EE T55 MEASUREMENTS AND INSTRUMENTATION

UNIT-I (INTRODUCTION TO MEASUREMENT)

Elements of Generalized measurement system- Methods of measurement- Classification of

instruments–Static & Dynamic characteristics of instruments-Mean, Standard deviation- Probability of

errors-Types of error Accuracy, Precision, Sensitivity, Linearity, Resolution, Hysteresis, Threshold,

Input impedance, loading effects.

MEASUREMENTS:

The measurement of a given quantity is essentially an act or the result of comparison

between the quantity (whose magnitude is unknown) & a predefined standard. Since two

quantities are compared, the result is expressed in numerical values.

Measurement system any of the systems used in the process of associating numbers with

physical quantities and phenomena. Although the concept of weights and measures today includes

such factors as temperature, luminosity, pressure, and electric current, it once consisted of only four

basic measurements: mass (weight), distance or length, area, and volume (liquid or grain measure).

The last three are, of course, closely related. Basic to the whole idea of weights and measures are the

concepts of uniformity, units, and standards. Uniformity, the essence of any system of weights and

measures, requires accurate, reliable standards of mass and length.

BASIC REQUIREMENTS OF MEASUREMENT:

i) The standard used for comparison purposes must be accurately defined & should be

commonly accepted

ii) The apparatus used & the method adopted must be provable.

MEASURING INSTRUMENT:

It may be defined as a device for determining the value or magnitude of a quantity or variable.

The measurement of a given quantity is essentially an act or result of comparison

between a quantity, whose magnitude (amount) is unknown with a similar quantity whose

magnitude (amount) is known, the latter being called standard.

An Instrument may be defined as a device or a system which is designed to maintain a

functional relationship between prescribed properties of physical variables and must include

ways and means of communication to a human observer.

1.1. FUNCTION OF INSTRUMENTS & MEASUREMENT SYSTEM:

Instruments or measurement system are classified based upon the function they performed.

Indicating Function:- Different kinds of methods for supplying information

concerning the variable quantity under measurement

Recording Function:- Stores or write the value of quantity under measurement.

Controlling Function:- In this case the information is used by the instrument or the

system to control the original measured

1.2. APPLICATION OF MEASUREMENT SYSTEM:

Monitoring of process and operation- simply indicating the value or condition of

parameter under study. For example- water and electricity meter

Control of process and operations- automatic control system a very strong association

between measurement and control for example: refrigeration with thermostatic control

Experimental Engineering analysis: engineering problem, theoretical and

experimental methods may be used depending upon the nature of the problem

1.3.TYPES OF INSTRUMENT:

Instruments can be classified on the following basis

Mode of measurement:- The instrument can be classified into three types

Primary Instrument: Direct Comparison with reference standard. For example the

length measurement by ruler

Secondary Instrument: indirect comparison by converting it into some other form. For

example temperature measurement by mercury in glass thermometer

Tertiary Instrument: two conversion of parameter are involved. For example measuring

of shaft speed by electrical tachometer

Nature of Contact:-The instruments can be classified into two types

Contact type: when initial sensing element comes in direct contact with the medium

whose parameter are to be measured. Temperature measurement by thermometer

Non Contact type: when the initial sensing element does not comes in contact with the

medium whose parameter are to be measured. Temperature Measurement by radiation

pyrometer.Signal Being Processed:- The instrument can be classified as

Analog Measuring Instrument: In form of continuous or stepless parameter

Digital Measuring Instrument: In form of digital signal

Condition of Pointer:-The Classification is as

Null Type: The pointer is maintained at a fixed position and measurement is

done by balancing

Deflection type: The pointer is deflected with respect to origin to get the

measured quantity.

Power Source Required:-The classification is as follows:

Self sufficient Instrument (Active ): do not need external power

Power operated instrument (Passive): need external source of power

1.4. FUNCTIONAL ELEMENT OF AN INSTRUMENT:

Any instrument or measuring system can be described in general with the

help of a block diagram. The block diagram indicates the necessary elements and

their functions in a general measuring system. The entire opearation of an instrument

can be studied interms of

these functional elements. The various elements can be grouped as,

Primary sensing element

Data conditioning element

Data presentation element

Primary Sensing Element: - The Measurand is first detected by primary sensing

element. The primary sensing element transfers the measurand to variable conversion

element for further processing. The output signal of a primary sensing element is a

physical variable such as displacement or voltage. In most of the cases, a transducer

follows primary sensing element which converts the measurand in to a electrical

signal.

