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29/06/2021

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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