LAWS OF RESISTANCE: The value of resistance of a conductor depends on its
►i) Length– l.
►ii) Cross section- A.
►iii)Nature of the conductor material.
►iv)Depends on the temperature of the conductor.

The value of resistance R of a conductor is directly proportional to its length, l.
So, R ∞ l.

The resistance is inversely proportional to the cross sectional area, A.
So, R ∞ 1/A.
By the combination of these two properties, we can write, R ∞ l/A,
Or, R = ρl/A, where ρ = constant.
ρ is the constant depending on the nature of the material of the conductor and known as specific resistance or Resistivity.

SPECIFIC RESISTANCE OR RESISTIVITY: Resistivity of a material is the resistance between two opposite faces of a meter cube.

Resistivity defines the power of opposition of electric current in a material. It depends on the nature of the material, that is, the chemical composition of the material. It does not depends on shape or size.

UNITS OF RESISTIVITY: To find the units of resistivity, at first write down the equation.
R = ρl/A ohm.
Or, ρ = RA/l
Or, ρ = ohm x m2/m.= ohm-m.
Hence, the unit of resistivity is ohm-m.
If l in centimeter, and A in cm2, then ρ = ohm-cm.

TEMPERATURE EFFECT ON RESISTIVITY: The resistivity of a material changes with temperature, that means the current carrying capacity of a material changes with temperature. At lower temperature the efficiency of current carrying capacity of most metal is high but at higher temperature the motion of electrons become slow due to increased jostling of atoms, which means resistivity increases.
So, we can say the resistivity of a material depends on the temperature.
If ρt = Resistivity at t℃, and ρ0 = Resistivity at 0℃,
We can write the equation as, ρt = ρ0(1+α0t).
Here α = temperature co-efficient of resistance.

CONDUCTANCE AND CONDUCTIVITY: It represents that, it allow the flow of electric current of a material. That means Conductance, G is reciprocal of resistance.
Or, G = 1/R.
Unit of conductance is mho.
Resistance opposes the flow of current, whereas conductance does the opposite.
As, R = ρl/A.
Or, G = 1/R = A/ρl= σA/l.
σ is called the conductivity or specific conductance of a conductor.
The unit of conductance is Siemens(S) or sometimes called mho.
From above equation, conductivity of material is written as,
G = σA/l,
Or, σ = G l/A Siemens/ meter.
So, the unit of conductivity is Siemens/m.


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