Variable Conversion Element: - The output signal of a primary sensing element may

require to be converted to more suitable variables while preserving its

information content. This function is performed by variable conversion element

and it may be considered as an intermediate transducer

Variable Manipulation Element: - This element is an intermediate stage of a

measuring system. It modifies the direct signal by amplification, filtering, etc; so that a

desired output is produced the physical nature of the variable remains unchanged during this

stage.

Data Transmission Element: - when the functional elements of the measuring system

are spatially separated then it becomes necessary to transmit signals from one element to

another. This function is performed by data transmission element. It is an essential functional

element where remote control operation is desired.

Data Presentation Element: - usually information about the quantity being measured is to

be communicated to human observer for monitoring control and analysis purpose. This

is therefore, to be presented in form of human sensory capability. This function is done by

data presentation element.

Fig.1.2. Simple analog meter

For example, consider a simple analog meter (fig.1.2.) used to measure current

or voltage. The moving coil is primary sensing element. The magnets and coil together

act as data conditioning stage to convert current in coil to a force. This force is

transmitted to the pointer through mechanical linkages which act as data transmission

element. The pointer act as a data presentation element.

Similarly the proper instrument for a particular type of measurand needs the

knowledge of the performance characteristics of an instrument. The performance

characteristics of an instrument are mainly divided into two categories.

Static characteristics

Dynamic characteristics.

1.5. STATIC CHARACTERISTICS:

The set of criteria defined for the instruments, which are used to measure the

quantities which are slowly varying with the time or mostly constant. (i.e.) do not vary with

time is called static characteristics. The various static characteristics are:

Accuracy

Precision

Resolution

Linearity

Resolution

Error Sensitivity

Reproducibility

Zero drift

Stability

Threshold.

Accuracy: It is an instrument can be defined as the ability of the instrument to respond to true

value of the measured variable under reference condition. In other word it is the closeness with

which the instrument reading reaches the true value of quantity being measured.

Precision: It is a measure of reproducibility of the measurement, given a fixed value of

quantity or the degree of exactness for which instrument is designed or intended to perform. In

other words, precision is measure of degree of agreement within the group of measurement.

Error: The most important static characteristics of an instrument is its accuracy, which os

generally expressed interms of the error called static error.

The algebraic difference between the indicated value ant the true value of the quantity

to be measured is called an error. Mathematically it can be expressed as,

e = At - Am

where, e = error

Am = measured value of the quantity

At = true value of the quantity

In this expression, the error denoted as e is called absolute error.the absolute error does

not indicate precisely the accuracy of the measurements.

Mathematically, the expressed as

er =

=

er = Percentage relative error is expressed as,

% er =

* 100

Linearity: The instrument requires the property of linearity that is the output varies linearly

according to the input. The linearity is defined as the ability to reproduce the input

characteristics symmetrically and linearly.

The linearity is defined as the ratio of maximum deviation of output from idealized

straight line to the full scale deviation.

Linearity = * 100

Zero drift: It is defined as the deviation in the instrument output with time, from its zero value,

when the variable to be measured is constant. The whole instrument calibration may gradually

shift by the same amount.

There are many environmental factors which affect the drift. These factors are stray

electric field, stray magnetic field, temperature changes, contamination of metal, changes in

atomic structure, mechanical vibrations, wear ant tear, corrosion, etc,.

Threshold: If the input quantity is slowly varied from zero onwards, the output does not

change until some minimum value of the input is exceed. This minimum value of the input

change is called threshold.

Resolution: It is the smallest increment of quan tity being measured which can be detected.

Resolution means the smallest measurable input changes.

Reproducibility: It is the degree of closeness with which a given value may be repeatability

measured. It may be specified in terms of units for a given period of time. The perfect

reproducibility indicates no drift in the instrument.

Fig.1.3. Reproducibility

Stability: The ability of an instrument to retain its performance throught its specified

operating life and the storage life is defined as its stability. Tolerance: The maximum allowable

error in the measurement is specified interms of the some value which is called tolerance. This

is closely related to the tolerance.

Range or span: The minimum and maximum values of the quantity for which of an

instrument is designed to measure is called its range or span.

Bias: The constant error which exists over the full range of measurement of an instrument is

called bias. Such bias can be completely eliminated by calibration.

Dead space: In some instruments, it is possible that till input increases beyond certain value,

the output does not change. So for certain range of input values there is no change in output.

