Question

what is electrical conductivity? Derive an expression for the same​

Answer 1

Answer:

R=mτLmAe2 is called the electric resistance of a conductor. and K=(nAe2mτL) is called the electric conductance of a conductor. the expression σ=nc2mτ is called the electrical conductivity and 1σ=mτ≠2 is called electrical resistivity.

Answer 2

Electrical conductivity:

• The measure of ease at which an electric charge or heat can pàss through a material is known as electrical conductivity.

• Materials are metals, insulators and semiconductors.

• Formula for electrical conductivity :-

$\qquad \bf R = \dfrac{l}{A} \rho$

Where,

• R = Resistance.
• l = distance.
• A = Area of a sample.
• $\sf \rho$ = Specific heat.

Derivation of expression of electrical conductivity :-

Conductivity of a material, $\sf \sigma = \dfrac{ne^2x}{m}$

We know that,

Volume of conductor, V = Al.

Total number of electrons = Aln ––(i)

• e = charge on each electron.

Total charge, Q = Alne ––(ii)

Time taken by electron tto cover the distance l with speed Vd :

• Time, $\sf t = \dfrac{l}{v}$

We know that, Current, I = $\dfrac{Q}{t}$

• $\sf Current, \ I \ = \ \dfrac{Alne}{\dfrac{l}{V_d}}$

$\qquad \bf I \ = \ neav_d$ ––(iv)

We know that,

$\implies \sf V_d = \bigg( \dfrac{Ee}{m} \bigg)$

Now,

$\implies \sf J = \sigma E$

• $\large{\underline{\boxed{\bf \sigma = \dfrac{ne^2x}{m}}}}$