Question

Write an expression for resistivity of a conductor and explain each term .

Answer 1

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Q)

 

Define the term electrical resistivity of a material. Write the S.I units. Derive an expression for the resistivity of a metal in terms of number density and mass of free electrons present in it .



A)

 

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Solution :

Electrical resistivity of a material of a conductor is the resistance offered by unit length and unit area of cross section of a wire of the material .

Its S.I unit is ΩmΩm

The drift velocity of free electron in a conductor is

Vd=eVmeVd=eVme

But I=VdenAI=VdenA

Substituting for VdVd we get,

I=(evml)I=(evml)ρnA=e2VInAmlρnA=e2VInAml

V=I(mlne2tA)V=I(mlne2tA)

By Ohm's law V=IRV=IR

∴IR=I(mlne2TA)∴IR=I(mlne2TA)

R=mlne2TAR=mlne2TA

Also R=ρlAR=ρlA

Where ρρ is the resistivity of the material.

∴ρA=mlne2TA∴ρA=mlne2TA

=> ρ=mne2T