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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