[tex]R = \frac{k}{A} [/tex] , where R=resistance , A=area, k=constant of variation
A thick wire would have less resistance than a thin wire.
Manipulating the equation will give us [tex]k=RA[/tex]
Since [tex]A=\pi r^2[/tex]
[tex]k=R\pi r^2 [/tex]
Given: R₁ = 5.62 Ω r₁=2.5mm
R₂ = ? r₂=4.25mm
[tex]R_1\pi (r_1)^2=R_2\pi (r_2)^2[/tex]
[tex]R_2 =\frac{R_1\pi (r_1)^2}{\pi (r_2)^2}[/tex]
[tex]R_2 =\frac{R_1(r_1)^2}{(r_2)^2}[/tex]
[tex]R_2 =\frac{(5.62)(2.5)^2}{(4.25)^2}[/tex]
[tex]\boxed{R_2=1.94ohms}[/tex]
