Answer:
The ratio of radius of A to that of B is [tex]1:\sqrt{5}[/tex].
Explanation:
The resistance of a wire is given by :
[tex]R=\rho \dfrac{l}{A}[/tex]
l is length of wire
A is area of cross section
Resistance of wire A is : [tex]R_A=\rho \dfrac{l_A}{A_A}[/tex] .......(1)
Resistance of wire B, [tex]R_B=\rho \dfrac{l_B}{A_B}[/tex] .....(2)
As [tex]l_A=l_B[/tex] and [tex]R_A=5R_B[/tex] (given)
From equation (1) and (2) and putting given condition, we get :
[tex]\dfrac{R_A}{R_B}=\dfrac{A_B}{A_A}\\\\\dfrac{R_A}{R_B}=\dfrac{r_B^2}{r_A^2}[/tex]
Since, [tex]R_A=5R_B[/tex]. So,
[tex]\dfrac{5R_B}{R_B}=\dfrac{r_B^2}{r_A^2}\\\\\dfrac{5}{1}=\dfrac{r_B^2}{r_A^2}\\\\(\dfrac{r_A}{r_B})^2=\dfrac{1}{5}\\\\\dfrac{r_A}{r_B}=\dfrac{1}{\sqrt{5} }[/tex]
So, the ratio of radius of A to that of B is [tex]1:\sqrt{5}[/tex].
