SOLUTION: The resistance, R, of a wire varies directly as its length and inversely as the square of the diameter. The resistance of a wire 500ft long and diameter 0.01 in. is 20ohms. What is
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-> SOLUTION: The resistance, R, of a wire varies directly as its length and inversely as the square of the diameter. The resistance of a wire 500ft long and diameter 0.01 in. is 20ohms. What is
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Question 715520: The resistance, R, of a wire varies directly as its length and inversely as the square of the diameter. The resistance of a wire 500ft long and diameter 0.01 in. is 20ohms. What is the resistance of a wire 1500ft long with diameter 0.02 in.? Answer by DrBeeee(684) (Show Source):
You can put this solution on YOUR website! If the longer wire has the same diameter, its resistance would increase to
(1) R = (1500/500)*20 or
(2) R = 60 ohms
However, it's diameter is twice as large, which means the resistance would decrease (a "fatter" wire has less resistance) by a factor of (d1/d2)^2 or
(2) Rnew = ((.01/.02)^2)*60 or
(3) Rnew = (1/4)*60 or
(4) Rnew = 15 ohms
Answer: The longer but larger diameter wire will have a resistance of 15 ohms.
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