A copper wire has diameter 0.5 mm and resistivity 1.6 x 10-8m. what wi

1.	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» $\underline{\underline{\Large{\bf{Given:-}}}}$ $\bull\sf Diameter\:of\:wire=d=0.5mm=5\times 10^{-4}m$ $\bull\sf Resistivity=\rho=1.6\times 10^{-8}\Omega m$ $\bull\sf Resistance=R=10\Omega$ $\underline{\underline{\Large{\bf{To\:Find:-}}}}$ $\bull\sf Length\:of\:wire=\ell=?$ $\underline{\underline{\Large{\bf{Solution:-}}}}$ $\bull\sf Area\:of\:wire=\dfrac{\pi d^2}{4}$ $\bf We\:know\:that$ $\boxed{\sf{\bigstar R=\rho\dfrac{\ell}{A}}}$ $\\ \sf\longmapsto \ell=\dfrac{RA}{\rho}$ $\\ \sf\longmapsto \ell=\dfrac{R\pi d^2}{4\rho}$ $\\ \sf\longmapsto \ell=\dfrac{10\times 22\times (5\times 10^{-4})^2}{4\times 7\times 1.6\times 10^{-8}}$ $\\ \sf\longmapsto \ell=\dfrac{220\times 25\times \cancel{10^{-8}}}{6.4\times 7\times \cancel{10^{-8}}}$ $\\ \sf\longmapsto \ell=\dfrac{5500}{44.8}$ $\\ \sf\longmapsto \ell=122.7m$ $\\ \therefore\underline{\sf Length\:of\:copper\:wire\:is\:122.7m}$