I = nAe(Veτ/2lm) I = V(ne2 τ/2m)(A/l) I (2m/ne2τ)(l/A) = V ......................(e)
In the above equation, mass of the electron (m) and charge of the electron (e) are constants because these values are characteristics of the electron.
The electron density (n) of a metal conductor depends on its nature so it is also constant for a particular conductor.
For a given conductor, the length (l) and cross section area (A) are also constants. The value of τ depends on temperature of the conductor. When the temperature increases the random motion of electrons increases hence the value of τ decreases.
For a constant temperature of a conductor the value of τ becomes constant.
Hence (2m/ne2τ) (l/A) becomes a constant for a particular conductor at constant temperature. Let this value be R (called resistance of a conductor). The we get
IR = V (from equation e) ...................(f) This is what we call Ohm's law. Where R = (2m/ne2τ) (l/A) ..................(g)
In the above equation 2m/ne2 τ is the characteristic value of a conductor. The value of resistance R is different for different geomentrical values for a particular conductor (material). Hence 2m/ ne2τ is taken as a constant independent of geomentrical values. Let it be ρ. It is called specific resistance
ρ = 2m/ne2τ From equation (g) we get R = ρl/A ..................(h) Note: Drift velocity and Drift speed are synonoum