Question

The length of a given cylindrical wire is increased by 100%. Due to the consequent decrease in diameter the change in the resistance of the wire will be

• A. 200%
• B. 100%
• C. 50%
• D. 300%

Answer 1

Answer: (D)

Given: $l=l+100$ Initial volume = final volume $ie,$ $\pi r^{2}l=\pi r{}^{2}l$ $\Rightarrow$ $r{}^2=\frac{r^{2}l}{l}=r^2\times \frac{l}{2l}$ $\Rightarrow$ $r{}^2=\frac{r^2}{2}$ $\therefore$ $R=\rho \frac{l}{A}=\rho \frac{2l}{\pi r{}^2}$ $\left(\because R=\frac{\rho l}{A}\right)$ Thus, $\Delta R=R-R=4R-R=3R$ $\therefore$ $=300$