current-electricity Question 33
Question: Q. 11. (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.
U [Delhi I, II, III 2016]
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Solution:
Ans. (i) When a potential difference is applied across a conductor, an electric field is produced and free electrons are acted upon by an electric force $\left(F_{e}=-E e\right)$. Due to this, electrons accelerate and keep colliding with each other and acquire a constant (average) velocity $v_{d}$, which is known as drift velocity.
$$ \begin{aligned} & \therefore \quad F_{e}=-E e \ & \therefore \quad F_{e}=\frac{-e V}{l} \end{aligned} $$
$$ \begin{aligned} & \text { As } \quad a=\frac{-F_{e}}{m}=\frac{-e V}{m l} \ & \text { as } \quad v=u+a t \ & v=v_{d^{\prime}} \quad u=0, t=\tau \text { (relaxation time) } \ & v_{d}=-a \tau \ & v_{d}=\frac{-e V}{l m} \tau \end{aligned} $$
(ii) Decreases, as time of relaxation decreases.
[CBSE Marking Scheme, 2016]
