SOLUTION: The conductance of a wire varies directly as the square of the wire's diameter and inversely as it's length. Fifty meters of wire with a diameter 2 mm has a conductance of 0.12 ohm

Algebra ->  Proportions -> SOLUTION: The conductance of a wire varies directly as the square of the wire's diameter and inversely as it's length. Fifty meters of wire with a diameter 2 mm has a conductance of 0.12 ohm      Log On


   

Question 617865: The conductance of a wire varies directly as the square of the wire's diameter and inversely as it's length. Fifty meters of wire with a diameter 2 mm has a conductance of 0.12 ohms. If a wire of the same material has length of 75m and diameter of 2.5mm, what is its conductance? I need help. I have been on this problem for over an hour.
Answer by MathTherapy(10551) About Me  (Show Source):
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The conductance of a wire varies directly as the square of the wire's diameter and inversely as it's length. Fifty meters of wire with a diameter 2 mm has a conductance of 0.12 ohms. If a wire of the same material has length of 75m and diameter of 2.5mm, what is its conductance? I need help. I have been on this problem for over an hour.

Let conductance of wire = C; D = diameter; and L = length

The we have: C+=+%28kD%5E2%29%2FL

0.12+=+%28k%282%29%5E2%29%2F50 ------- Substituting values for C, D, and L

0.12+=+%284k%29%2F50

4k = 50 * 0.12 ---- Cross-multiplying

4k = 6

k = 6%2F4, or 3%2F2, or 1.5

With k = 1.5; D = 2.5; and L = 75, C+=+%28kD%5E2%29%2FL becomes: C+=+%281.5%282.5%29%5E2%29%2F75

C+=+%281.5%286.25%29%29%2F75

C+=+%289.375%29%2F75
C = highlight_green%280.125%29

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