Question

(i) Derive an expression for drift velocity of free electrons.
(ii) How does drift velocity of electrons in a metallic conductor vary with increase in temperature? Explain.

Answer 1

(i) Expression for drift velocity of free electrons:

When electric potential is applied, the electric field is produced and electric force acts on the free electrons.

Since, electrons collide and accelerate, they acquire constant average velocity.

$\mathrm{F}_{\mathrm{e}}=-\mathrm{Ee}$

$\Rightarrow F_{e}=\frac{-e V}{I}$

The acceleration is given by the formula:

$a=\frac{-F}{m}$

$a=\frac{-e V}{m}$

On applying the below equation of motion, we get,

$v=u+at$

When u = 0; t = T, we get,

$v_{d}=-a T$

$v_{d}=\frac{-e V}{m} T$

(ii) Drift velocity of electrons in a metallic conductor:

From equation above, we get,

When the temperature increases, then drift velocity of electrons in a metallic conductor decreases.

$\mathrm{v}_{\mathrm{d}} \propto \mathrm{T}$

When the temperature increases, the relaxation time increases as there is more collision among the electrons. Thus, the drift velocity decreases.