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Question: Answered & Verified by Expert
The resistance of a wire is 5 Ω. Its new resistance in ohm, if stretched to 5 times of its original length will be :
PhysicsCurrent ElectricityJEE MainJEE Main 2023 (25 Jan Shift 2)
Options:
  • A 625
  • B 125
  • C 5
  • D 25
Solution:
2173 Upvotes Verified Answer
The correct answer is: 125

The resistance of a wire (R) is related to its resistivity ρ, length(l)  and cross-sectional area A as:

R=ρlA

As the length of wire increases, the cross-sectional area decreases. The cross-sectional area in terms of volume (V) and length (l) is

A=Vl

 R=ρl2V

Taking the volume of wire constant,

Rl2

So if R' is the resistance of wire after getting redrawn and R is the initial resistance of wire,

 R'R=(5l)2l2=25R'=25×R=125 Ω

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