Answer:
resistance is 1.5 ohms (1.5 Ω)
Step-by-step explanation:
R varies directly with l
R 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 = 1.50
l = 2
d = 1.5
We 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 = 8
d = 3
and
k = 1.6875
We 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)
