Find the resistance of a wire (conductor)

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Homework Help Overview

The discussion revolves around the resistance of a wire (conductor) and how it changes when the diameter is halved. Participants are examining the relationship between the diameter, cross-sectional area, and resistance in the context of electrical properties.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants explore the formula for resistance and its dependence on cross-sectional area, questioning the proportionality of surface area to radius squared. There is also a discussion about the distinction between surface area and cross-sectional area, and how these concepts relate to resistance.

Discussion Status

The discussion is actively exploring different interpretations of the problem, particularly regarding the definitions of surface area and cross-sectional area. Some participants have provided clarifications about the relationships involved, but there is no explicit consensus on the correct answer to the original question.

Contextual Notes

There is some confusion regarding the term "dimidiated" and its implications for the problem. Participants are also referencing textbook definitions and relationships that may not be universally understood.

prishila
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Homework Statement


If the diameter of a wire (conductor) is dimidiated , then its resistance:
A Remains unchangable
B is diminiated
C Becomes two times greater
D Becomes 4 times greater

Homework Equations


R=constant*length/Surface

The Attempt at a Solution


Cross sectional area=pi r^2=pi (D/2)^2=piD^2/4
Then the resistance becomes 4 times greater.
But in my book the answer is C.
 
Last edited:
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Is the surface area really proportional to r^2?
 
Dr. Courtney said:
Is the surface area really proportional to r^2?
I think it is. Only if you consider pi to affect that
 
Are you confusing surface area and cross sectional area?
 
Dr. Courtney said:
Are you confusing surface area and cross sectional area?
Can you tell me the difference. in my book it says Resistance is in disproportional to the cross section of the resistance.
 
prishila said:
Can you tell me the difference. in my book it says Resistance is in disproportional to the cross section of the resistance.
Surface area means area of the entire surface of the conductor. Cross sectional area is the area "through" which the current flows. Resistance is inversely proportional to the cross sectional area of the conductor.
 
cnh1995 said:
Surface area means area of the entire surface of the conductor. Cross sectional area is the area "through" which the current flows. Resistance is inversely proportional to the cross sectional area of the conductor.
I understand. But how can this affect the solution of my exercise?
 
prishila said:
I understand. But how can this affect the solution of my exercise?
If "dimidiated" means halved, I agree that the answer is D.
 

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