In order to make the measurement of a physical quantity we have, first of all, to evolve a standard for that measurement so that different measurements of same physical quantity can be expressed relative to each other. That standard is called a unit of that physical quantity.
System of Units:
(a) C.G.S (Centimeter-Grand-Second) system.
(b) F.P.S. (Foot-Pound-Second) system.
(c) M.K.S. (Meter-Kilogram--Second) system.
(d) M.K.S.A. (Meter-Kilogram-Second-Ampere) unit.
Dimensional formula of a physical quantity is the formula which tells us how and which of the fundamental units have been used for the measurement of that quantity.
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.
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.
Mechanical Physical Quantities (derived)
meter per second
radians per second
meter per square second
radians per square
watt or joule/sec
D or ρ
kilogram per cubic meter
Newton per square meter
Kilogram square meter
lumen (4Pi candle for point source)
lumen per square meter
joule per degree
Volume rate of flow
cubic meter per second
square meter per second
Newton second per square meter
Newton per cubic meter
Electrical Physical Quantities (derived)
|emf, voltage, potential||E||ML2T-2Q-1||Volt||Kg m2/sec2C|
|resistance or impedance||R||ML2T-1Q-2||ohm||Kgm2 /secC2|
|Electric conductivity||s||M-2L-2TQ2||mho||secC2/Kg m3|
|inductance||L||ML2Q-2||Henry||Kg m2 /C2|
|Current density||J||QT-1L-2||ampere per square meter||C/sec m2|
|Charge density||r||QL-3||coulomb per cubic meter||C/m3|
|magnetic flux, Magnetic induction||B||MT-1Q-1||weber per square meter||Kg/sec C|
|magnetic intensity||H||QL-1T-1||ampere per meter||C/m sec|
|magnetic vector potential||A||MLT-1Q-1||weber/meter||Kg m/sec C|
|Electric field intensity||E||MLT-2Q-1||volt/meter or newton/coulomb||Kg m/sec2 C|
|Electric displacement||D||QL-2||coulomb per square meter||C/m2|
|permeability||m||MLQ-2||henry per meter||Kg m/C2|
|permittivity,||e||T2Q2M-1L-3||farad per meter||sec2C2/Kgm3|
|frequency||f or n||T-1||Hertz||sec-1|
|angular frequency||W||T-1||radians per second||sec-1|
Principle of homogeneity:
It states that “ the dimensional formulae of every term on the two sides of a correct relation must be same.”
Types of error:
(a) Constant errors:- An error is said to be constant error if it affects, every time, a measurement in a similar manner.
(b) Systematic errors:- Errors which come into existence by virtue of a definite rule, are called systematic errors.
(c) Random error or accidental error:- Error which takes place in a random manner and cannot be associated with a systematic cause are called random or accidental errors.
(d) Absolute error:-