A wire of \( 10\,\Omega \) resistance is stretched to thrice its original length. Its new resistance would be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 90\,\Omega \)
The resistance of a wire is \( R = \rho L/A \). When a wire is stretched, its volume stays constant, so the area of cross-section falls as the length grows.
\( \displaystyle A L = A' L' \;\Rightarrow\; A' = \frac{A L}{3L} = \frac{A}{3} \)
The resistivity does not change (same material), so
\( \displaystyle R' = \frac{\rho\,(3L)}{A/3} = 9\,\frac{\rho L}{A} = 9R \)
\( \displaystyle R' = 9 \times 10\,\Omega = 90\,\Omega \)