Resistance
The resistance of a conductor is the obstruction posed by the conductor to the flow of electric current through it.
Resistance (R) of a conductors defined as the ratio of the potential difference (V) across the ends of the conductor to the current (I) flowing through it R = V/I
The S.I. unit of resistance is ohm (O) where
1 ohm = 1 volt / 1 ampere = 1V / 1A
Thus l ohm is the resistance of a conductor through with a current of 1 ampere flows when a potential difference of 1 volt is applied across the ends of the conductor.
Dimensions of electric resistance = [M1 L2 T-3 A-2]
International ohm it is defined as the resistance of 106.3 cm long mercury column of 1 mm2 cross-sectional area and mass 14.4521 gram at 0°C
Cause of resistance of a conductor resistance of a given conducting wire is due to the collisions of free electrons with the ions or atoms of the conductor while drifting towards the positive end of the conductor which in turn depends upon the arrangement of atoms in the conducting material on the kind of material (silver copper etc.) as well as on the length and thickness of the conducting wire.
Resistivity
The resistance of a conductor depends upon the following factors.
Length (1) consider two identical conductors in the form of slabs each of length/ and area of cross-section A. let V be the potential difference applied across either slab and I be the current through it. The resistance of each slab is
R = V/I
Area of cross-section (A) divide a conductor slab into two equal parts cutting it length wise, so that the slab may be considered as a combination of two identical slabs each of length having a cross-sectional area A/2 when the same potential difference V is applied across each of the two half slabs, the current flowing through each is l/2 which is half of the current through the full slab. The resistance of each of the half slab is R = V / l / 2 = 2 V / l = 2R
The resistance of a conductor also depends upon the nature of material and temperature of the conductor.
From above; R∝l / A or R = pL / A
Where p is constant of proportionality and is known as specific resistance or electrical resistivity of the material of the conductor
If L = 1,A = 1, then form (8) R = P
Thus specific resistance (or electrical resistivity) of the material of a conductor is defined as the resistance offered by unit lend and unit area of cross section by a wire of the given material of conductor it is also defined as the resistance of unit cube of a material of the given conductor.
Unit of resistivity; form (8), p = RA/L
In SI unit of resistivity = ohm x m2 = ohm – m or O m.
Factors affecting electrical resistivity
Form (7), we have
R = V / I = Ml / Ane2τ = m/ ne2 τ x L / A
P ∝ l / n the resistivity of the material of conductor is inversely proportional to the number density of electrons (n) number of the electrons per unit volume of the conductor since the value of n depends upon the nature of material hence the resistively of the conductor depends upon the nature of material.
P ∝l/ τ the resistivity of the material of conductor is inversely proportional to the average relaxation time (τ) of the free electrons in the conductor.
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