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

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SUMMARY

The discussion centers on the relationship between cross-sectional area (A) and electron drift velocity (v) in a copper wire carrying a constant current (I). It is established that as the cross-sectional area increases, the electron drift velocity decreases, due to the inverse proportionality defined by the equation I=nAve. The conversation clarifies that while the current remains constant, variations in cross-sectional area affect the resistance and consequently the voltage (e), which must adjust to maintain the constant current. This understanding is illustrated through an analogy with water flow in pipes.

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MBBphys
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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
 
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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?
 
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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
 
MBBphys said:
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. :smile:
 
berkeman said:
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.
 
TSny said:
I believe "e" here stands for the magnitude of the electric charge of an electron.
LOL. :smile:

If they start varying that in future problems, I'd be a little worried... :wink:
 
berkeman said:
If they start varying that in future problems, I'd be a little worried... :wink:
:biggrin:
 

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