Question

A given piece of wire of length $l$, radius $r$ and resistance $R$ is stretched uniformly to a wire of radius $\left(r/2\right)$. The new resistances will be :

• A. $2R$
• B. $4R$
• C. $8R$
• D. $16R$

Answer 1

The correct option is D $16R$

Volume $=\pi r^{2}L=A\times L$

We know,

R $=\frac{\rho \times L}{A}$

Hence,

$\frac{R^{\prime }}{R}=\frac{L^{\prime }}{L}\times \frac{A}{A^{\prime }}=\frac{4L}{L}\times \frac{A}{\frac{A}{4}}=16$

Hence,

$R^{\prime }=16R$