A copper wire is 2 m2m long and has a cross-sectional area of 1×10−6 m2. Given that the resistivity of copper is ρ=1.7×10−8 Ω⋅m. calculate the resistance of the wire.

Given:
$L = 2 \text{ m}$
$A = 1 \times 10^{-6} \text{ m}^2$
$\rho = 1.7 \times 10^{-8} \Omega \cdot \text{m}$

$$R = (1.7 \times 10^{-8} \Omega \cdot \text{m}) \frac{2 \text{ m}}{1 \times 10^{-6} \text{ m}^2}$$

$$R = \frac{1.7 \times 10^{-8} \times 2}{1 \times 10^{-6}} \Omega$$ $$R = \frac{3.4 \times 10^{-8}}{1 \times 10^{-6}} \Omega$$ $$R = 3.4 \times 10^{-8 - (-6)} \Omega$$ $$R = 3.4 \times 10^{-2} \Omega$$ $$R = 0.034 \Omega$$

The resistance of the wire is $\text{0.034 } \Omega$.