# Does the drift velocity of an electron in a wire with constant current depend on the area of its cross section?

Suppose current, $I=nevA$ with the electron density $n$, the cross section of the conductor $A$ and the drift velocity $v = \frac{V}{RneA}$ where $R$ is the resistance of the wire. This equation becomes $v/dlne$ where $d$ is the resistivity of the wire if we break the $R$ into the formula $R=\frac{dl} A$. So drift velocity should not depend on $A$ or area of cross section. Which way am I wrong?

• have a look here, hyperphysics.phy-astr.gsu.edu/hbase/electric/miccur.html , drift velocity does not depend on area. The current does. – anna v Apr 19 '18 at 9:14
• @annav is my derivation right. And I didn't get it in your link – TIME RUB Apr 19 '18 at 10:10
• in the same site , hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html . It has a calculation of resistance. I was refering to your title. – anna v Apr 19 '18 at 10:46
• Where does your second equation come from? – BowlOfRed May 9 '18 at 17:29
• @BowlOfRed sorry to reply that later. Put I=V/R in my first equation. Cross multiplying you'll get the amount of v or drift velocity as my second equation. – TIME RUB May 10 '18 at 1:04

$V$ in your equation is the voltage drop over the restive element. It's not the voltage in the circuit.