Question

Two wires of same material are having lengths in the ratio 2:3and radii 1:2 Find the ratio of their resistances

Answer 1

resistance= raw × length /area

look at the pic...

hope it helps..

Answer 2

Answer:

Explanation:

• Resistance (R) of a material is an electrical quantity that measures the opposition to the flow of current which depends on the length (L) and area (A) of the material in which the current is flowing.  

       $R= \frac{\rho L}{A} }$

        $\rho$ is a constant and area is given by $\pi r^{2}$

• That is,

        $R=\frac{\rho L}{\pi r^{2} }$     or        $R \propto\frac{L}{r^2}$

• Let $\text L_1$  and $\text L_2$ are  the lengths and $\text r_1$ and $\text r_2$ are the radii of two materials.

         $\therefore \frac{R_{1}}{R_{2}}=\frac{L_{1}}{L_{2}} \times \frac{r_{2}^{2}}{r_{1}^{2}}$     ....(1)

     

In the question, it is given that,

$L_1:L_2 = 2:3$     or       $\frac{L_1}{L_2} =4:9$

$r_1:r_2 = 1:2$        or     $\frac{r_1}{r_2} = \frac{1}{2}$

Using equation(1),

$\therefore \frac{R_{1}}{R_{2}}=\frac{2}{3} \times \frac{2^{2}}{1^{2}}$

         $=\frac{8}{3}$

$R_1:R_2 = 8:3$

• The ratio of their radii will be $8:3$