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# General Principles of Measurement... Prabhat Patel
02/05/2017 0 0

### Measurement is the process by which one can convert physical parameters into meaningful numbers. The measurement of a given quantity is the result of comparison between the quantity to be measured, and a definite standard. The instruments which are used for such measurements are called measuring instruments.

The necessary requirements for any measuring instruments are:

1)      With the introduction of the instrument in the circuit, the circuit, the circuit conditions should not be altered. Thus, the quantity to be measured should not get affected due to the instrument used.

2)      The power consumed by the instruments for their operation should be as small as possible.

Some important terms in ‘measurement’ are;

Instrument:

A device for finding the value, or magnitude of a quantity or variable.

Accuracy:

It is the nearness of the measured value towards the true value. ie, the measure of conformity to the true value.

Precision:

It refers to the degree of agreement within a group of measurements or instruments. ie,The measure of repeatability or reproducibility. Precision has two characteristics: conformity and the no. of significant figures to which measurements may be made.

Resolution:

It is defined as the smallest change in input that can be detected by an instrument.

Sensitivity:

It is the ratio of output signal to a change of input.

Or

It is the ratio of response of an instrument to a change in a measured variable.

True value:

It is the average of the infinite no. of measurements when the average deviation tends to become zero.

Error:

An error is the deviation from the true value of the measured variable.In order to understand the concept of errors in measurement, we should know the two terms that defines the error and these two terms are written below:

### True Value:

It is not possible to determine the true of quantity by experiment means. True value may be defined as the average value of an infinite number of measured values when average deviation due to various contributing factor will approach to zero.

### Measured Value:

It may be defined as the approximated value of true value. It can be found out by taking means of several measured readings during an experiment, by applying suitable approximations on physical conditions.

Now we are in a position to define static error. Static error is defined as the difference of the measured value and the true value of the quantity. Mathematically we can write an expression of error as, dA = Am - At where dA is the static error Am is measured value and At is true value.

It may be noted that the absolute value of error cannot be determined as due to the fact that the true value of quantity cannot be determined accurately.

Let us consider few terms related to errors.

### Limiting Errors or Guarantee Errors:

The concept of guarantee errors can better clear if we study this kind of error by considering one example. Suppose there is a manufacturer who manufacture an ammeter, now he should promises that the error in the ammeter he is selling not greater the limit he sets. This limit of error is known as limiting errors or guarantee error.

### Relative Error or Fractional Error:

It is defined as the ratio of the error and the specified magnitude of the quantity. Mathematically we write as,

Where dA is the error and A is the magnitude.

Now here we are interested in computing resultant limiting error under the following cases:

• By taking the sum of two quantities: Let us consider two measured quantities a1and a2. The sum of these two quantities can be represented by A. Thus we can write A = a1 + a2. Now the relative incremental value of this function can be calculated as

Separating the each term as shown below and by multiplying and dividing a1 with the first term and a2 with the second term we have

From the above equation we can see that the resultant limiting error is equal to the sum of products formed by multiplying the individual relative limiting errors by the ratio of each term to the function. Same procedure can be applied to calculate the resultant limiting error due to summation of more than two quantities. In order to calculate the resultant limiting error due to difference of the two quantities just change the addition sign with subtraction and rest procedure is same.

(b) By taking the product of two quantities: Let us consider two quantities a1 and a2. In this case the product of the two quantities are expressed as A = a1.a2. Now taking log both sides and differentiating with respect to A we have resultant limiting errors as

From this equation we can see that the resultant error is summation of relative errors in measurement of terms. Similarly we can calculate the resultant limiting error for power of factor. Hence the relative error would be n times in this case.

## Types of Errors:

Basically there are three types of errors on the basis; they may arise from the source.

### Gross Errors:

This category of errors includes all the human mistakes while reading, recording and the readings. Mistakes in calculating the errors also come under this category. For example while taking the reading from the meter of the instrument he may read 21 as 31. All these types of error are come under this category. Gross errors can be avoided by using two suitable measures and they are written below:

(i) A proper care should be taken in reading, recording the data. Also calculation of error should be done accurately.
(ii) By increasing the number of experimenters we can reduce the gross errors. If each experimenter takes different reading at different points, then by taking average of more readings we can reduce the gross errors.

### Systematic Errors:

In order to understand these kinds of errors, let us categorize the systematic errors as

#### (i) Instrumental error:

These errors may be due to wrong construction, calibration of the measuring instruments. These types of error may be arises due to friction or may be due to hysteresis. These types of errors also include the loading effect and misuse of the instruments. Misuse of the instruments results in the failure to the adjust the zero of instruments. In order to minimize the gross errors in measurement various correction factors must be applied and in extreme condition instrument must be re-calibrated carefully.

#### (ii) Environmental Errors:

This type of error arises due to conditions external to the instrument. The external condition includes temperature, pressure, humidity or it may include external magnetic field. Following are the steps that one must follow in order to minimize the environmental errors:

(A)Try to maintain the temperature and humidity of the laboratory constant by making some arrangements.
(B)Ensure that there should not be any external magnetic or electrostatic field around the instrument.

