Two copper wires, one of length 1 ~m and the other of length 9 ~m have the same resistance. The diameters are in the ratio

Step-by-step solution

For first copper wire, l₁=1 ~m For second copper wire, l₂=9 ~m We have to find, diameter ratio of two wires, i.e. d₁ d₂ = ? Since, both copper wires have same resistances. i.e. R₁=R₂ array ll & l₁ A₁ = l₂ A₂ & (R= l A ) & l₁ ( d₁² 4 ) = l₂ ( d₂² 4 ) & l₁ d₁² = l₂ d₂² & d₁ d₂ = l₁ l₂ = 1 9 = 1 3 or 1: 3 array