Posted by **Amber** on Friday, September 22, 2006 at 3:04am.

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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