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The electrical resistance of a wire varies directly with the length of the wire and inversely with the square of the diameter of the wire. If a wire 432 feet long and 4 millimeters in diameter has a resistance of 1.26 ohms, find the length of a wire of the same material whose resistance is ohms and whose diameter is millimeters.



Answer :

Let

R ----> resistance in ohms

L ---> the length of the wire in ft

D ---> the diameter of the wire in mm

In this problem, the equation is of the form

[tex]R=K\frac{L}{D^2}[/tex]

we have

L=432 ft

D=4 mm

R=1.26 ohms

so

Find out the value of K (constant of proportionality)

substitute the given values

[tex]\begin{gathered} 1.26=K\frac{432}{4^2} \\ \\ K=\frac{1.26*16}{432} \\ \\ K=0.0467 \end{gathered}[/tex]

Part 2

The formula is

[tex]R=0.0467\frac{L}{D^2}[/tex]

For

R=1.41 ohms

D=5 mm

substitute in the formula above

[tex]\begin{gathered} 1.41=0.0467\frac{L}{5^2} \\ solve\text{ for L} \\ L=\frac{1.41*25}{0.0467} \\ L=754.8\text{ ft} \end{gathered}[/tex]

The answer is 754.8 feet

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