Question

state and derive Ohm's law using concept of drift velocity

Answer 1

Hey dear . . 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 ⭐^_^⭐
Thanks ⭐(^^)⭐

Answer 2

Explanation:

let, us consider a conductor having potential difference at it's 2end's let as consider a small. cross section A B C D of the conducter. supposed an electron moving from AC to BD in time T sec with a drift velocity V'd

then (CD=AB=vdt).........(1)

let 'a' is the area of cross sectional of conducter volume of conducter (ABCD=CD×a)

( VAT. a )......2

let 'N' is the no of electrons per unit volume then no. of free electrons in volume,

a vat. t =n. a vdt

let 'e'en be the charge of an electron the naval t

no of electrons have charge is givin by q=na.evd.t

.

. .the electric current thou

yh the. conducter is given by I=q/t

naevat/t =naevd...........3

[I inverse vd]ie electric current the is describing propen onal drift velocity

here eq n (3) =I =na ev/me +t

(= I= nae^t.v/me ).........4

(i=i/r.v) ................5

when i/R .v= nae^t/me............6

since n, a, e, m, l, and t are constant I inverse v which stat that

at a constant uniform cross sectional area is directly proportionalte 'v'bet.n the 2 ends of it

eq n (6) can be written as R =me/nae^t...........7

Resistance :-

Let Ces consider a conduction through which a current (I) flows due to the pointal difference (v) across the 2nds then according to ohm 's law iΔv

i=i/r.v.

R=v/i ..........1

when R is the resistance of the conducter from eq n (1) it is clear that for a fixed value of 'V' is a 'R' increase then I decnceases .

hence the qualitative definition of resistance states that resistance is nothing but an opposite upparatus by a conductar to a flow of electric current passing through it

I is one

if eq, n (I) if unity then R=V

Hence Resistance of aconductorcan asso be defined as the potential difference bet n the 2nds of conducter through which a unity amount of current flows.

from eq 'n (1) it self resistance of a conducter can also be quantitatively de find as the conducter through the unit current flow through it