Answer:
Correct option: C
Explanation:
Resistance and Resistivity
The resistance of a conductor with cross-section area A, length L and resistivity \rho is given by
[tex]\displaystyle R=\frac{\rho L}{A}[/tex]
If we know the value of R, then we can solve for [tex]\rho[/tex] as follows
[tex]\displaystyle \rho=\frac{AR}{L}[/tex]
The coiled spring has n=75 coils with a diameter of d=3.5 cm = 0.035 m. This will be used to compute the total length of the conductor. The length of a circle of diameter d is:
[tex]L_c=\pi d[/tex]
For 75 turns, the total length is
[tex]L=75\pi d=75\pi \times 0.035[/tex]
[tex]L=8.25\ m[/tex]
The cross-section area is computed as the area of a circle
[tex]\displaystyle A=\frac{\pi d_c^2}{4}[/tex]
The diameter of the conductor is dc = 3.25 mm = 0.00325 m
[tex]\displaystyle A=\frac{\pi 0.00325^2}{4}[/tex]
[tex]A=8.30\times 10^{-6}\ m^2[/tex]
We now compute the resistivity
[tex]\displaystyle \rho=\frac{8.30\times 10^{-6}\ m^2\times 1.74\ \Omega }{8.25\ m}[/tex]
[tex]\boxed{\rho=1.75\times 10^{-6}\ \Omega .m}[/tex]
Correct option: C
