Question

The resistance of a wire is 15 ohm. What is length of another wire of same material and resistance but radius half
of the first wire?
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Answer 1

Answer:

4 times the original length

Explanation:

as

R=(ρl)/A (ρ is specific resistance which is different for every material)

and area of the cross section of a wire is πr² (as it's a circle)

so we are given that the material is same hence the value of ρ is same for both the condition

and also the resistance is same!

so

R=(ρl)/A

AND for another wire of half the radius of the given wire the value for the area of the next wire (say) A' = π(r/2)²

that makes it

A= πr²/4

now comparing both the condition:

R=(ρl)/A OVER R'=(ρl')/A'

WE GET

15/15= [(ρl)/A] / [(ρl')/A']

NOW THAT MAKES

l'= 4l

....

hope this might help