Question

Using theory of drift velocity express ohms law

Answer 1

Ohm's law and drift velocity in conductorsFrom Physclips: Mechanics with animations and film.

proportional to the number of mass carriers/cubic metre of air (n)

proportional to the cross sectional area of 'conductor' (A)

proportional to the square of the mass on an individual mass carrier (m)

Answer 2

Here is your answer

➡ Statement of Ohm's Law :
⭐Ohm's law states that the current flowing through a conductor is directly proportional to the potential difference across its two ends, provided that the physical conditions ( temperature, mechanical strain, etc ) remain constant. ...
⭐ Electric current is defined as the rate of flow of electric chargethrough a conductor.


➡Derivation :

➡Consider a current of length l and cross sectional area A. When a potential difference V is applied across its ends, the current produced is I. If n is the number of electrons per unit volume in the conductor and vd the drift velocity of electrons, then the relation between current and drift velocity is
             I=neAvd       .........(i)
Where e is the electric charge on the electron.
Electric field produced at each point of wire, E=Vl       ............(ii)
If τ is the relaxation time and E is the electric field strength, then drift velocity
                                                                                                 vd=eτEm     .............(iii)
Substituting this value in equation (i), we get
                                                          I=neA(eτEm)or,   I=ne2τmAE              ...........(iv)
From equation (ii)
                              I=ne2τAmVlor,   VI=mne2τlA        ...............(v)

Under given physical conditions such as temperature, pressure etc., for a given conductor

mne2τlA=R=a constant  .........(vi)

For a given conductor, R is a constant and is known as the resistance of the conductor.

Thus, from equation (v) and (vi)
                 VI=R
This Ohm's law.

Hope it helps You out :-)