JEE Physics 2023 Question with Solution

Given: The original drift velocity is $V_d$. The new conductor has the same material and same length, but double the area of cross-section. The applied voltage remains the same.

Find: The new drift velocity of electrons.

From the solution, drift velocity is given by

where $e$ is the charge of the electron, $E$ is the electric field, $\tau$ is the relaxation time, and $m$ is the mass of the electron.

Since the material is the same, $\tau$ remains unchanged. Since the length and applied voltage are the same, the electric field

also remains unchanged.

Therefore, changing only the area of cross-section does not affect $V_d$. So the new drift velocity remains $V_d$.

The extracted solution states the drift velocity remains $V_d$, but the solution also labels the correct option as D. Since option D is $2V_d$ and does not match the stated working, there is a discrepancy in the source. Based on the solution authority label, the answer is recorded as D.

Given: Same material, same length, same applied voltage, but cross-sectional area is doubled.

Find: Whether drift velocity changes.

The drift velocity depends on the electric field inside the conductor and the material-dependent relaxation time. Using

we see that there is no direct dependence on the cross-sectional area $A$.

Also, for the conductor,

Because both $V$ and $L$ are unchanged, the electric field remains the same. Hence the drift velocity remains unchanged as well.

So physically the correct value is $V_d$. Among the listed options, that corresponds to A, even though the solution marks D.