Question

Electrical Resistance The electrical resistance R of a wire varies inversely with the square of its diameter d. If a 25-foot wire with a diameter of 2 millimeters has a resistance of 0.5 ohm, find the resistance of a wire having the same length and a diameter of 3 millimeters.

Answer 1

The answer is below

Explanation:

The electrical resistance R of a wire varies inversely with the square of its diameter d:

R ∝ 1 / d

Let k represent the constant of proportionality, hence we can represent the statement as an equation:

`R=(k)/(d^2)\\ \\when\ R=0.5 \Omega,d=2\ mm\\\\0.5=(k)/(2^2) \\\\k=2\\\\The\ equation\ becomes :\\\\R=(2)/(d^2)\\ \\When\ d=3, we\ find\ R\\\\R=(2)/(3^2) \\\\R=0.22\ \Omega`