d= diameter = 0.5 mm, ρ = 1.6 × 10^–8 Ωm, R = 10Ω

Assume wire length as l

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r = d/2

r = (0.5 x 10^-3)/2                 // 1 m = 1000 mm

A = πd²/4

R =  ρ (l/A)

   = ( ρl)/(πd²/4)

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⟹ l = (Rπd²)/4ρ

      l = 10 x 3.14 x ((0.5 x 10^-3)/2 )² / (4 x 1.6 × 10^–8 )              // π = 3.14

      l = 10 x 3.14 x ((0.5 x 10^-3)/2 )² / (4 x 1.6 × 10^–8 )  

      l = (10 x 314 x 10^-2 x 25 x 10^-6)/ (4 x 16 x 10^-1 x 10^-8)

      l = 3140 x 25 x 10^-8/ 64 x 10^-9

     l = 122.7 m

∴  Length of wire = 122.7 m

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If diameter is doubled then d = 0.25mm

d = 25 x 10^-2 x 10^-3 m

d = 25 x 10^-5m

and R = ( ρl)/(πd²/4)

R = (1.6 × 10^–8 X 122.7) / ((3.14 X 25 x 10^-5) / 4)

R = 490.5m

Thus, we can say,

Since R ∝ 1/d²

So, if d is doubled, then R becomes 1/4th time.