Question

derive the expression for electrical condutivity of a material in terms of reboration time?
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Answer 1

Answer:

Explanation:

As per Newton's law we know F = ma

If E is the field intensity and e is the charge of the electron, then the force experienced by the electron is F = eE

equating above two equations

eE = ma

Here m is mass of electron

a =     ....(i)

If we assume initial velocity be 0 i.e after each collision we have assumed that electron starts from zero velocity then as per first equation of motion (v = u+at)

u = 0

v = aT

where T is mean time between collisions and v is drift velocity of electron

a =     .....(ii)

equating (i) and (ii)

we get  v =               ....(iii)

We know current density is J =      ....(iv)

Let us consider a solid metal (S) of length 'l' and area of cross-section 'A'. Let 'n' be the number of electrons per unit volume

Total charge present in the solid  Q  =  nAl(-e)    ....(v)

Then current is I =        ....(vi)

Putting (v) in (vi)

I =       .....(vii)

and v =          .....(viii)

Putting (viii) in (vii)

I = -neAv                                    .....(ix)

Putting (ix) in (iv)

J = nev                                        ....(x)

putting value of v from (iii) in (x)

we get

J = ne      ....(xi)

We know  σ = 1 /  p

p here denotes resistivity and σ is conductivity

We also know p = RA/L

where R is resistance L is length and A is area

σ =            .....(xii)

As per Ohm's Law

R =                .....(xiii)

Putting (xiii) in (xii) we get

σ =  

σ =  

σ =  

As J = I/A and E = V/L

σ = J/E

Putting value of J from (xi)

σ =