Question

What length of copper wire of resistivity 1.7 × 10^-8 Ω m and radius 1 mm is required so that its resistance is 2Ω? 

Answer 1

Resistance (R) = 2 ohm

Resistivity (ρ) = 1.7 × 10^-8 ohm metre

Radius (r) = 1 mm = 10^-3 m

Length (l) = ? 

${\displaystyle R=\rho \frac{l}{A}}$  

${\displaystyle \rho =\frac{l}{\pi r^2}}$ 

Substituting the values in the formula above we get,

${\displaystyle 2=1.7\times {10}^{-8}\frac{l}{\pi {\left({10}^{-3}\right)}^2}}$

${\displaystyle 2=1.7\times {10}^{-8}\frac{l}{3.14\times {\left({10}^{-3}\right)}^2}}$

${\displaystyle 2=\frac{1.7\times {10}^{-2}\times l}{3.14}}$

${\displaystyle 2=\frac{1.7\times l}{314}}$

⇒ l = ${\displaystyle \frac{314\times 2}{1.7}}$ 

⇒ l = 369.4 m

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