How can an increase in area cause a decrease in drift speed?

[MBBphys]

Homework Statement

We have:
I=nAve
Imagine a copper wire with a constant current through it:
I=constant
e=constant
n (for copper)=constant

Hence, we obtain:

A is inversely proportional to electron drift velocity.

My question is: how does that make sense? Why would the cross sectional area increasing lead to the electron drift velocity decreasing?

Thanks

Homework Equations

I=nAve

The Attempt at a Solution

N/A

 

[TSny]

Suppose you had a pipe carrying water at a rate of 100 gallons per minute.

A second pipe also carries water at 100 gallons per minute, but has twice the cross-sectional area. How does the speed of the water in the second pipe compare to the speed in the first pipe?

 

[MBBphys]

Ah. Now I get it; the second pipe can carry a larger volume, so it has to reduce the speed to keep the discharge of 100 gallons per minute constant. How silly of me!

Thank you very much

 

[berkeman]

Imagine a copper wire with a constant current through it:
I=constant
e=constant

Actually, the first equation "I=constant" is sufficient for answering the question. Given a constant current, the average drift velocity of the electrons is inversely proportional to the cross-sectional area of the conductor.

The second equation "e=constant" will not be true in general when you vary the cross-sectional area of a conductor. Doing so will vary the resistance of the conductor, so to maintain a constant current I, the voltage "e" will need to change.

 

[TSny]

The second equation "e=constant" will not be true in general when you vary the cross-sectional area of a conductor. Doing so will vary the resistance of the conductor, so to maintain a constant current I, the voltage "e" will need to change.

I believe "e" here stands for the magnitude of the electric charge of an electron.

 

[berkeman]

I believe "e" here stands for the magnitude of the electric charge of an electron.

LOL.

If they start varying that in future problems, I'd be a little worried...

 

[TSny]

If they start varying that in future problems, I'd be a little worried...