Question

What length of copper wire of specific resistance $1.7\times {10}^{-8}\Omega$ m and radius 1 mm is required so that its resistance is $1\Omega$

Answer 1

Here, radius, $r=1mm={10}^{-3}m$

Resistance, $R=1\Omega$

Resistivity, $\rho =1.7\times {10}^{-8}\Omega$

Now, $R=\frac{\rho l}{\pi r^2}\Rightarrow 1\Omega =\frac{1.7\times {10}^{-8}\times l}{\pi (1\times {10}^{-3}{)}^2}$

$\therefore l=184.7m$