Current Density Conductance and Conductivity:
Current Density (J)- It is defined as the amount of current flowing per unit area of the conductor at a particular point, provided the area is held perpendicular to the direction of the current.
Let ‘I’ be the current distributed uniformly over the cross-sectional area A of the conductor, then
| J = I/A |
Current density, J is a vector quantity. Its direction is the direction of motion of the positive charge. The S.I. unit of current density if ampere/metre2.
| We know, I = nAeνd ⇒ I/A = neνd ⇒ J = neνd |
Conductance (G)- The inverse of resistance is called conductance of the conductor i.e.
| G = 1/R |
The S.I. unit of conductance is mho or siemen (S).
Conductivity (σ)- The inverse of resistivity is called the conductivity of the conductor i.e.
| σ = 1/ρ |
The S.I. unit of conductivity is mho-m-1 or siemen-m-1.
Relation between Current Density Conductance and Conductivity:
| We know, I = nAeνd ————(I) But, νd = Eeτ/m —————–(II) Put (II) in (I) ⇒ I = nAe (Eeτ/m) ⇒ I = nAe2Eτ/m ⇒ I/A = ne2τ/m x E ⇒ J = ne2τ/m x E But, ne2τ/m = 1/ρ ⇒ J = 1/ρ x E But, 1/ρ = σ = conductivity of the conductor ⇒ J = σE It is microscopic form of Ohm’s Law. |
Comments (No)