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

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Question 83016: The electrical resistance (R) of a wire varies directly 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 made from the same material? The answer is multiple choice.
a. 24 ohms
b. 27 ohms
c. 30 ohms
d. 48 ohms
Answer by funmath(2873) About Me  (Show Source):
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The electrical resistance (R) of a wire varies directly as its length(L) and inversely as the square of its diameter (d). 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 made from the same material? The answer is multiple choice.
a. 24 ohms
highlight%28b%29. 27 ohms
c. 30 ohms
d. 48 ohms
Directly means multiply, inversely means divide, k is the constant of proportionality.
R=kL%2F%28d%5E2%29 when L=20 and d=.6, R=36, find k
36=k%2820%29%2F%28%28.6%29%5E2%29
36=20k%2F.36
%28.36%2F20%29%2A36=%28.36%2F20%29%2A%2820k%2F.36%29
.648=k
Therefore the formula is: R=.648L%2F%28d%5E2%29, let L=60 and d=1.2 and solve for R.
R=.648%2860%29%2F%281.2%5E2%29
R=27 ohms
Happy Calculating!!!!