Resistance, Unit of Resistance,Laws of Resistance,Resistivity,Resistivities and Temperature Coefficients of materials
Resistance
The property of a substance due to which it opposes (or restricts) the flow of electricity (i.e., electrons) through it.
Metals (as a class), acids and salts solutions are good conductors of electricity.
Amongst pure metals, silver, copper and aluminium are very good conductors in the given order.
This is due to the presence of a large number of free or loosely-attached electrons in their atoms.
These vagrant electrons assume a directed motion on the application of an electric potential difference. These electrons while flowing pass through the molecules or the atoms of the conductor, collide and other atoms and electrons, thereby producing heat.
Those substances which offer relatively greater difficulty or hindrance to the passage of these electrons are said to be relatively poor conductors of electricity like bakelite, mica, glass, rubber, p.v.c. (polyvinyl chloride) and dry wood etc.
Amongst good insulators can be included fibrous substances such as paper and cotton when dry, mineral oils free from acids and water, ceramics like hard porcelain and asbestos and many other plastics besides p.v.c.
The Unit of Resistance
The practical unit of resistance is ohm.
A conductor is said to have a resistance of one ohm if it permits one ampere current to flow through it when one volt is impressed across its terminals.
For insulators whose resistances are very high, a much bigger unit is used i.e., mega-ohm = 10^6 ohm (the prefix ‘mega’ or mego meaning a million) or
kilo-ohm = 10^3 ohm (kilo means thousand).
In the case of very small resistances, smaller units like milli-ohm = 10^−3 ohm
Laws of Resistance
The resistance R offered by a conductor depends on the following factors :
(i) It varies directly as its length, l.
(ii) It varies inversely as the cross-section A of the conductor.
(iii) It depends on the nature of the material.
(iv) It also depends on the temperature of the conductor
Neglecting the last factor we can say that
R ∝ l/A
or R =ρl/A
where ρ is a constant depending on the nature of the material of the conductor and is known as its specific resistance or resistivity.
If in the above equation,
l = 1 metre and A = 1 metre^2, then R = ρ
Hence, specific resistance of a material may be defined as the resistance between the opposite faces of a metre cube of that material.
Units of Resistivity
we have ρ = AR/l
In the S.I. system of units,
ρ =metre^2* ohm/metre
= ohm-metre
Hence, the unit of resistivity is ohm-metre (Ω-m).
It may, however, be noted that resistivity is sometimes expressed as so many ohm per m^3.
Although, it is incorrect to say so but it means the same thing as ohm-metre.
If l is in centimetres and A in cm^2, then ρ is in ohm-centimetre (Ω-cm).
Values of resistivity and temperature coefficients for various materials are given in Table below
The resistivities of commercial materials may differ by several per cent due to impurities etc.
Resistivities and Temperature Coefficients
Material Resistivity Temperature coefficient at
in ohm-metre 20ºC (× 10^−4)
at 20ºC (× 10−8)
Aluminium 2.8 40.3
Brass 6 – 8 20
Carbon 3000 – 7000 −5
Constantan/Eureka 49 +0.1 to −0.4
Copper (annealed) 1.72 39.3
German Silver 20.2 2.7
(84% Cu; 12% Ni; 4% Zn)
Gold 2.44 36.5
Iron 9.8 65
Manganin 44 – 48 0.15
(84% Cu ; 12% Mn ; 4% Ni)
Mercury 95.8 8.9
Nichrome 108.5 1.5
(60% Cu ; 25% Fe ; 15% Cr)
Nickel 7.8 54
Platinum 9 – 15.5 36.7
Silver 1.64 38
Tungsten 5.5 47
Amber 5 × 10^14
Bakelite 10^10
Glass 10^10 – 10^12
Mica 10^15
Rubber 10^16
Shellac 10^14
Sulphur 10^15
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