Question

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. $16.6\Omega$
• E. $18.6\Omega$

Answer 1

Answer: (C)

$R=\frac{\rho \lambda }{A}$
For given problem
$R\propto {\lambda }^2$
Hence $\frac{R_1}{R_2}=\frac{{\lambda }_1^2}{{\lambda }_2^2}$
$R_2={\left(\frac{{\lambda }_2}{{\lambda }_1}\right)}^2\times R_1=15.6\Omega$