There are two conductor X and Y of the same material, having length l and 4l, and radii r and $\frac{r}{4}$ respectively. The ratio of their resistivity is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1 : 64
The resistance of a given material is -
$R=ρ\frac{l}{A}$
where,
$ρ$ = Resistivity (Material property)
$l$ = Length of conductor
$A$ = Area of conductor = $πr^2$
$R_1=ρ\frac{I}{A}$ and $R_2=ρ\frac{\frac{4I}{πr^2}}{16}=64\frac{ρI}{A}$
$∴\frac{R_1}{R_2}=\frac{1}{64}$