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A uniform wire of resistance R is stretc...

A uniform wire of resistance R is stretched to four times its.length. Its new resistance will be

A

4 R

B

64 R

C

8 R

D

16 R

Text Solution

Verified by Experts

The correct Answer is:
D
As `R=(rhol)/(S)`, Initially, I denotes length and S. denotes area.
When stretched, length inreases radius decreases but volume remains constant.
Volume =`lxxS` initially
Volume `=(4//S)` finally
`4//S=lS rArr S.=S rArr. =(S)/(4)`
Finally resistance is R.
`R.=rho ((4l))/(S.)=(rhoxx4l)/(S//4)=16(rhol)/(S)=16R`
`R.=16R`
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