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Question

A wire of resistance 1 ohm is stretched to double its length. What is the new resistance?

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Solution

Given: a wire of resistance 1Ωis stretched to double its length.
To find the new resistance
Solution:
Here,
R=1Ω,Length=L,Cross sectional area, CSA=A
The formula used is,
R=ρLAρLA=1..........(i)
The new length, L=2L
And new CSA = A
So we have,
Volume of the wire= AL
Now after the act of stretching the volume remains constant.
Therefore, AL=AL
AL=2LAA=A2
Now the new resistance of the wire becomes
Rnew=ρLARnew=ρ2LA2Rnew=4ρLA
Rnew=4×1 by using equation (i)
Therefore the new resistance is 4Ω

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