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Resistance,R = ρl/A
Where,
So, now if you increase the length of wire by n times but volume of the wire has to remain constant.
Let, the initial and final radius of the wire be r1,&r2 respectively.
Since the initial and final volume are equal, so
2π(r1^2)l = 2π(r2^2)(nl)
So, r2=r1/√n
So, the cross-sectional area becomes 1/n times the initial value.
Putting the values in the formula for resistance, we get the new resistance n^2 times greater than the initial value of resistance….
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