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How does the resistance of a wire stretched by n times increase by n^2 times its original resistance

How does the resistance of a wire stretched by n times increase by n^2 times its original resistance

Grade:12th Pass

1 Answers

Arun
25763 Points
2 years ago

Resistance,R = ρl/A

Where,

  • ρ=Resistivity of the wire
  • l=lenght of wire
  • A= cross section of the wire

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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