Ohm calculation - Please Help

[H-Town]

A conductor of 117ft in length and 980sq-mils in cross-sectional area has a resistance of 1 ohm, What is the resistance of 1987ft of wire of 9862sq-mils of cross-sectional area?

 

[tom baker]

Hmm this seems like a test question which we won’t answer, but can help you.
Hint: try looking at ratios

 

[H-Town]

A 2:1 ratio. Would the answer be 0.5 ohms?

 

[gar]

210916-2145 EDT

H-Town:

Why a 2:1 ratio?

.

 

[H-Town]

210916-2145 EDT

H-Town:

Why a 2:1 ratio?

.

980/117 = 8 and 9862/1987 = 4. So, 2:1.

 

[tom baker]

What is common between the two wire lengths?

 

[LarryFine]

980/117 = 8 and 9862/1987 = 4. So, 2:1.

Wrong ratios. You have approx. 17x the length and approx. 10x the area.

 

[H-Town]

So the resistance would smaller but I can't figure out how to factor it all together.

 

[GoldDigger]

980/117 = 8 and 9862/1987 = 4. So, 2:1.

980/117= 8.376 and 9862/1987 = 4.963 for what that is worth.
You should also ask yourself which measurement increases resistance when it increases and which measurement decreases resistance when it increases.

 

[winnie]

The basic rule is that resistance is proportional to length and inversely proportional to cross sectional area.

Double the length you double the resistance.

Multiply the cross section by 10, get 1/10 the resistance.

As an equation: R2 = L2/L1 * A1/A2 * R1

Jon

 

[wwhitney]

Wrong ratios. You have approx. 17x the length and approx. 10x the area.

Actually, you can use either set of ratios: (A₁ / L₁) / (A₂ / L₂) is the same as (A₁ / A₂) / (L₁ / L₂).

Cheers, Wayne

 

[H-Town]

17/10(1ohm)
R2= 1.7 ohms

 

[H-Town]

17/10(1ohm)
R2= 1.7 ohms
Is this right?

 

[H-Town]

Am I on the right track?

 

[wwhitney]

I suggest doing the problem in two steps. Your starting point is 117' @ 980 sq mils = 1 ohm. Now what happens if you lengthen the conductor to 1987 ft? And then what happens if you increase the conductor size to 9862 sq mils?

P.S. You may have the right answer already, I haven't checked, but you certainly haven't explained it in a way that makes it easy to know if you did it right. I.e. it would be easy to inadvertently flip a ratio and get the reciprocal of the correct answer.

Cheers, Wayne

 

[winnie]

17/10(1ohm)
R2= 1.7 ohms

That looks approximately correct and the numbers look like you took the correct ratios.

Wayne's suggestion of writing out the steps would let us tell you if you got it right or simply got lucky.

Jon

 

[tom baker]

No charge for this answer. The next will cost you a dozen doughnuts.

 

[Dennis Alwon]

I also got 1.7 ohms

 

[H-Town]

1987/117 = 16.98
9862/980= 10.06
1ohm(16.98/10.06) = 1.68ohms

 

[H-Town]

Thank you guys!!