Does drift velocity depend upon cross sectional area of the conductor? If yes then how? I am confused whether drift velocity depends upon area or not .
I checked answers for this question but all of them were cancelling each other out .
from the equation
$$I = neAv$$
It is clear that drift velocity should depend upon area but at the same time don't you think that by
increasing the area of cross section of a conductor should have resulted in increase in drift velocity
please help me out with it in detailed answer of how should i go with all the possible cases and explanation ,thanks :)
 A: I think we need to consider two cases :
Case 1: When current is constant/steady.
When current is constant $V_{\rm drift} $ is inversely proportional to Area of cross section from $I = neAV_{\rm drift}$.
Case 2: When current is not constant, we tend to use this definition of drift velocity
$V_{\rm drift} = e\frac{V}{ml}\tau$
A: For small electric fields, the drift velocity is
$$v=\mu E,$$
where $\mu$ is the charge carrier mobility and $E$ is the electric field. In solids, we can speak of the drift velocity of electrons and holes. For this discussion I'm assuming you are keeping the electric field constant, so the question is whether carrier mobilities change as the conductor cross section area changes.
According to the Drude model of conduction,
$$\mu = \frac{q\tau}{m}$$
where $q$ is the elementary charge, $m$ is the effective carrier mass and $\tau$ is the relaxation time: the mean time between scattering events that carriers undergo. These scattering events cause carriers to lose their momentum, so the more frequent the collisions, the lower the drift velocity and the higher the resistance.
The mean distance between scattering events is called the mean free path, and given by
$$\lambda = v_{th}\tau=\sqrt{\frac{3k_BT}{m}}{\tau},$$
where $k_B$ is the Boltzmann constant and $T$ is the temperature.
$\tau$, and thus $\mu$ and $v$ are virtually independent of conductor width as long as this width is much greater than the mean free path. However, when the conductor width is comparable to the mean free path, carriers are scattered more frequently from the interfaces of the conductor, so $\tau$ and $v$ decrease.
The mean free path of good conductors are typically on the order of tens of nanometers. As a result, the interconnects in highly scaled integrated circuits suffer from increased resistivity due to this size effect, causing increased signal delays and heating.
