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Two wires of same material and length ha...

Two wires of same material and length have resistances `5 Omega` and `10 Omega` respectively. Find the ratio of radii of the two wires.

Text Solution

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Resistance of first wire `R_1 = 5 Omega`,
Radius of first wire = ` r_1`
Resistance of second wire ` = R_2 = 10 Omega,`
Radius of second wire = `r_2`
Length of the wires = l,
Specific resistance of the material of the wires = `rho`
`R = (rho l)/A , A = pi r^2`
` :." R"_1 = (rho l)/(pi r_1^2) , R_2 = (rho l)/(pi r_2^2)`
`R_2 /R_1 = r_1^2/r_2^2`
`" or "r_1/r_2 = sqrt(R_2/R_1) = sqrt(10/5) = sqrt2/1`
`r_1 : r_2 = sqrt2 : 1 `
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