This range of input is called dead space.

Hysteresis: If the input to the instrument is increased from a negative value, the output also

increases. This is shown by curve1 in the figure. But if the curve is now decreased steadily, the

output does not follow the same curve but lags by certain value. It traces the curve2. The

difference between the two curve is called hysteresis.

Fig.1.4. Hysteresis loop

1.6. DYNAMIC CHARACTERISTICS:

When the instrument is subjected to rapidly varying inputs, the relation between

input and output becomes totally different than that in case of static or constant inputs. As the

input varies from instant to instant, output also varies from instant to instant. The behavior of

system under such conditions is called dynamic response of the system.

The dynamic behavior of the measuring system is determined by applying some known

and predetermined variations of input to the sensing element. The standard variations in the

input, used practically to obtain the dynamic behavior, are as follows:

Step input: This represents sudden, instantaneous and finite change in the input. The examples

are sudden application of force to a mechanical system.

figure.

The step input of magnitude A is denoted as A u(t) and can be indicated as shown in

Fig.1.5. Step input

The laplace transform of ramp is given by, F(s) =

When A=1, it is called unit step input.

Ramp input: This represents linear change in input. A variable to be measured varies linearily

with time. It changes at a constant rate with respect to the time.

figure.

The ramp input of the magnitude A is denoted as At u(t) and can be shown in the

Fig.1.6. Ramp input

The laplace transform of ramp is given by, F(s) = A / S2

When A=1, it is called unit ramp input.

Parabolic input: This represents an input signal which is proportional to the square of the time

and hence represents constant acceleration.

The parabolic input of magnitude A is denoted as At2

u(t) and can be shown as figure.

Fig.1.7. Parabola input

The laplace transform of parabola is given by, F(s) = 2A / S

3

Impulse input: it exists only at t=0 and has zero value at any other time.

f(t) = 0 for t ≠ 0 and area under it is its magnitude. If it is unity, it is called delta

function denoted as δ(t). it is shown in figure.

Fig.1.8. Impulse input

It is basically a pulse with its base t approaching to zero.

The laplace transform of δ(t) is 1.

Sinusoidal input: This represents an input which changes in accordance with a sinusoidal

function of constant amplitude. Frequency is independent variable in this case. For a linear

system subjected to sinusoidal input, the output is also sinusoidal in steady state, but it differs

from input in amplitude and phase. The sinusoidal input is given by ASinὠt. where A is the

amplitude as shown in fig.

Fig.1.9. Sinusoidal input

The various dynamic

characteristics of an

instrument are speed of

response, fidelity,

lag and the dynamic error.

Speed of response: It is the rapidity with which the system responds to the changes in

the quantity to be measured. It indicates the activeness of the system. The system

should respond very quickly to the changes in the input.

Fidelity: It is the ability of an instrument to produce a wave shape identical to wave

shape of input with respect to time. It is defined as the degree to which an instrument

indicates the change in the measured variable without dynamic error.

Lag: Every system takes some time, whatever small it may be to respond to the

changes in the measured variable. This retardation or delay in the response of a system

is called lag. This is also called measuring lag.

The lags are of two types:

Retardation lag: in this case, the response of the system begins immediately

after a change in the variable has occurred.

Time delay: In this case, the response begins after sometime called dead time,

after the application of input.

Dynamic error: it is difference between the true value of the variable to be measured,

changing with timemand the value indicated by the measurement system, assuming

zero static error.

Fig.1.10. Dynamic error

1.7. ERROR:

The error of a measuring instrument is the numerical difference between the

true value of a quantity and its value as obtained by measurement (i.e) repeated measurement

of the same quantity given different indications.

Different types of errors that occur in measurements have been classified into

three categories.

These include

Gross errors.

Systematic errors.

Random errors.

This will enable users to avoid these errors and thus prove and increase the correctness in

measurement.

Gross error: These are basically human errors caused by the operator or person using

the instrument. The instrument may be good and may not give any error but still the

measurement may go wrong due to the operator.

The different types of gross errors are:

Taking wrong readings.

Reading with parallax error.

Incorrect adjustments of zero and full-scale adjustments.

Improper applications of instruments: Using a 0–100 V voltmeter to measure

0.1 V, etc.

Wrong computation: When power is to be determined, ‘V’ and ‘I’ are

measured. If the computation goes wrong, even though ‘V’ and ‘I’ have been

measured correctly, the measurement of power will be wrong. Thus, wrong

computation can result in error.

