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Q.
A wire of a certain material is stretched slowly by ten percent. Its new resistance and specific resistance become respectively
AIPMTAIPMT 2008Current Electricity
Solution:
$\frac{\Delta l}{l}=0.1 $
$\therefore l=1.1$
but the area also decreases by $0.1.$
mass $=\rho l A=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.