Question

the ratio of resistivity's of two materials A and B IS 1:2, ratio of their length is 3:4 and if the ratio of radii is 2:3 , find the ratio of resistance of A and B

Answer 1

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Answer 2

Answer: 27:32

Step-by-step explanation:

Given: the ratio of resistivity's of two materials A and B IS 1:2, ratio of their length is 3:4 and if the ratio of radii is 2:3

The formula to calculate resistance is given by :-

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

The ratio of resistance of A and B is given by :-

$\dfrac{R_A}{R_B}=\dfrac{\rho_A\dfrac{l_A}{A_A}}{\rho_B\dfrac{l_B}{A_B}}\\\\\\\Rightarrow\dfrac{R_A}{R_B}=\dfrac{1\dfrac{3}{\pi r_A^2}}{2\dfrac{4}{\pi r^2_B}}\\\\\\\Rightarrow\dfrac{R_A}{R_B}=\dfrac{\dfrac{3}{2^2}}{\dfrac{8}{3^2}}\\\\\\\Rightarrow\dfrac{R_A}{R_B}=\dfrac{\dfrac{3}{4}}{\dfrac{8}{9}}\\\\\\\Rightarrow\dfrac{R_A}{R_B}=\dfrac{27}{32}$