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.


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


The we have: {{{C = (kD^2)/L}}}


{{{0.12 = (k(2)^2)/50}}} ------- Substituting values for C, D, and L


{{{0.12 = (4k)/50}}}


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


4k = 6


k = {{{6/4}}}, or {{{3/2}}}, or 1.5


With k = 1.5; D = 2.5; and L = 75, {{{C = (kD^2)/L}}} becomes: {{{C = (1.5(2.5)^2)/75}}}


{{{C = (1.5(6.25))/75}}}


{{{C = (9.375)/75}}}

C = {{{highlight_green(0.125)}}}


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