Calculating Resistance for a Wire with Different Dimensions

[Rowie25]

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!

 

[rogerbacon]

Do you know the difference between resistance and resistivity?

 

[Rowie25]

I know that Resistance is voltage over current and resistivity of the material is E/J which the units are ohms *m right?

 

[tiny-tim]

Hi Rowie25!

Hint: a thick wire is like lots of thin wires in parallel, a long wire is like lots of short wires in series.

 

[Rowie25]

Hmmm okay thank you! I'll try to figure it out.

 

[Rowie25]

Is the resistance the same? 78 ohms? That is what I am getting but I am not sure that works.

 

[tiny-tim]

Hi Rowie25!

(just got up :zzz: …)

Is the resistance the same? 78 ohms? That is what I am getting but I am not sure that works.

Yup!

1/4 the length, and 1/4 the area, so the total resistance is the same!

 

[Rowie25]

Ohhh! Well it's actually 1/4 the length, 1/2 the diameter. So does that still make sense?

 

[tiny-tim]

1/2 the diameter = 1/4 the area

 

[Rowie25]

Oh right right! I thought you wrote diameter. My bad! Thank you sooo much!