Question

two wires of same material are having length in the ratio 2 :3 and radii 1: 2 find the ratio of their resistance​

Answer 1

answer in attachment...

Answer 2

$\huge \bold{RESISTANCE}$

Resistance is the obstruction offered in the path of the current.

◼Resistance is directly proportional to length, which means if lenght will increase, resistance will also increase.

◼Resistance is inversely proportional to area, which means if area of cross section increaes resistance decreases.

$\large \bold{FOR \: QUESTION }$

▶Ratio of length of first wire to second wire = 2 :3

▶Ratio of there radii = 1 : 2

So, ratio of there area will be

$\mathsf{\dfrac{\pi \times 1^{2}}{\pi \times 2^{2}}}$

$\mathsf{\dfrac{\cancel{\pi} \times 1}{\cancel{\pi} \times 4}}$

= $\mathsf{\dfrac{1}{4}}$

So, the ratio of there resistance will be =

$\boxed{ \mathsf{\dfrac{Resistance \: of \:first \: wire }{Resistance \: of \: second \: wire}}}$

$\boxed{ \mathsf{\dfrac{R_1}{R_2} = \dfrac{\frac{l}{a}}{\frac{l_2}{a_2}}}}$

$\mathsf{\dfrac{R_1}{R_2} = \dfrac{l \times a_2}{a \times l_2}}$

$\mathsf{\dfrac{R_1}{R_2} = \dfrac{2 \times4 }{ 3\times 1}}$

$\boxed{ \mathsf{\dfrac{R_1}{R_2} = \dfrac{8 }{ 3}}}$