​ What will be the change in the resistance of a circular wire when its radius is halved and length is reduced by 1/4 th of its original length? ​

Question

What will be the change in the resistance of a circular wire when its radius is halved and length is reduced by \(\frac{1}{4}th\)  of its original length?

Answer 1

In first case,

R = \(\frac{pl}{A} = \frac{pl}{\pi r^2}\)

In second case,

R' = \(\frac{p\frac{1}{4}}{\pi(\frac{r}{2})^2}\) = \(\frac{pl}{\pi r^2} \) =R.

So there is no change in the resistance.