CBSE 2024 · Region 1 · Set 3 · Q17 · 2 marks
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 $\displaystyle 25 \%$. Calculate the percentage increase in the resistance of the wire.
Marking-scheme solution
Calculating the percentage increase in the resistance As the wire is uniformly stretched;
\[\begin{aligned}
& \Rightarrow A l=A^{\prime} l^{\prime} \Rightarrow A^{\prime}=\frac{l A}{1.25 l} \\
& A^{\prime}=\frac{4}{5} A \\
& R^{\prime}=\frac{\rho l^{\prime}}{A^{\prime}}=\frac{\rho(1.25 l)}{\dfrac{4}{5} A} \\
& R^{\prime}=\frac{25}{16} R
\end{aligned}
\]
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