What length of copper wire of specific resistance 1.7 x 10^-8 Ω m and radius 1 mm is required so that it's resistance is 2 Ω.

Given,

Specific resistance ρ = 1.7 × 10^-8Ω m

Radius r = 1 mm = 10^-3m

Resistance R = 2 Ω

Length l = ?

From relation

R = ρ $\dfrac{l}{a}$ = ρ $\dfrac{l}{πr^2}$

Substituting the values in the formula above we get,

$2 = 1.7 \times 10^{-8} \dfrac{l}{π(10^{-3})^2} \\[0.5em] 2 = 1.7 \times 10^{-8} \dfrac{l}{3.14 \times (10^{-3})^2} \\[0.5em] 2 = \dfrac{1.7 \times 10^{-2} \times l}{3.14} \\[0.5em] 2 = \dfrac{1.7 \times l}{314} \\[0.5em] \Rightarrow l = \dfrac{314 \times 2}{1.7} \\[0.5em] \Rightarrow l = 369.4 \text{ m} \\[0.5em]$

Hence, the length of the copper wire = 369.4 m.