Current density , conductance and electrical conductivity

Current density , conductance and electrical conductivity  –

In this topic we will discuss about what is Current density , conductance and electrical conductivity  ? and also the relation between them .

Before to learn about this topic students must have to know about Drift velocity , Ohm’s law , resistance and resistivity ( without know about them students can’t understand this topic explained below )

To  know about drift velocity click here-

To know about Ohm’s law click here-

To know about resistance and resistivity click here-

Current density , conductance and electrical conductivity  –

Current density

Current density of a conductor at a point is the amount of current flowing per unit area of the conductor .

If ‘I’ is the current flowing through the conductor and A is the area of cross-section the conductor at a given point then current density  J = I/A . Its unit is ampere per meter square ( Am-2)

Again as we know  I = neA Vd ;

Then current density J = neA Vd /A =  ne Vd

Conductance (G) of a resistor

Conductance of a conductor is the inverse of resistance (R) .

G = 1/R   , Its unit is ohm-1 or mho or siemen (S) ;

Electrical conductivity

Electrical conductivity is the inverse of resistivity . It is represented by (σ) .

So, σ = 1/ƍ  its SI unit is ohm-1m-1  ,

and its dimension is [ M-1 L-3 T3 A2]

So we can write  electrical conductivity , σ = ne2Ʈ/m

 

Relation between J , E and σ

[ microscopic form of Ohm’s law ]-

I =neAVd = neA (eEƮ/m) = nAe2EƮ/m

Or   J=I/A   = (nAe2EƮ/m)/A = E/ƍ = E(1/ƍ)=Eσ

J=Eσ

Relation between electrical resistivity and electron mobility –

As we know , I =neAVd ; Vd = μ(mobility)E

And  J = I/A = E/ƍ = neVd =neEμ    or , ƍ=1/neμ . 

 

 Next topic colour code of  carbon resistors – click here-

 

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