Question

The resistance of a $10\, m$ long wire is $ 10\,\Omega $ . Its length is increased by 25% by stretching the wire uniformly. Then the resistance of the wire will be

• A. $ 12.5\,\,\Omega $
• B. $ 14.5\,\,\Omega $
• C. $ 15.6\,\,\Omega $
• D. $ 16.6\,\,\Omega $
• E. $ 18.6\,\,\Omega $

Answer 1

Answer: (C)

$ R=\frac{\rho \lambda }{A} $
For given problem
$ R\propto {{\lambda }^{2}} $
Hence $ \frac{{{R}_{1}}}{{{R}_{2}}}=\frac{\lambda _{1}^{2}}{\lambda _{2}^{2}} $
$ {{R}_{2}}={{\left( \frac{{{\lambda }_{2}}}{{{\lambda }_{1}}} \right)}^{2}}\times {{R}_{1}}=15.6\,\Omega $