The resistance of the cylindrical wire is [tex] R=\frac{\rho l}{A} [/tex].
Here [tex] R [/tex] is the resistance, [tex] l [/tex] is the length of the wire and [tex] A [/tex] is the area of
cross section. Since the wire is cylindrical [tex] A=\frac{\pi d^2}{4} [/tex] .
From the above 2 equations,
[tex] R=\frac{\rho l}{\frac{\pi d^2}{4}} \\
d^2=\frac{4 \rho l}{\pi R} \\
d=\sqrt{\frac{4 \rho l}{\pi R} } [/tex]
The resistance of the wire is given by
[tex] R=\frac{E}{I} \\
R=\frac{1.2}{2} \\
R=0.6 [/tex]
Thus, the diameter of the wire is
[tex] d=\sqrt{\frac{4 (1.72)10^{-8} (178)}{\pi (0.6)} }\\
d=0.00255 [/tex]
The diameter of the wire is [tex] 2.55 \;mm [/tex]
