Question

A piece of resistance $20\Omega$ is drawn so that its length increases to twice its original length. Calculate the resistance of the wire in the new situation.

Answer 1

When length of wire is doubled i.e 2l (say)

Also its area of cross-section becomes half i.e A/2

Resistance $R=\frac{\rho l}{A}=20$

Resistance in new situation

$R^{\prime }=\frac{\rho l}{a}$

$R^{\prime }=\frac{\rho \times 2l}{\frac{A}{2}}$

$R^{\prime }=\frac{4\rho l}{A}$

$R^{\prime }=4\times 20$

$R^{\prime }=80ohms$