Question

two wires of A and B with circular cross section made up of same material with equal length. suppose R1=3R2. then what is the ratio of the ratio of radius of wire A to that of B​

Answer 1

1:root3

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Answer 2

The ratio of the ratio of radius of wire A to that of B​ is $\dfrac{1}{\sqrt{3}}$

Explanation:

It is given that two wires of A and B with circular cross section made up of same material with equal length such that,

$R_1=3R_2$

R is the resistance

$\rho \dfrac{l}{A_1}=3\times \rho \dfrac{l}{A_2}$

As material and length are same, there resistivity will be same

$\dfrac{1}{\pi r_1^2}=3\times \dfrac{1}{\pi r_2^2}$

$\dfrac{1}{r_1^2}=3\times \dfrac{1}{r_2^2}$

$\dfrac{r_1}{r_2}=\dfrac{1}{\sqrt{3} }$

So, the ratio of the ratio of radius of wire A to that of B​ is $\dfrac{1}{\sqrt{3}}$

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Resistance

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