Question

The resistance of wire is 20 $\Omega$. The wire is stretched to three time its length. Then the resistance will now be

• A. $6.67\Omega$
• B. $60\Omega$
• C. $120\Omega$
• D. $180\Omega$

Answer 1

The correct option is D $180\Omega$

Volume $=A\times L$

$L^{\prime }=3L⟹A^{\prime }=\frac{A}{3}$
We know,

R $=\frac{\rho \times L}{A}$
Hence,
$\frac{R^{\prime }}{R}=\frac{L^{\prime }}{L}\times \frac{A}{A^{\prime }}=\frac{3L}{L}\times \frac{A}{\frac{A}{3}}=9$
Hence,
$R^{\prime }=9R⟹R^{\prime }=9\times 20=180\Omega$