Answer:
The resistivity of this wire is approximately [tex]2.1\times 10^{-7}\; \rm \Omega \cdot m[/tex].
The conductivity of this wire is approximately [tex]4.7\times 10^6\; \rm (\Omega \cdot m)^{-1}[/tex].
Assumption: the perpendicular cross-section of this wire is circular.
Explanation:
Convert all unit to standard ones:
- Length of this wire: [tex]l = 100\; \rm cm = 1.00\; \rm m[/tex].
- Diameter of this wire: [tex]0.3\; \rm mm = 3\times 10^{-4}\; \rm m[/tex].
Assume that a wire has a resistivity of [tex]\rho[/tex], a length of [tex]l[/tex], and a cross-section area of [tex]A[/tex]. The formula for the resistance of this wire would be:
[tex]R = \displaystyle \frac{\rho \cdot l}{A}[/tex].
Rearrange this equation to find an expression for [tex]\rho[/tex], the resistivity of this wire:
[tex]\displaystyle \rho = \frac{R\cdot A}{l}[/tex].
For the wire in this question, both length [tex]l[/tex] and resistance [tex]R[/tex] are already given. However, the cross-section area [tex]A[/tex] of this wire needs to be calculated from its diameter, [tex]d[/tex]:
[tex]A = \displaystyle \pi\, \left(\frac{d}{2}\right)^2 \approx 7.08\times 10^{-8}\; \rm m^2[/tex].
Calculate the resistivity of this wire:
[tex]\displaystyle \rho = \frac{R\cdot A}{l} \approx \frac{3.0\; \Omega\times 7.08\times 10^{-8}\; \rm m^2}{1.00\; \rm m} \approx 2.1\times 10^{-7}\; \rm \Omega\cdot m[/tex].
The conductivity of a material is the reciprocal of its resistivity:
[tex]\displaystyle C = \frac{1}{\rho} \approx \frac{1}{2.1\times 10^{-7}\; \Omega\cdot m}\approx 4.7\times 10^{6}\; \rm (\Omega \cdot m)^{-1}[/tex].
