The resistance of a wire is 5Ω . Its new resistance in ohm, if...

The resistance of a wire $( R )$ is related to its resistivity \left(ρ\right)$, length$( l )$and cross-sectional area \left(A\right)$ as:

$R = ρ\dfrac{l}{A}$

As the length of wire increases, the cross-sectional area decreases. The cross-sectional area in terms of volume $( V )$ and length $( l )$ is

$A = \dfrac{V}{l}$

$∴ R = ρ\dfrac{{l}^{2}}{V}$

Taking the volume of wire constant,

$R ∝ {l}^{2}$

So if ${R}^{'}$ is the resistance of wire after getting redrawn and $R$ is the initial resistance of wire,

$∴ \dfrac{{R}^{'}}{R} = \dfrac{( 5l{)}^{2}}{{l}^{2}} = 25 ⇒ {R}^{'} = 25 \times R = 125Ω$