# Does the drift velocity of electrons in a wire having constant length and a constant voltage applied across a depends on the area of cross section?

I used the formula
Current=charge density× e × area × drift velocity
i.e. i=neAV
So this yield that drift velocity inversely proportional to area of cross section
But the answer to this question is that drift velocity don’t depend on cross section
Please explain why can’t I use this formula

Please explain why can't I use this formula

You still have an unknown, the current $$i$$, in your formula.

You need to use some other knowledge to eliminate $$i$$ and get the velocity in terms of the independent quantities in your problem (the voltage and the wire geometry) before you can determine whether the drift velocity depends on any particular quantity.

Correct answer by The Photon on January 6, 2021

You can use the formula but for a fixed voltage and conductor length, $$I$$ and $$A$$ are not independent variables.

For a given length of conductor, the resistance of the conductor is inversely proportional to the cross sectional area. Then, per Ohm’s law, for a fixed voltage the current is proportional to the cross sectional area, per your equation.

For a given amount of charge per unit volume, the drift velocity $$V$$ is proportional to the current density, or $$I/A$$. Since for a fixed voltage if $$A$$ increases $$I$$ increases and if $$A$$ decreases $$I$$ decreases, the drift velocity remains constant.

Hope this helps.

Answered by Bob D on January 6, 2021