deduce ohms law by the concept of drift velocity - Physics - Electricity

Question

deduce ohms law by the concept of drift velocity

Malka Tarannum · Accepted Answer

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=neAeτEmor,   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