Calculating Resistance for a Wire with Different Dimensions

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Homework Help Overview

The discussion revolves around calculating the resistance of a wire based on its dimensions and material properties. The original poster presents a scenario involving a wire with a known resistance and queries about a second wire that is shorter and has a smaller diameter.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply a formula for resistance but expresses confusion about the outcome. Some participants question the understanding of resistance versus resistivity, while others provide hints about the relationship between wire dimensions and resistance.

Discussion Status

Participants are actively engaging with the problem, offering hints and clarifications. There is a mix of interpretations regarding the resistance of the second wire, and some guidance has been provided without reaching a definitive conclusion.

Contextual Notes

There is a focus on the assumptions related to the dimensions of the wires and their impact on resistance, with some participants clarifying the relationship between diameter and cross-sectional area.

Rowie25
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Homework Statement


A certain wire has a resistance of 78 Ω. What is the resistance of a second wire, made of the same material, that is 1/4 as long and has 1/2 the diameter?

I tried figuring out the equation and I ended up getting R2= 4p L1/4 divided by pi(d1/2)^2 and then I got that the resistance would be four times as great but that isn't correct. Please help! I'm not sure how to figure this out and it looks easy but I'm stuck. Thanks!
 
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Do you know the difference between resistance and resistivity?
 
I know that Resistance is voltage over current and resistivity of the material is E/J which the units are ohms *m right?
 
Hi Rowie25! :smile:

Hint: a thick wire is like lots of thin wires in parallel, a long wire is like lots of short wires in series. :wink:
 
Hmmm okay thank you! I'll try to figure it out.
 
Is the resistance the same? 78 ohms? That is what I am getting but I am not sure that works.
 
Hi Rowie25! :smile:

(just got up :zzz: …)
Rowie25 said:
Is the resistance the same? 78 ohms? That is what I am getting but I am not sure that works.

Yup! :biggrin:

1/4 the length, and 1/4 the area, so the total resistance is the same! :wink:
 
Ohhh! Well it's actually 1/4 the length, 1/2 the diameter. So does that still make sense?
 
1/2 the diameter = 1/4 the area :wink:
 
  • #10
Oh right right! I thought you wrote diameter. My bad! Thank you sooo much! :biggrin:
 

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