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Question

A wire of length L and resistance R is stretched so that its length its doubled. How will

(i) Resistance change (ii) Resistivity change?


A

Resistance increases 2 times; resistivity remains same

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B

Resistance increases 4 times; resistivity remains same

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C

Resistance decreases 4 times; resistivity increases 2 times

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D

Resistance decreases 2 times; resistivity increases 4 times

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Solution

The correct option is B

Resistance increases 4 times; resistivity remains same


Volume of wire remains same

V=L×A

So if l increases 2 times so the A should decrease 2 times

New L = 2L; New A = A2

R=ρlA

New R= ρ×2×l×2A = 4×ρ×lA = 4 Old R

As ρ is dependent on temp directly so when temperature increases the resistivity increases.

Here ρ remains unchanged as there is no change in temperature.


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