## 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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