Derive the expression of for the conductivity of a wire in terms of number density and russian time
Answers
first of all it not russian time it is relaxation time
next
we have a formula
I=neAV -------1
where
I=current
n=number density of electrons
A=area of cross section of wire
V=drift velocity
e=charge of electron
now,
V=eE/m(T) ------2
where
E=electric field intensity
T=relaxation time
m=mass of electron
put 2 in equation 1
we get I=(ne^2AE/m)T ------3
we know that
E=V/lt ------4
where
V=potential
lt=length
put 4 in 3
I=(ne^2T/m)AV/lt
I/V=(ne^2T/m)A/lt
reciprocate,
V/I=(m/ne^2T)lt/A
we know that V/I=R
R=(m/ne^2T)lt/A --------5
we also know that
R=(resistivity*lt)/A ------6
hence compare 5 and 6
we get
resistivity=m/ne^2T
we know that conductivity=1/resistivity
hence the required expression is
conductivity=(ne^2T)/m
:)