is produced by spring control method and damping
torque is provided by air friction damping.
Working- When the instrument is connected in the circuit, current flows through the coil. This current sets up magnetic field in the coil. The magnetic field
magnetizes both iron pieces in the same direction i.e. both pieces become similar magnets and hence they repel each other. Due to this force of repulsion only
movable iron piece moves as the other piece is fixed and cannot move. The result is that the pointer attached to the moving system moves from zero position.
Deflecting Torque. The deflecting torque results due to the repulsion bet ween t he similarly magnetized iron pieces. If two pieces develop pole strengths m1 and m2 respectively, then,
Since deflection thita is proportional to square of current through the coil, therefore, scale of such instruments is non-uniform being crowed in the beginning. However, scale of such instruments can be made uniform by using tongue shaped iron pieces.
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