SOLUTION: The electrical resistance R of a wire varies as its length L and inversely as the square of its diameter. A wire 20 meters long and 0.6 centimeters in diameter made from a certain

Algebra ->  Rational-functions -> SOLUTION: The electrical resistance R of a wire varies as its length L and inversely as the square of its diameter. A wire 20 meters long and 0.6 centimeters in diameter made from a certain       Log On


   

Question 72401: The electrical resistance R of a wire varies as its length L and inversely as the square of its diameter. A wire 20 meters long and 0.6 centimeters in diameter made from a certain alloy has a resistance of 36 ohms. What is the resistance of a piece of wire 60 meters long and 1.2 centimeters in diameter from the same material?
Please show me how you came across the solution.Thanks
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The equation for computing the resistance of a wire is:
.
R+=+%28K%2AL%29%2Fd%5E2
.
where R is resistance in ohms, L is length in meters, and d is the diameter of the wire in
centimeters. Notice that R varies directly as L and inversely as the square of the diameter.
.
The problem is that we don't know K which is just a constant of proportionality. But with
the information given in the problem we can find K. We know for a wire that is 20 meters
long and has a diameter of 0.6 cm, the resistance is 36 ohms. Plug those values into the
equation above and you get:
.
36+=+%28K%2A20%29%2F0.6%5E2
.
Do the squaring and division on the right side and you get:
.
36+=+K%2A55.5556
.
Then divide both sides by 55.5556 to solve for K. When you do, you find that K = 0.6480.
This value of K takes into account the material used for the wire as well as the fact that
we will express the length of the wire in meters and the diameter of the wire in centimeters,
not meters.
.
Now return to the original equation and substitute 0.6480 for K to get:
.
R+=+%28%280.6480%29%2AL%29%2Fd%5E2
.
Now you have an equation you can do something with. You know the new piece of wire has a
length of 60 meters and a diameter of 1.2 centimeters. Substitute those into the equation
to get:
.
R+=+%28%280.6480%29%2A60%29%2F%281.2%29%5E2
.
Calculator time ... If you work this out you should get 27 ohms for the value of R (the resistance).
.
Hope this helps you with this problem.