When a wire is stretched and its radius becomes r / 2 , then its resistance will be

Step-by-step solution

Initial radius of wire, r₁=r and final radius of wire, r₂=r / 2=0.5 r . Since volume of the wire after stretch remains constant, therefore l₁ A₁=l₂ A₂ or l₁ l₂ = A₂ A₁ = r₂^2 r₁^2 = ( 0.5 r r )^2= 1 4 . The resistance (R)= l A l A . Therefore R₁ R₂ = l₁ l₂ A₂ A₁ = 1 4 1 4 = 1 16 or R₂=16 R₁=16 R .