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Question

A wire is stretched by 10 percentage of its original length. Calculate the percentage change in its resistance.

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Solution

Let the length of wire = 100 cm.

Let its area of cross section = a cm²

Then resistance R of wire= resistivity× 100/a….(1)

Length of wire after stretching = 110 cm

Let the new area of cross section = a' cm²

Volume of wire must be same before and after stretching, ie

100 a = 110 a' or a' = 10a/ 11 cm²

New resistance R'= (resistivity)×110× 11/10a= (resistivity)× 121/a …………….(2)

Dividing (2) by (1) we get,

R'/R = 121/100

( R' - R/R) = 121–100/100= 21/100

Therefore % change= 21% increase in resistance


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