Factors on which the resistance of a conductor depends

The resistance (R) of a conductor depends on the geometric dimensions (length, cross-sectional area) of the conductor, the nature of the material, and various physical factors given below:

i. Dependence on length (l): If the cross-sectional area (A) of a given material of conductor be uniform then

R ∝ l

ii. Dependence on cross-sectional area (A): For a given length and for a given material of a conductor.

R ∝ l/A

iii. Dependence on material: For the same length (l) and cross-sectional area (A), resistances are different for different materials.

R ∝ l/A

or R = ρ. l/A

where the proportionality constant ρ is called the resistivity or the specific resistance of the material of the conductor. The value of ρ mainly depends upon:

i. The material of the conductor.
ii. The temperature of the conductor.

Note: Resistivity doesn’t depend on the length and the cross-sectional area of the conductor and that is why resistivity is more fundamental than resistance.

iv. Dependence on temperature: The resistivity and hence resistance of all conductors (metals and most of the alloys) increases with the rise of temperature and if the temperature isn’t too large, the relationship between them is approximately given by,

Rt = R0(1 + αt)

R0 = resistance of the conductor at 0°C
Rt = resistance of the conductor at t°C
α = temperature coefficient of resistance of the material of the conductor
= (Rt – R0) / R0t

v. Dependence on magnetic field: There are certain substances for which resistance increases when they are placed in the magnetic field.

vi. Dependence on pressure: For most metals resistance decreases with the increase in pressure.

vii. Dependence on light: There are some metals for which resistance decreases when they are placed under light.