Question

The resistivity of the material of a wire is 1.76 × 10-8 ωm. if the diameter of the wire is 2 × 10-3 m and its length is 2 m, what is its resistance?

Answer 1

The resistance of a piece of wire is given by:
$R= \frac{\rho L}{A}$
where $\rho$ is the resistivity, L the length of the wire and A the cross-sectional area.
In our problem, $\rho=1.76\cdot 10^{-8}\Omega \cdot m$, the length is L=2.0 m, while given the  diameter the area is
$A=\pi r^2 = \pi ( \frac{d}{2})^2 = \pi ( \frac{2 \cdot 10^{-3}m}{2})^2 = 3.14 \cdot 10^{-6}m^2$
Substituting these numbers, we can calculate the value of the resistance of the wire:
$R= \frac{(1.76\cdot 10^{-8}\Omega \cdot m)(2.0 m)}{3.14 \cdot 10^{-6}m^2}=0.011 \Omega$