Hi there!
1)
We can use the following equation to solve for resistivity.
[tex]R = \frac{\rho L}{A}[/tex]
R = Resistance (30 Ω)
ρ = Resistivity (? Ωm)
L = Length (100cm = 1 m)
A = Cross-sectional area of wire (r = 0.15m, A = πr², A = 0.0707 m²)
Rearrange the equation to solve for resistivity.
[tex]\rho = \frac{RA}{L}\\\\\rho = \frac{30 * 0.0707}{1} = \boxed{2.121 \Omega m}[/tex]
2)
The conductivity of a resistor is equivalent to:
[tex]\sigma = \frac{1}{\rho}[/tex]
σ = Conductivity (S/m)
ρ = Resistivity (2.121 Ωm)
Solve:
[tex]\sigma = \frac{1}{2.121} =\boxed{0.472 \frac{S}{m}}[/tex]
3)
We can use the equation for resistivity to solve. Rearrange the equation for length:
[tex]R = \frac{\rho L}{A}\\\\L = \frac{AR}{\rho}\\\\L = \frac{0.0707 * 5}{2.121} = \boxed{0.167 m}[/tex]
