Question

Two wires of same material and length have resistances $5\Omega$ and $10\Omega$ respectively. Find the ratio of radii of the two wires

Answer 1

The resistance is given as,

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

$R=\frac{\rho l}{\pi r^2}$

The ratio of resistances is given as,

$\frac{R_1}{R_2}=\frac{{r_2}^2}{{r_1}^2}$

$\frac{5}{10}=\frac{{r_2}^2}{{r_1}^2}$

$\frac{r_1}{r_2}=\frac{\sqrt{2}}{1}$

Thus, the ratio of radii is $\sqrt{2}:1$.