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The resistance(r)of a wire varies directly as the length(L)of the wire and inversely as the square of the diameter(d). If the resistance is 9ohms in 50ft of wire that has a diameter of 0.05in, find the resistance in 50ft of a similar wire that has a diameter of 0.02in.


Two ways you can work this:
1) In the equation, solve for the constant (you have resistance 9 ohms, Length 50, and diameter .05). Then use that constant in the equation to solve for the new conditions,

2) Notice the length is the same, however...




now dividing the second equation by the first, and noting that the length1 and length 2 are the same..


or resistance2=resistance1(diameter2/diameter1)^2

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