Systematic error: These error occurs due to shortcomings of the instrument , such as

defective or worn parts or ageing or effects of the environment on the instrument. These

errors are sometimes referred to as bias and they influence all measurements of a quantity

alike. A constant uniform deviation of the operation of the instrument is known as

systematic error.

These are divided into three categories are Instrumental errors, Environmental errors,

Observational errors.

Instrumental errors. Even if human errors are avoided or proper care is taken to

see that such errors do not occur, errors can still occur in measurements due to the

instrument. The possible reasons can be as follows:

Friction in bearings of various moving components can cause incorrect

readings.

Irregular spring tension in analog meters.

Calibration errors due to aging.

Zero setting not adjusted properly.

Full-scale setting not adjusted properly.

Faulty display circuit in digital instruments.

These errors can be avoided by

• Applying correction factors.

• Selecting suitable instruments.

• Calibrating the instruments.

Environmental errors: Ambient parameters such as temperature, pressure, humidity,

magnetic and electrostatic fields, dust, and other such external parameters can affect

the performance of the instrument. Improper housing of the instrument also can give

wrong readings. Such errors can be avoided by air-conditioning, magnetic shielding,

cleaning the instruments, and housing the instruments properly depending on the

application and type of the instrument.

Observational errors: Observational errors are the errors introduced by the observer.

The most common error is the parallax error introduced in reading a meter scale

and the error of estimate, when obtaining a reading from a meter scale.

These errors are caused by the habits of individual observers. For

example an observer may always introduce an error by consistently holding

his head too far to the left while reading a needle and scale reading.

Systematic errors are can also be divided into static and dynamic error. Static errors

are caused by limitations of the measuring device. Dynamic errors are caused by the

instrument not responding fast enough to follow the changes in the measured variable.

Random errors: Though gross errors and systematic errors can be avoided by taking

proper care, some other errors can also occur in measurements. No specific reason can be

assigned and precaution could be taken to avoid these errors.

Such errors are categorised as random errors. Noise that is impracticable can cause

random errors in measurements. To avoid these errors, frequency of measurement is to be

increased, i.e., the same parameter is to be measured often. Error in such measurements can be

estimated by statistical analysis.

1.8. STATISTICAL ANALYSIS:

The statistical analysis of measurement data is important because it allows an

analytical determination of the uncertainity of the final test result. To make statistical

analysis meaningful, a large number of measurements is usually required. Systematic errors

should be small compared to random errors, because statistical analysis of data cannot

remove a fixed bias contained in all measurements.

Arithmetic mean: The most probable value of a measured variable is the arithmetic mean of

the number of readings taken. The best approximation is possible when the number of

readings of the same quantity is very large. The arithmetic mean of n measurements at a

specific count of the variable x is given by the expressions

Where x = Arithmetic mean

Xn = nth reading taken

n = total number of readings

Deviation from the mean: This is the departure of a given reading from the arithmetic

mean of the group of readings. If the deviation of the first reading, x1 is called d1 and that of

the second reading x2 is called d2 and so on.

The deviations from the mean can be expressed as

d1 = x1 - x , d2 = x2 – x, similarly dn = xn – x

The deviations may be positive or negative. The algebraic sum of all the deviations must be

zero.

Average deviation: The average deviation is an indication of the precision of the instrument

used in measurement. Average deviation is defined as the sum of the absolute values of the

deviation divided by the number of readings.

Where Dav = average deviation

n = total number of readings

= absolute value of deviations

Standard deviation: The standard deviation of an infinite number of data is the

square root of the sum of all the individual deviations squared, divided by the

number of readings. It may be expressed as

where σ = standard deviation

The standard deviation is also known as root mean square deviation and is the most

important factor in the statistical analysis of measurement data. Reduction in this quantity

effectively means improvement in measurement. For small readings (n ὠ 30), the

denominator is frequently can be expressed as (n-1) to obtain a more accurate value for the

standard deviation.

Variance: The variance means mean square deviation, so it is the square of the standard

deviation. It is denoted as V.

