Question

A wire of resistance $3\Omega$ and 10 cm length is stretched to 30 cm length. Assuming that it has a uniform cross-section, find its new resistance.

Answer 1

We have,
$R=\frac{\rho L}{A}$
According to question, $\rho$ and A are constant.
$R_1=\frac{\rho L_1}{A}$
$3=\frac{\rho \times 10}{A}\dots \dots \left(i\right)$
$R_2=\frac{\rho L_2}{A}$
$R_2=\frac{\rho \times 30}{A}\dots \dots \left(ii\right)$
Dividing (i) by (ii), we get,
$\frac{3}{R_2}=\frac{1}{3}$
$R_2=9\Omega$