The resistance of a 10 ~m long wire is 10 . Its length is increased by 25 % by stretching the wire uniformly. The new resistance is

Step-by-step solution

The resistance R of a wire is given by R = L A , where is resistivity, L is length, and A is the cross-sectional area. Since the volume V = AL remains constant during stretching, A = V L . Substituting A into the resistance formula, we get R = L V/L = L^2 V . This implies R L^2 . Given the initial length L₁ = 10 m and initial resistance R₁ = 10 . The length is increased by 25 % , so the new length L₂ = L₁ + 0.25 L₁ = 1.25 L₁ . The ratio of the new resistance R₂ to the initial resistance R₁ is R₂ R₁ = ( L₂ L₁ )^2 .