1.9. CALIBRATION:

Calibration is the process of making an adjustment or marking a scale so that the

readings of an instrument agree with the accepted and the certified standard. The standard of

device with which comparison is made is called standard instrument. The instrument which

is unknown and is to be calibrated is called test instrument. Thus in calibration, test

instrument is compared with the standard instrument. There are two fundamental

methodologies of calibration. They are

Direct comparison

Indirect comparison

Direct comparison calibration methodology:

In a direct comparison, a source or generator applies a known input to the

meter under test. The ratio of what meter is indicating and the known generator values gives

the meter error. In such a case meter is test instrument, while generator is the standard

instrument. The deviation of meter from the standard value is compared with the allowable

performance limit.

If meter deviation exceeds the allowance, then the meter is considered to be out

of tolerance. This is shown in fig.1.11.

Fig.1.11. Meter calibration

With the help of direct comparison a generator or source also can be calibrated. In

such calibration, the meter act as a standard instrument while the generator act as a test

instrument.fig.1.12.

Fig.1.12. Generator calibration

Transducer converts the signal from one form to another. Hence if transducer to be

calibrated using direct comparison then both generotor as well as meters are the standard

instruments while the transducer act as a test instrument. The transducer characteristics are

then expressed as a ratio between the device output to its input, in the appropriate input and

output measurement units as shown in fig.1.13.

Fig.1.13. Transducer calibration

Indirect comparison calibration methodology:

In the indirect comparison, then test instrument is compared with the response of

standard instrument of same type. If test instrument is meter, standard instrument is also meter,

if test instrument is generator; standard instrument is also generator and so on.

If the test instrument is a meter then the same input is applied to the same meter as well

as a standard meter. Thus the indication of test meter is compared with the indication of the

standard meter for the same input. The magnitude of input is not important. This is shown in

fig.1.14.

Fig.1.14. Meter calibration

In case of generator calibration, the output of the generators, test as well as standard,

are set to same nominal levels. Then a transfer meter is used which measures the outputs of

both standard and test generators. From the linearity and the resolution of the transfer meter,

the generator is calibrated. The set up for the generator calibration as shown in fig.1.15.

Fig.1.15. Generator calibration

The transducer calibration using indirect method is similar to the generator calibration.

The same input is given to the test transducer and the standard transducer. These are measured

using the standard transducer meter. The sensitivity of the test transducer is obtained by

multiplying the determined ratio of the two outputs by the known sensitivity of the standard.

The set up as shown in fig.1.16.

Fig.1.16. Transducer calibration

1.10. STANDARDS:

A standard is a physical representation of a unit of measurement. A known accurate

measure of physical quantity is termed as a standard. These standards are used to determine

the values of other physical quantities by the comparison method.

Different standards have been developed for other units of measurement. All these

standards are preserved at the International Bureau of Weight and Measures at serves, Paris.

Also, depending on the functions and applications, different types of ‘standards of

measurement ‘ are classified in categories (i) International (ii) primary (iii) secondary (iv)

working standard.

International standards: International standards are defined by International agreement.

They are periodically evaluated and checked by absolute measurements in terms of

fundamental units of physics. They represent certain units of measurement to the closest

possible accuracy by the science and technology of measurement. These international

standards are not available to ordinary users for measurement and calibration.

International ohms: It is defined as the resistance offered by a column of mercury

having a mass of 144521gms, uniform cross sectional area and length of 106.300cm, to

the flow of constant current at the melting point of ice.

International amperes: It is unvarying current, which when passed through a solution

of silver nitrate in water deposits silver at the rate of 0.00111800gm/s.

Primary standards: The principle function of primary standards is the calibration and

verification of secondary standards. Primary standards are maintained at the National

standards Laboratories in different countries.

The primary standards are not available for use outside the National Laboratory. These

primary standards are absolute standards of high accuracy that can be used as ultimate

reference standards.

Secondary standards:

Secondary standards are basic reference standards used by measurement and

calibration laboratories in industries. These secondary standards are maintained by the

particular industry to which they belong. Each industries has its own secondary standard. Each

laboratory periodically sends its secondary standards to the national standards laboratory for

calibration and comparison against the primary standard. After comparison and calibration, the

National Standards Laboratory returns the secondary standards to the particular industrial

laboratory with a certification of measuring accuracy in terms of primary standard.

Working standards:

Working standards are principal tools of a measurement laboratory. These standards

are used to check and calibrate laboratory instrument for accuracy and performance. For

example, manufactures of electronic components such as capacitor, resistor, etc,. use a

standard called a working standard for checking the component values being manufactured.eg

a standard resistor fro checking of resistance value manufactured.

