Resistance & Resistivity

• The resistance of a particular metal / conductor depends upon its length, area and nature of material and temperature. 
• The resistance is directly proportional to length and inversely proportional to area.

       R α L

       R α 1 / a

       Combining these two

       R α L / a

       R = ρL / a  ………. ( 1 )

Where

       ρ = Electrical resistivity of conductor, constant

       L = Length of conductor

       a = Area of conductor

The unit of resistance is ohm.

from equation ( 1 )

ρ = Ra / L

The unit of resistivity ρ is = unit of resistance × Unit of area / Unit of length

                                             = Resistance × meter² / meter

                                             = Resistance × meter

If L = 1, a = 1, then ρ = R

Definition of resistivity

• The resistivity of any material is equal is the resistance of that material having unit length and unit cross section area.

Resistivity of material

• The conductivity of material like conductor, semiconductor and insulator depends upon their resistivities. 
• The metals have low resistivities in the range of 10 ^{– 8} ohm meter to 10 ^{– 6} ohm meter. 
• The insulators have resistivities 10¹⁸ times greater than metal whereas the resistivities of semiconductor lies between insulator and conductor.
•  As the temperature increases, the resistivity decreases. 
• The resistivity of semiconductor material is also affected by the small amount of impurities whether it is trivalent or pentavalent.

 

Material	Resistivity in ohm meter at 0 oC	Temperature co-efficient of resistance ( Per degree centigrade ) at 0 oC
Metal
Silver	1.6 × 10 – 8	0.0041
Copper	1.7 × 10 – 8	0.0068
Aluminum	2.7 × 10 – 8	0.0043
Tungsten	5.6 × 10 – 8	0.0045
Iron	10 × 10 – 8	0.0065
Platinum	11 × 10 – 8	0.0039
Mercury	98 × 10 – 8	0.0009
Nichrome	100 × 10 – 8	0.0004
Manganin	48 × 10 – 8	0.002 × 10 – 3
Semiconductor
Carbon	3.5 × 10 – 5
Germanium	0.46
Silicon	2300
Insulators
Pure water	2.5 × 10 5
Glass	1010 to 1014
Hard rubber	1013 to 1016
NaCL	1014

  

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