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Please tell. 
question image
Asked by riyamaths | 30 May, 2018, 07:15: PM
answered-by-expert Expert Answer
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
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......................................(1)
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
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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