derive an expression for the resistivity of material
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Answered by
11
if you want simple expression for resistivity,then follow below procedure...
EXPRESSION FOR RESISTIVITY OF MATERIAL
we know that the resistance of material body is directly proportional to its length
R ∝ L
also,the resistance is depend inversly on area of cross-section of body.
R ∝ A
COMBINNIG ABOVE TWO FACTORS,WE GET,
R ∝ L/A
R=ρ× L/A
where rho{ρ} is proportionality constant called specific resistance or resistivity
so we say,
→ ρ= R×A/L ←
Answered by
1
Explanation:
let n = number density of free electrons
A = Cross sectional area of conductor
e = electrons charge
Number of free electrons present in l length of conductor = nAl
Total charge contained in length l which can contribute in current
q = (n A l)e
The time taken by free electron to cross the l length of conductor is
t = l/vd
where, vd = drift speed of electron
current through the conductor
I = q/t
I = ( n A l )e/ t
= ( n A l ) e / ( l/vd )
=n e A vd
current density(i) = i/A = n e A vd/A = n e vd
( j= n e vd i.e. j ∞ vd )
thus current density of conductor is proportional to drift speed.
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