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Asked by riyamaths | 30 May, 2018, 19:15: PM
When the wire is stretched its lengthis increased. But to keep the volume constant, its cross section area decreased.
Let r and l be the initial radius and length of wire.
After stretching the wire to twice its initial length, the radius rnew of new cross section is given by
![begin mathsize 12px style pi r squared l space equals space pi r subscript n e w end subscript superscript 2 left parenthesis 2 l right parenthesis space
h e n c e space r subscript n e w end subscript equals space space fraction numerator r over denominator square root of 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/559bfebd5039371e2312598054a2e4be.png)
Let the initial resistance is R and is given by
![begin mathsize 12px style R space equals space rho fraction numerator l over denominator pi cross times r squared end fraction
end style](https://images.topperlearning.com/topper/tinymce/cache/ec21592ea2badd7ff5ccce459e892de4.png)
Resistance Rs after stretching the wire is given by
![begin mathsize 12px style R subscript S space equals space rho fraction numerator 2 l over denominator pi open parentheses fraction numerator r over denominator square root of 2 end fraction close parentheses squared end fraction space equals space 4 rho fraction numerator l over denominator pi r squared end fraction equals space 4 R end style](https://images.topperlearning.com/topper/tinymce/cache/93954306756fa80632681ddfbc872764.png)
Resistivity is material property. It does not change by stretching the wire
Answered by Thiyagarajan K | 31 May, 2018, 12:54: PM
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