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Two wires of same material and length ha...

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

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`R = (rho l )/( A),`
`therefore R _(1) = (rho l )/( pi r _(1) ^(2))`
`and 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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