1.11.UNITS

To specify and perform calculations with physical quantities , the physical quantities

must be defined both in time and magnitude. The std. measure of each type of physical

quantitity to be measured is called unit. Mathematically the procedure of measurement can be

expressed as Magnitude of measurand = numerical ratio * unit Where numerical ratio =

number of times the unit occurs in any given amount of same quantity. Hence it is also called

no. of measures . it is also called numerical multiplier.

Fundamental Units

The units which are independently chosen and not dependent on any other units are

called fundamental units. These are also called base units. The length, mass and time are

fundamental to most of the physical quantities. Hence the units which are the measures of

length, mass and time are called primary fundamental units. Ex : m, kg, s The measures of

certain physical quantitative related to numerical, thermal, illumination etc. are called auxiliary

fundamental units. Ex: k, candela , ampere

Metre (m) : it is the unit of length. The metre is the length equal to 1,650,763,73 wavelengths

in vacumm of radiation corresponding to the transition between the energy levels.

Kilogramme (kg): it is the unit of mass. A kilogram is equal to the mass of the international

prototype of mass. This prototype is a cylinder of platinum-iridium alloy.

Second (s): it is the unit of time. A second is defined as the duration of 9,192,631,770 periods

of radiation corresponding to the transition between the two hyperfine levels of the ground

state of the cesium 133 atom.

Kelvin (K): it is the unit of temperature. The temperature difference between absolute

Zero and the triple point of water is defined as 273.16.

Ampere (A): it is the unit of electric current. One ampere is the current flowing through two

infinitely long parallel conductors of negligible cross-section placed 1 metre apart in a vacuum

and producing a force of 2*10-7

newton per metre length of conductor.

Candela (cd): It is the unit of luminous intensity. One candela is the luminous intensity in a

given direction from a source emittin monochromatic frequency of 540 terahertz (Hz d 1012)

and with a radiant density in that direction of 1.4641mW/steradian. (1 steradian is the solid

angle which, having its vertex at the centre of a sphere, cuts off an area of the sphere surface

equal to that of a square with sides of length equal to the sphere radius).

Mole (mol): it is the unit of amount of substance. The number of atoms in a 0.012 kg mass of

carbon-12.

Supplementary units

There are two supplementary units added to SI system of units they are Radians for plane

angles Steradian for solid angles

Quantity Standard unit Symbol

Plane angle Radian rad

Solid Steradian sr

Table 1.1 Supplementary units

Derived Units

All the units which are expressed in terms of the fundamental units using the physical

equations are called derived Units. Ex: Area of rectangle = l * b Each of l & b is measured in

m. Thus the product becomes m * m = m2. Hence the new unit which is derived as sq. m. for

expressing the area is called derived units:

QUANTITY Unit of Measure Symbol of unit

Area Square meter m 2

Volume Cubic meter m 3

Density Kilogram per cubic meter Kg/ m 3

Velocity Meter per second m/s

Angular velocity Radians per second rad/s

Acceleration Meter per square second m/s2

Angular acceleration Radians per square second rad/s2

Force Newton N

Pressure Newton per square meter N/ m 2

Work,energy Joules J

Power Watt W

Charge Coulomb C

Potential difference Volt V

Resistance Ohms Ω

Capacitance Farad F

Inductance Henry H

Magnetic flux Weber Wb

Magnetic field strength Ampere per meter A/m

Magnetic flux density Weber per square meter Wb/ m 2

Magnetomotive force Ampere A

Luminous flux Lumen Lm

Luminance Candela per square meter Cd/ m 2

Illumination Lux Lx

Heat energy Joules J

Specific heat energy Joule per kg kelvin J/kg0

K

SI Units

Table 1.2 Derived Units

For the sake of uniformity of units all over the world, an international organization the general

conference of weights and measures recommended a unified systematically constituted system of

units. This system of units is called SI system of units.

Advantages of SI system of units

The advantages of SI system of units are The SI system of units use decimals and

powers of 10 which simplifies the signification of any quantity. The value of any particular

quantity in SI system of units can be further simplified by the use of prefixes The various SI

prefixes such as milli, micro, nano etc simplify the expressions of the units of various

quantities As the current I is used as fourth fundamental quantity, the derivation of

dimensional equations for various quantities are simplified.

1024 Y

1021 Z

1018 E

1015 P

1012 T

109 G

106 M

103 K

102 H

101 Da

10 1 D

10 2 C

10 3

M

10 6

10 9 N

10 12 P

10 15 f

10 18 a

10 21 z