Particle flow in wires of same current but diff diameter?

[toforfiltum]

Homework Statement

Homework Equations

I=Q/t

The Attempt at a Solution

I chose B because since current is equal in both wires, I thought that the rate of charge flow is equal. Isn't that the definition of current?? Apparently I'm wrong since the answer is D. How can this be?

 

[cpsinkule]

the resistance of a wire depends on it's cross section. the smaller the cross section, the higher the resistance. if the resistance is higher, you need a higher voltage to produce the same current. that's why the answer is D...none of these answers are really satisfactory...

 

[toforfiltum]

the resistance of a wire depends on it's cross section. the smaller the cross section, the higher the resistance. if the resistance is higher, you need a higher voltage to produce the same current. that's why the answer is D...none of these answers are really satisfactory...

But won't the higher voltage be offset by the higher resistance, since I=V/R?

 

[cpsinkule]

the current is the same in both wires, if the resistance goes up, the only way for that equation to remain true is if the voltage goes up as well

 

[toforfiltum]

the current is the same in both wires, if the resistance goes up, the only way for that equation to remain true is if the voltage goes up as well

So does that mean that the charged particles will move faster through the wire?

 

[cpsinkule]

yes, the net amount of charge passing through one point in the wires is proportional to the area of the wire and the speed of the electrons. both of these have equal current so that a smaller area requires a larger velocity to produce the same current

 

[Hesch]

Maybe D is the correct answer, but it's a weird way of thinking.

Instead think of an hourglass whre sand is flowing through a narrow hole. Where in the hourglass will the sand flow fastest? At the biggest/smallest cross section area?
And why?

 

[toforfiltum]

yes, the net amount of charge passing through one point in the wires is proportional to the area of the wire and the speed of the electrons. both of these have equal current so that a smaller area requires a larger velocity to produce the same current

Ah, I see, so to confirm, to produce the same amount of charge flowing through a smaller cross-sectional area per unit time, the velocity of the particles must be higher, right?

 

[cpsinkule]

that's the idea

 

[toforfiltum]

Maybe D is the correct answer, but it's a weird way of thinking.

Instead think of an hourglass whre sand is flowing through a narrow hole. Where in the hourglass will the sand flow fastest? At the biggest/smallest cross section area?
And why?

Wow, nice question, though I'm not sure about the answer. I suppose it should be at the smallest cross-sectional area, since it's at point of lowest pressure? Add also, rate of flow must be equal everywhere, so to make up for the smaller cross-sectional area, the sand there must flow faster...but what I say seems contradictory...