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The length of a given cylindrical wire i...

The length of a given cylindrical wire is increased by `100%`. Due to the consequent decrease in diameter the change in the resistance of the wire will be

A

2

B

1

C

0.5

D

3

Text Solution

Verified by Experts

Given I=1+1=2I, Initial volume =Final volume
i.e., `pir^2l=pi(r')^2 or r'^2=r^2/2=r^2 times 1/21 or r^2=r^2/2 therefore R'=p1/A=p 21/(pi r'^2) (because R=(pl)/A))=(p.41)/(pir^2)=4R`
Thus `Delta R=R'-R=4R-R=3R therefore % (Delta R)/R=(3R)/R times 100%=300%`
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