what will be the percentage change in resistance if the radius of a wire is increased by 25percent
Answers
Answer : 25 /16 times initial resistance.
Explanation:r /r' = ( r' / r ) ^2
Given : radius of a wire is increased by 25percent
To find : percentage change in resistance
Solution:
R = ρ L/A
ρ = Resistivity
L = Length
A = Area = πr²
two cases : Volume is changed ( length Same)
, Volume same ( Length reduced)
Volume is changed ( length Same)
R₁ = ρ L₁/A₁
A₁ = π r₁²
R₁ = ρ L₁/π r₁²
R₂ = ρ L₂/π r₂²
r₂ = 1.25r₁ (r₁ + (25/100)r₁)
L₂ = L₁
=> R₂ = ρ L₁/π (1.25r₁)²
=> R₂ = R₁ /(1.25 )²
=> R₂ = 0.64R₁
Decrease in resistance = 0.36R₁
% change = 36%
percentage change in resistance = 36 % decrease
, Volume same ( Length reduced)
R₁ = ρ L₁/A₁
A₁ = π r₁²
R₁ = ρ L₁/π r₁²
R₂ = ρ L₂/π r₂²
r₂ = 1.25r₁ (r₁ + (25/100)r₁)
L₂A₂ = L₁A₁
L₂π r₂² = L₁π r₁²
=> L₂ = L₁ (1/1.25)²
=> R₂ = ρL₁ (1/1.25)²/π (1.25r₁)²
=> R₂ = R₁ /(1.25 )⁴
=> R₂ = 0.4096R₁
Decrease in resistance = 0.5904R₁
% change = 59.04%
percentage change in resistance = 59.04 % decrease
Learn More:
A wire is stretched to increase its length by 5% calculate percentage ...
https://brainly.in/question/4307117
If a copper wire is stretched by one tenth of its original length then ...
https://brainly.in/question/7412862
Two copper wire of length l and 2l have radii r and 2r respectively ...
https://brainly.in/question/8525705