Question

A wire of a certain material is stretched slowly by ten percent. Its new resistance and specific resistance become respectively

• A. both remain the same
• B. 1.1 times, 1.1 times
• C. 1.2 times, 1.1 times
• D. 1.21 times, same

Answer 1

Answer: (D)

$\frac{\Delta l}{l}=0.1$
$\therefore l=1.1$
but the area also decreases by $\mathrm{0.1.}$
mass $=\rho lA=V\rho$
$\ln l+\ln A=\ln$ mass.
$\therefore \frac{\Delta l}{l}+\frac{\Delta A}{A}=0$
$\Rightarrow \frac{\Delta l}{l}+\frac{-\Delta A}{A}$
Length increases by $0.1,$ resistance increases, area decreases by $0.1,$ then also resistance will increase.
Total increase in resistance is approximately $1.2$ times, due to increase in length and decrease in area. But specific resistance does not change.