Question

The length of a metallic wire of $50\Omega$ resistance is stretched two times its initial length. Its new resistance is:

• A. $25\Omega$
• B. $50\Omega$
• C. $100\Omega$
• D. $200\Omega$

Answer 1

The correct option is D $200\Omega$

Resistance of wire $R=\rho \frac{L}{A}=\rho \frac{L^2}{AL}=\rho \frac{L^2}{V}$
$⟹R\propto L^2$ (Since $V$ and $\rho$ are constant)
Given : $L^{\prime }=2L$
$⟹\frac{R^{\prime }}{R}=\frac{(L^{\prime }{)}^2}{L^2}=\frac{4L^2}{L^2}=4$
$⟹$ $R^{\prime }=4R=4\times 50=200\Omega$