Q. The resistance of a 10m 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$\ \Omega$
Explanation
(c) Resistance,$R = \frac{\rho\lambda}{A}$
For given problem,
$\ \ \ \ R \propto \lambda^{2}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \frac{R_{1}}{R_{2}} = \frac{\lambda_{1}^{2}}{\lambda_{2}^{2}}$
$R_{2} = \left( \frac{\lambda_{2}}{\lambda_{1}} \right)^{2} \times R_{1} = 15.6\ \Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.