### Observational Errors:

As the name suggests these types of errors are due to wrong observations. The wrong observations may be due to PARALLAX. In order to minimize the PARALLAX error highly accurate meters are required, provided with mirrored scales.

### Random Errors:

After calculating all systematic errors, it is found that there are still some errors in measurement is left. These errors are known as random errors. Some of the reasons of the appearance of these errors are known but still, some reasons are unknown. Hence we cannot fully eliminate these kinds of error

### Instruments- Basics:

The essential elements of an instrument are;

• A detector
• An intermediate transfer device
• An indicator, recorder or a storage device

The history of the development of instruments shows three phases of instruments.

1. a)Mechanical, b) Electrical,  and c) Electronic instruments
1. a)Mechanical instruments

These instruments are very reliable for static and stable conditions. But, these instruments have moving parts that are rigid, heavy, and bulky and hence have a large mass. Mass presents inertia problems and hence, these instruments cannot faithfully follow the rapid changes, which are involved in dynamic measurements. Thus, the disadvantages of mechanical instruments are:

• They are unable to respond rapidly to measurements of dynamic and transient conditions.
• Most of them are a potential source of noise and cause noise pollution.
1. b)Electrical instruments:

Electrical method of indicating the output of detectors is more rapid than mechanical methods. But, electrical instruments depends on the mechanical movement of an indicating device, having some inertia and thus have a limited time response (0.5 – 24 s).

1. c)Electronic instruments:

These instruments are used for fast responses required for scientific and industrial measurements. They are used for the detection of electromagnetically produced signals such as radio, video, and micro waves, space applications, and computers.     These instruments make use of semiconductor devices. In electronic devices, the only movement involved is that of electrons. Thus, the response time is extremely small on account of very small inertia of electrons.

eg: nano seconds- A Cathode Ray Oscilloscope (CRO) is capable of following dynamic and transition changes of the ordnanoseconds(10-9s).

1.             Can detect very weak signals. ( eg:- In the area of Bio Instrumentation, the bio electric potentials are very weak, ie lower than 1 mV)
2.             They can monitor inaccessible or dangerous locations.

iii.            They can be used to measure non-electrical quantities.

1.  They have
•  higher sensitivity,
• Lower weight
• Lower power consumption
• Higher degree of reliability compared to electrical or mechanical instruments

Classification of Instruments:

Instruments can be broadly classified in to

• Absolute instruments
• Secondary instruments

Absolute instruments give the magnitude of the quantity under measurement in terms of physical constants of the instruments.

e.g:- Tangent galvanometer, Rayleigh’s current balance.

In secondary instruments, the quantity under measurement can only be measured by observing the output of the instrument. The secondary instruments should be calibrated by comparing with an absolute instrument or another secondary instrument which has already been calibrated against an absolute instrument.

e.g:- Voltmeter, pressure gauge.

The secondary instruments are  the commonly  used instruments compared to the absolute instruments.

Electrical measuring instruments may be classified according to their functions as;

(i)  Indicating instruments (ii)Integrating instruments (iii) Recording instruments

i.Indicating instruments:-

These instruments directly indicate the value of the electrical quantity at the time when it is being measured. In these instruments, a pointer moving over a graduated scale directly gives the value of the electrical quantity being measured.

e.g:- Ammeter, voltmeter, wattmeter.

• Integrating instruments

The instruments which measure the total quantity of electricity (in Ampere hours ) or electrical energy (in Watt hours) in a given time are called integrating instruments. In such instruments, there are a set of dials and pointers which register the total quantity of electricity or electrical energy supplied to the load.

e.g:- Ampere- Hour meter, Watt-hour meter.

• Recording instruments

Recording instruments give a continuous record of the variations of the electrical quantity to be measured. A recording instrument is merely an indicating instrument with a pen attached to its pointer. The pen rests lightly on a chart wrapped over a drum moving with a slow uniform speed. The motion of the drum is in a direction perpendicular to the direction of the pointer. The path traced out by the pen indicates the manner in which the quantity being measured, has varied during the time of the record.

e.g:- Recording voltmeters, Recording ammeters in supply stations.

………………………………………………………………

TYPES OF INSTRUMENTS:

(1) Permanent Magnet Moving Coil (PMMC) instruments .

(2) Moving iron instruments.

(3) Electrodynamometer instruments.

(4) Thermal instruments

(5) Induction instruments.

(6) Electrostatic type instruments.

(7) Rectifier type instruments.

The PMMC instruments can be used for direct measurement only, and the induction type for alternating current measurements only.

The moving iron(MI) and moving coil(MC) types both depend for their action upon the magnetic effect of current. The MI instruments can be used for either direct or alternating current measurements, and is the cheapest.

Electrodynamometer type of instruments can be used both on a.c as well as on d.c. They are useful as “transfer instruments” , as their calibration for both d.c and a.c is the same.

The calibration for d.c and a.c is same for the

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