Question

A copper wire has diameter 0.5 mm and resistivity 1.6 x 10-8m. what will be the length of this wire to make its resistance 10 ohm​

Answer 1

$\underline{\underline{\Large{\bf{Given:-}}}}$

$\bull\sf Diameter\:of\:wire=d=0.5mm=5\times 10^{-4}m$

$\bull\sf Resistivity=\rho=1.6\times 10^{-8}\Omega m$

$\bull\sf Resistance=R=10\Omega$

$\underline{\underline{\Large{\bf{To\:Find:-}}}}$

$\bull\sf Length\:of\:wire=\ell=?$

$\underline{\underline{\Large{\bf{Solution:-}}}}$

$\bull\sf Area\:of\:wire=\dfrac{\pi d^2}{4}$

$\bf We\:know\:that$

$\boxed{\sf{\bigstar R=\rho\dfrac{\ell}{A}}}$

$\\ \sf\longmapsto \ell=\dfrac{RA}{\rho}$

$\\ \sf\longmapsto \ell=\dfrac{R\pi d^2}{4\rho}$

$\\ \sf\longmapsto \ell=\dfrac{10\times 22\times (5\times 10^{-4})^2}{4\times 7\times 1.6\times 10^{-8}}$

$\\ \sf\longmapsto \ell=\dfrac{220\times 25\times \cancel{10^{-8}}}{6.4\times 7\times \cancel{10^{-8}}}$

$\\ \sf\longmapsto \ell=\dfrac{5500}{44.8}$

$\\ \sf\longmapsto \ell=122.7m$

$\\ \therefore\underline{\sf Length\:of\:copper\:wire\:is\:122.7m}$