Lecture - 1

Topics to be discussed

• Definition of measurements.

• Fundamentals of units

• Rules of notation.

• Dimensions.

• Different parameters with units.

• GMS (general building blocks of measuring

instruments) with live example.

• References

Definition of Measurements:WHAT is Measurement?❖ Measurement of a quantity is the “act or the result of a quantitative

comparison between a predefined standard and an unknownmagnitude”.

✓ The result is meaningful, when(1) the standard must be accurately known and internationally accepted.(2) the apparatus and the experimental procedure adopted for

comparison must be provable.

Known value or character of

physical variable

universally accepted

Unknown becomes

known quantity

Place where estimation

through comparison

takes place

Fundamentals of units and dimensions.

• Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit.

• The result of a measurement of a physical quantity is expressed by a number (or numerical measure) accompanied by a unit.

• A unit of measurement is a definite magnitude of a quantity, defined and adopted by either convention or law, that is used as a standard for measurement of the same quantity.

• Any other value of that quantity can be expressed as a simple multiple of the unit of measurement.

The base units for length, mass and time in these systems are as follows:

– In CGS system they were centimetre, gram and second respectively.

– In FPS system they were foot, pound and second respectively.

– In MKS system they were meter, kilogram and second respectively

• The system of units which is at present is the SystèmeInternationale d’ Unites (French for International System of Units), abbreviated as SI.

Fundamentals of units and dimensions cont...

• The units for the fundamental or base quantities are called

fundamental or base units.

Fundamentals of units and dimensions cont...

The units of all other physical quantities can beexpressed as combinations of the base units – Derivedunits

Fundamentals of units and dimensions cont...

Rules and conventions for writing SI units and their symbols

1. The units named after scientists are not written with a capital initial letter.

For example : newton, henry, watt

2. The symbols of the units named after scientist should be written by a capital letter.

For example : N for newton, H for henry, W for watt

3. Small letters are used as symbols for units not derived from a proper name.

For example : m for metre, kg for kilogram

Rules of notation.

4. No full stop or other punctuation marks should be used within or at the end of symbols.

For example : 50 m and not as 50 m.

5. The symbols of the units do not take plural form.

For example : 10 kg not as 10 kgs

6. When temperature is expressed in kelvin, the degree sign is omitted.

For example : 273 K not as 273o K

(If expressed in Celsius scale, degree sign is to be included. For example 100o C and not 100 C)

Rules of notation...

Rules of notation...

7. Use of solidus is recommended only for indicating a division of one letter unit symbol by another unit symbol. Not more than one solidus should be used For example : m s-1 or m / s, J / K mol or J K-1 mol-1 but not J / K / mol.

8. Some space is always to be left between the number and the symbol of the unit and also between the symbols for compound units such as force, momentum, etc.For example, it is not correct to write 2.3m. The correct representation is 2.3 m; kg m s-2 and not as kgms-2.

9. Only accepted symbols should be used. For example : ampere is represented as A and not as amp. or am ; second is represented as s and not as sec.

10. Numerical value of any physical quantity should be expressed in scientific notation.

Definition of dimensions:

The nature of a physical quantity is described by its dimensions. All the physical quantities represented by derived units can be expressed in terms of some combination of seven fundamental or base quantities

(or)

Dimension is an expression of the character of a derived quantity about fundamental quantities, without regard for its numerical value

How to write dimensions of physical quantities

(a). Write the formula for that quantity, with the quantity on L.H.S. of the

equation.

(b). Convert all the quantities on R.H.S. into the fundamental quantities

mass, length and time.

(c). Substitute M, L and T for mass, length and time respectively.

(d) Collect terms of M,L and T and find their resultant powers (a,b,c) which give the dimensions of the quantity in mass, length and time respectively.

Fundamentals of units and dimensions cont...

Quantity Formula Dimensions

Area Length x Length [L]2

Volume Length x Length x Length [L]3

Velocity Length/ Time [L][T]-1

Acceleration Velocity/ Time [L][T]-2

Force Mass x Acceleration [M][L][T]-2

Energy Force x Length [M][L]2[T]-2

Power Energy/ Time [M][L]2[T]-3

Pressure Force/ Area [M][L]-1[T]-2

Momentum Mass x Velocity [M][L][T]-1

Characteristics of Dimensions

(a). Dimensions of a physical quantity are independent of the

system of units.

(b). Quantities having similar dimensions can be added to

or subtracted from each other.

(c). Dimensions of a physical quantity can be obtained from

its units and vice-versa.

(d). Two different physical quantities may have same

dimensions.

(e). Multiplication/division of dimensions of two physical

quantities (may be same or different) results in

production of dimensions of a third quantity.

GMS (general building blocks of measuring instruments) with live example.

Output

InstrumentOr

System

Input

References:

A Electrical and electronic Measurement and Instrumentation by A.K.Sawhney,

publisher: Gagan Kapur, Danpat Rai & Co.

http://ncert.nic.in/ncerts/l/keph102.pdf

http://ncerthelp.com/cbse%20notes/class%2011/physics/Physics%20Notes%20Class%

2011%20CHAPTER%202%20UNITS%20AND%20MEASUREMENTS%20.pdf

http://www.careerpoint.ac.in/download/smp_sample/IIT_Physics_Unit_Dimension.pdf

http://physics.nist.gov/cuu/pdf/sp811.pdf