Question

If a wire of resistance $1\Omega$ is stretched to double its length, then the resistance will become

• A. $\frac{1}{2}\Omega$
• B. $2\Omega$
• C. $\frac{1}{4}\Omega$
• D. $4\Omega$

Answer 1

The correct option is D $4\Omega$

On stretching a wire its length increases and are of cross section decreases but volume remains same.

$V=AL$=volume

$R=\rho \frac{L}{A}$

$⟹R=\rho \frac{L^2}{V}$

Hence, $R\propto L^2$

On, stretching wire to double its length, resistance becomes $4$ times.

Hence, final resistance $=4\times 1\Omega =4\Omega$

Answer-(D)