Question

How will the resistance of a wire change when : Its length is doubled.

Answer 1

Resistance of wire is proportional to length and inversely proportional to area.
$Are{a}^{\prime }\times Length=Volume$
$⟹Area=\frac{V}{L}$
Volume of wire is always constant.
As length is doubled,
$Area\times \left(2L\right)=V$
$⟹Area=\frac{V}{2L}\Rightarrow$ Area is halved.
So, $R_1=\frac{\rho L_1}{A_1}$
$⟹R_2=\frac{\rho \left(2L\right)}{\left(\frac{A}{2}\right)}=\frac{4\rho L}{A}$
Resistance of wire increases by four times.