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AS Physics question on drift velocity

Hi all,

I was wondering whether anyone could explain why the answer to this question is that the drift velocity stays the same?:

"A copper wire of length l and diameter d has potential difference V applied across its two ends. The drift velocity is v. if the diameter of the wire is made 0.5d, then the drift velocity becomes what?"

I used the appropriate equation (Current = (Drift velocity)(cross sectional area)(number density)(charge on each charge carrier)) and I came to the answer that the drift velocity should be four times larger, assuming all other values in the equation remain the same.

Please explain.

Thank you!
Original post by londoncricket
Hi all,

I was wondering whether anyone could explain why the answer to this question is that the drift velocity stays the same?:

"A copper wire of length l and diameter d has potential difference V applied across its two ends. The drift velocity is v. if the diameter of the wire is made 0.5d, then the drift velocity becomes what?"

I used the appropriate equation (Current = (Drift velocity)(cross sectional area)(number density)(charge on each charge carrier)) and I came to the answer that the drift velocity should be four times larger, assuming all other values in the equation remain the same.

Please explain.

Thank you!


Current won't be the same in a wire of smaller diameter with the same PD across it.
Original post by Joinedup
Current won't be the same in a wire of smaller diameter with the same PD across it.


Ah of course! Thank you.

How would I quantify the change in current though? For example, how would I be able to specify that the drift velocity is the same?
Original post by londoncricket
Ah of course! Thank you.

How would I quantify the change in current though? For example, how would I be able to specify that the drift velocity is the same?


R=resistance
ρ=resistivity
A=area (x sectional)
L=length

ρ=R A/L [formula sheet]
so
R=ρ L/A

plus ohms law

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