Question

If length of a wire is doubled after stretching, then what will be its resistance?

Answer 1

Let, L be initial length of wire with resistance R and its area of cross section is A.
We know that,
$R\alpha L$
and $R\alpha \frac{1}{A}$
If the L length of wire is stretched to $2$L length then its Area of cross section.
becomes half, i.e., $=\frac{A}{2}$
We know that, $R=\frac{\rho L}{A}$
Where $\rho$ is known as resistivity of an conductor.
On putting values, $R=\frac{\rho 2L}{A/2}$
$R=4\frac{\rho L}{A/2}$
Then Resistance becomes $4$ times of the resistance of L length with A cross section.