A uniform wire of length L and area of cross-section A has resistance R. The wire is uniformly stretched so that its length increases by 25 %.…

Calculating the percentage increase in the resistance As the wire is uniformly stretched; \[\begin{aligned} & \Rightarrow A l=A^{\prime} l^{\prime} \Rightarrow A^{\prime}=\frac{l A}{1.25 l} \\ & A^{\prime}=\frac{4}{5} A \\ & R^{\prime}=\frac{\rho l^{\prime}}{A^{\prime}}=\frac{\rho(1.25 l)}{\dfrac{4}{5} A} \\ & R^{\prime}=\frac{25}{16} R \end{aligned} \]