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.
Resistance=constant*Length/diameter^2
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...
Resistance1=constant*Length1/diameter1^2
and
Resistance2=constant*Length2/diameter2^2
now dividing the second equation by the first, and noting that the length1 and length 2 are the same..
Resistance2/resistance1=(diameter2/diameter1)^2
or resistance2=resistance1(diameter2/diameter1)^2
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