SOLUTION: The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. If a wire with length 100cm and diameter 2 mm has a resistance of 1.

Question 414085: The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. If a wire with length 100cm and diameter 2 mm has a resistance of 1.5 Ohms, find the resistance of a wire with length 300cm and diameter 3mm.

I tried to find something similar to this in my textbook and couldn't. My guess was that the formula to use would be r=k(L/D^2), then solve for k which would be the constant. Once I have solved for k I can plug the new length and diameter into the formula and solve for r, am I on the right track?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. If a wire with length 100cm and diameter 2 mm has a resistance of 1.5 Ohms, find the resistance of a wire with length 300cm and diameter 3mm.
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r = k*L/d^2
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Solve for "k" using "If a wire with length 100cm
and diameter 2 mm has a resistance of 1.5 Ohms".
----
1.5 = k*100/2^2
100k = 6
k = 0.06
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Equation for this problem:
r = 0.06*L/d^2
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Now "find the resistance of a wire with length 300cm and diameter 3mm".
r = 0.06*300/3^2
r = 0.06*100/3
r = 2 Ohms
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Cheers,
Stan H.
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