# Homework Help: Finding an unknown resistance

1. Feb 1, 2010

### Rowie25

1. The problem statement, all variables and given/known data
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!

2. Feb 1, 2010

### rogerbacon

Do you know the difference between resistance and resistivity?

3. Feb 1, 2010

### Rowie25

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

4. Feb 1, 2010

### 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.

5. Feb 1, 2010

### Rowie25

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

6. Feb 1, 2010

### Rowie25

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

7. Feb 2, 2010

### tiny-tim

Hi Rowie25!

(just got up :zzz: …)
Yup!

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

8. Feb 2, 2010

### Rowie25

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

9. Feb 2, 2010

### tiny-tim

1/2 the diameter = 1/4 the area

10. Feb 2, 2010

### Rowie25

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