A wire of circular cross section has inner portion of radius $R$ made of material of resisitivity $\rho$ and is surrounded by an outer portion of thickness $R$ made of a material of double resisitivity. Find the resistance of length $l$ of such wire
Medium
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${\rm{R}} = \frac{{{{\rm{R}}_1}{{\rm{R}}_2}}}{{{{\rm{R}}_1} + {{\rm{R}}_2}}} = \frac{{\frac{{\rho \times l}}{{\pi {{\rm{R}}^2}}} \times \frac{{2\rho \times l}}{{\pi \left( {{{(2{\rm{R}})}^2} - {{\rm{R}}^2}} \right)}}}}{{\frac{{\rho l}}{{\pi {{\rm{R}}^2}}} + \frac{{2\rho l}}{{\left( {{{(2{\rm{R}})}^2} - {{\rm{R}}^2}} \right)}}}}$
$\frac{{\frac{{2{p^2}{l^2}}}{{3\pi {{\rm{R}}^4}}}}}{{\frac{{\rho l}}{{\pi {{\rm{R}}^2}}}\left( {1 + \frac{2}{3}} \right)}} = \frac{{2\rho {\rm{l}}}}{{3\pi {{\rm{R}}^2}}} \times \frac{3}{5}$
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