Physics, asked by MSAI3872, 11 months ago

4 wire is stretched so that its length is 20% more than its initial length the percentage increase in the resistance of the wire is

Answers

Answered by poonambhatt213
3

Percentage increase in resistance of wire is 44%.

Explanation:

=> Suppose the resistance of wire is R₁

Radius of the wire = r₁

Length of the wire = l

Resistivity of wire = ρ

=> Thus, R₁ = ρ * l / πr₁²

Volume remains constant.

V₀ = Vnew

πr₁²l = π r²new * l.new

=> Now, According to the question, wire is stretched so that its length is 20% more than its initial length.

Rnew = ρ * l.new/ πr²new

∴ πr₁²l = π * r²new * l.new

= π * r²new * (1.2 l )

∴ r₁² = r²new (1.2)

r²new = r₁² /1.2

r.new = r₁ / √1.2

=> New resistance of the wire:

Rnew = ρ . (1.2* l) / π (r₁ / √1.2)²

          = ρ * l * 1.2 * 1.2 / πr²

          = 1.44 ρ * l / πr²

          = 1.44 R₁

=> Thus, percentage change in resistance:

% change in resistance = (Rnew - R₁ / R₁)

                                       = 1.44 R₁ - R₁ / R₁

                                       = 0.44 R₁ / R₁

                                       = 0.44

                                       = 44%

Thus, percentage increase in resistance of wire is 44%

Learn more:

Q:1 A cylindrical wire is stretched to increase its length by a 10%. calculate the percentage increase in resistance.

Click here: https://brainly.in/question/1216733

Q:2 An electric wire is stretched to increase its length by 25%.by what %will the resistance be increased and what will be increase in its resistivity?

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