The resistance, R of a wire varies directly as the length, l, and inversely as the diameter, d, squared. If R is 1.50ohms when l=2.0 m and d=1.5 mm, what is the resistance of a wire made of the same material that is 8.0 m long and has a diameter of 3.0 mm?

Answer: resistance is 1.5 ohms (1.5 Ω)Step-by-step explanation:R varies directly with lR varies inversely with [tex]d^2[/tex]We can set-up a proportionality statement as shown below:[tex]R=k\frac{l}{d^2}[/tex]Now, Given,R = 1.50l = 2d = 1.5We substitute and find k (the proportionality constant):[tex]R=k\frac{l}{d^2}\\1.5=k\frac{2}{1.5^2}\\1.5=\frac{2k}{2.25}\\2k=1.5*2.25\\2k=3.375\\k=1.6875[/tex]Now, we will use this value of k to solve the problem.Given, l = 8d = 3andk = 1.6875We find R:[tex]R=k\frac{l}{d^2}\\R=1.6875\frac{8}{3^2}\\R=\frac{1.6875*8}{9}\\R=1.5[/tex]The resistance is 1.5 ohms (1.5 Ω)