Question

A wire of resistance 10( has a length l. Half the portion of the wire is stretched so that total length becomes 2l. The resistance of the wire now will be ? is the answer attached above , correct explanation to it ?
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Answer 1

Answer:

it is not the correct explanation.

Explanation:

ACTUAL ANSWER IS 40 ohm

let resistance of wire = R₁ = 10Ω

length of wire = l

area of cross section of wire = A

resistivity = ρ

WHEN WIRE IS STRETCHED,

resistance of wire = R₂

length of wire = 2l

area of cross section of wire = A/2   [since wire is streched]

resistivity = ρ    [remains same always]

NOW,

R₁ = ρ*l/A --------(1)    [by formula of resistivity]

R₂ = ρ * 2l/A/2      [by formula of resistivity]

R₂ = ρ * 4l/A ------(2)    

dividing (1) by (2),

R₁/R₂ = ρ*l/A/ρ * 4l/A

R₁/R₂ = 1/4

ie. R₁:R₂ = 1:4

ie. if R₁ = 10Ω,

R₂ = 10*4 = 40Ω

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