Question

The electrical resistance R of a wire varies directly as the length l of the wire and inversely as the square of its diameter d. If 20 meters of wire of diameter 1.5 mm has a resistance of 12 ohms, what is the resistance of 20 meters of the same wire if the diameter is increased to 5 mm?

Answer 1

First solve for k, then find R with the new diameter:
$$
R=\cfrac{kl}{d^2}\\
12=\cfrac{k\times20}{(.0015)^2}\\
\implies\\
k=\cfrac{12\times(.0015)^2}{20}\\
R=\cfrac{20k}{(.005)^2}
$$

Answer 2

Im really confused. Here on the answers they give me to choose from:
1.08
5
42
85.3

Answer 3

Do you understand the 1st equation why we have l and k at the top and d at the bottom?

k is just a constant of proportionality when given that something is proportional to another it only varies by a factor. I'm calling that factor k.

Also, I've converted from mm to meters. 1.5 mm = .0015 m and 5 mm = .005 m

Answer 4

Were you able to calculate the factor k?

Answer 5

If you run down the calculations I've given above, one of your options appears quite easily.

Good luck.

Answer 6

I got 1.35E-6

Answer 7

OMG I got 1.08 which is an answer to choose from. Thanks!!! (is this correct?)

Answer 8

yw