Free POLYTECHNIC notes on internet For the first time by PRONAB BARUAH
Define resistance ? Explain the laws of resistance & give the unit of resistivity.
Ans.
It may be derfine as the property of a substance due to which it opposes the flow of electricity through it.
Unit of resistance
V ∝ I
V = R I
R = V/ I volt/ampere = ohm (Ω)
Laws of resistance are explained below……………….
The resistance of a conductor depends on the following factors :-
(a) LENGTH :- The resistance of a conductor is directly proportional to its length i.e., R ∝ L ( R= resistance, L = length )
(b) CROSS-SECTIONAL AREA :- The resistance of a conductor is inversely proportional to its cross-sectional area i.e., R ∝ (1/A)
(c) NATURE OF THE MATERIAL :- It depends upon the nature of the material. As different material offers different resistance to the flow of electricity.
(d) TEMPERATURE :- Resistance depends upon the temperature of the conductor i.e., if the temperature of a conductor increases, resistance directly varies ; In case of semi-conductor if the temperature increases, resistance inversely varies.
Neglecting the last factor ( temperature ) we have……….
R ∝ (L/A)
R = þ(L/A)…….(i)
Where þ is constant and is known as specific resistance or resistivity, it depends on the nature of the material.
Now we putting in equation (i)……….. L = 1 meter & A = 1 m2
Then, R = þ( L/A )
= þ (1/1)
R = þ
Unit of resistivity :-
We know that R ∝ (L/A)
R = þ( L/A )
Þ = RA/L
Hence the unit of resistivity will be depend upon the unit of area of cross-section (A) & length (L).
If the length is measured in metres and area of cross-section in square metres, then the unit of resistivity will be ohm-metre (Ω-m) i.e.,
R = þ( L/A )
Þ = RA/L
= ohm×m2/m
Þ = ohm-m
