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Question

How is resistance and resistivity affected if length of the wire is doubled. 


Solution

The Resistivity of the wire will not change with the change in length. Resistivity is a property of the wire, it doesn't depend upon it’s length or cross-sectional area.

However, If you are asking about Resistance, it will increase to 4 times it’s initial value.

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 2 times it’s cross-sectional area will decrease by 2 times, because the 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)(2l)

So, r2=r1/√2

So, the cross-sectional area becomes 1/2 times the initial value.

Putting the values in the formula for resistance, we get the new resistance 4 times greater than the initial values of resistance

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